JP2011081543A - Contribution degree analysis method and apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To calculate a contribution degree of a transmission path for which a force input and an acceleration input are combined arbitrarily. <P>SOLUTION: A contribution degree calculation method includes: an input setting process for setting a physical quantity transmitted at an input point 12 of a structure 10 as a force input or an acceleration input; a function calculation process for calculating a force input transfer function P for a plurality of input points 12 of the force input to a response α at an evaluation point 14 of the stricture 10, and an acceleration input transfer function Q for a plurality of input points 12 of the acceleration input to a response α at the evaluation point 14; and a contribution degree calculation process for calculating a force input contribution degree Cp of the force input to the response α based on the force input value of the structure 10 and the force input transfer function P and calculating an acceleration input contribution degree Cq of the acceleration input to the response α based on the acceleration input value and the acceleration input transfer function Q. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a transmission path analysis technique, and in particular, in order to obtain a guideline for efficient improvement in a transmission system having a plurality of vibration sources and causing them to be the cause of sound and vibration at an evaluation point. The present invention relates to an analysis technique for identifying a vibration source having a large contribution (influence) on the sound / vibration surface.

  This analysis technique can be applied to fields such as automobiles, general mechanical devices, building structures, OA equipment, and railways.

In Patent Document 1, for the purpose of obtaining an optimal part for performing acoustic countermeasures with a small amount of processing, based on the material data of each node from the excitation point to the evaluation point by the finite element method (FEM), A technique (paragraph 0029) for determining the stiffness matrix and mass matrix of each node is disclosed. Then, the transmission force of each node according to the mass and rigidity of the structure is calculated, and the contribution to the acoustic level of the evaluation point is obtained by summing the transmission force of all the nodes (paragraph 0031). Furthermore, in the method described in Patent Document 1, the contribution of each transmission force component is calculated by separating the transmission force component from the transmission matrix and the transmission force component that changes according to the mass matrix according to the stiffness matrix of each node. (Paragraph 0034). By separating the transmission force at each node for each component, it is determined whether the stiffness countermeasure or the mass countermeasure is effective as a member to be inserted into each node in order to reduce the contribution to the evaluation point. (Paragraph 0035).
In Patent Document 2 and Non-Patent Document 1, in the noise / sound pressure transmission characteristic analysis with vehicle interior noise as an evaluation point, analysis including not only the transmission in the structure but also the effect of the air-borne sound is performed. For this purpose, the vibration detection signal between the vibration source and the response point and the sound pressure detection signal between the sound source and the response point are normalized to treat both as the same (paragraphs 0012, 0020, [0021] A method is disclosed in which the degree of contribution between solid-borne sound and air-borne sound is ascertained (paragraph 0013).
In Patent Document 3, for the purpose of specifying a portion having a large effect on vibration reduction of an evaluation point, a nodal force at each node is calculated at a phase having a maximum amplitude (paragraph 0010), and an elastic force and a nodal force are calculated as follows. The inertial force is calculated, and the contribution based on the elastic force and the contribution based on the inertial force are calculated (paragraphs 0012 and 0036). Patent Document 3 discloses a method of taking a measure for increasing rigidity when the contribution of elastic force is large, and taking a measure of increasing mass when the contribution of inertial force is large (paragraph). 0013,0048).
Patent Document 4 discloses a method for obtaining individual transmission characteristics for a suspension, a body, and a seat for the purpose of grasping components to be improved with respect to the vibration transmission characteristics of a vehicle. Further, Patent Document 4 discloses a method in which the suspension transmission characteristic is suspension transmission force / ground surface displacement, the body characteristic is body acceleration / suspension transmission inertia, and the seat characteristic is seat acceleration / body acceleration. ing.

JP 2006-185193 A JP 2007-57460 A JP 2008-224503 A JP 2009-97973 A

Kosuke Nomura = Junfumi Yoshida "Transfer Route Analysis Method Using Actual Operational Data" Japan Society of Automotive Engineers 2006 Spring Academic Lecture Preprints No55-06, p.7-12 (2006)

In the above-mentioned Patent Document 1, it is disclosed that a node having a large contribution to the evaluation point is displayed and a member inserted into the node is presented as a countermeasure for rigidity or a countermeasure for mass (paragraph 0035). However, in the actual structure, possible countermeasures are limited depending on the position of the node, etc. Even if it is determined that the contribution of the transmission force according to the rigidity is large, there is no rigidity countermeasure for that node. Sometimes it is possible. That is, with the method described in Patent Document 1, it is not possible to perform analysis according to measures that can be actually applied. In this respect, the method described in Patent Document 3 is also the same (paragraph 0048).
In the methods described in Patent Documents 1 and 3, a large number of nodes are defined in the structure on the premise of the finite element method, and the contribution of the transmission force is obtained in the entire structure. Compared with the analysis executed by force input or vibration of the second, the accuracy is low, and secondly, it is possible to obtain only the distribution of the contribution of the entire structure, not the contribution of the part of interest, and thirdly, If measures for rigidity and mass are taken on the premise of the analysis results before the countermeasures, and analysis is performed after the countermeasures, there is a disadvantage that transmission force and the like differ before and after the countermeasures, making it difficult to judge whether the countermeasures are good or bad.
In the methods described in Patent Document 2 and Non-Patent Document 1, since the transfer function of the response point with respect to the input point is calculated, the contribution degree of the input point to the response point can be calculated, but since the acceleration is input, It is not always clear what the relationship is with the contribution level using the conventional force as input, and measures according to the contribution level will not actually achieve the expected effect.

  In Patent Document 4 described above, the contribution to the response in units of components of the structure is obtained by using together the inertance with the input as the force and the output as the acceleration and the transfer function from the displacement amount to the transfer force. A technique is disclosed. Then, by using a plurality of transfer functions using acceleration and force, the contribution of each component to the vibration characteristics of the vehicle that receives vibration equivalent to actual road travel is calculated (paragraph 0053). However, according to the method described in Patent Document 4, first, the contribution cannot be calculated by arbitrarily combining force input and acceleration input. Secondly, even if the frequency band and component to which countermeasures should be taken can be specified, no information can be obtained about what countermeasures are effective, and thirdly, after the countermeasures have been taken. Even if the effectiveness of the countermeasure is to be confirmed, the transfer function group has to be newly calculated by exciting again, and it is difficult to make an effective comparison before and after the countermeasure.

[Problem 1] As described above, the conventional example has a disadvantage that it is impossible to calculate the contribution degree of a transmission path in which force input and acceleration input are arbitrarily combined. The subject of the combination of the nature of the acceleration input and the force input and the acceleration input will be further examined in the embodiment including the disclosure of the analysis specific to the present application.
[Problem 2] The conventional example described above has a disadvantage that it is impossible to analyze the degree of contribution based on the type and position of applicable measures.
[Problem 3] Furthermore, the conventional example described above has a disadvantage that it is impossible to perform an analysis that can clearly determine the effectiveness of the countermeasure before and after the provision of the countermeasure.
That is, in the conventional example, the prediction of the effect of the countermeasure is inaccurate, and only the prediction with high uncertainty can be performed.

[Object of the Invention] An object of the present invention is to calculate the contribution degree of a transmission path in which force input and acceleration input are arbitrarily combined.
A further object of the present invention is to analyze the contribution of the position (input point) to the response of the evaluation point, assuming the type and position of applicable measures.

  [Focus Point] The inventor of the present invention has focused on the point that acceleration at an input point of force input can be regarded as acceleration input. Then, by assuming an acceleration corresponding to the force at the input point of the force input and assuming a force corresponding to the acceleration at the input point of the acceleration input, the above problem is solved by devising a transfer function calculation method. I came up with the idea that I could do it.

[Problem Solving Means 1] The present invention corresponding to the first embodiment includes an input setting step of setting a physical quantity transmitted at an input point of a structure as a force input or an acceleration input, and a plurality of input points of the force input. A function calculating step of calculating a force input transfer function until a response of the evaluation point of the structure and an acceleration input transfer function from a plurality of the input points of the acceleration input to the response of the evaluation point; and the structure A force input contribution to the response of the force input based on the force input value and the force input transfer function, and to the response of the acceleration input based on the acceleration input value and the acceleration input transfer function. And a contribution degree calculating step for calculating the acceleration input contribution degree.
Thereby, the said subject 1 and 2 were solved.

[Problem Solving Means 2] In the present invention in which suitable elements are added in the first embodiment, the contribution calculation step includes the force input value or the acceleration input value after the countermeasure for the force or acceleration, and the countermeasure before the countermeasure. Based on the force input transfer function and the acceleration input transfer function, a step of calculating the force input contribution after the countermeasure and the acceleration input contribution is provided.
Thereby, the said subject 3 was solved.

  The present invention interprets the meaning of the terms described in each claim in consideration of the description of the present specification and the drawings, and certifies the invention according to each claim. There are the following advantageous effects in relation to

[Functional Effect 1 of the Invention] In the contribution analysis method of the problem solving means 1, the input setting step sets the physical quantity transmitted at the input point of the structure as force input or acceleration input, and the function calculation step includes the force calculation step. A force input transfer function for a plurality of input points of the input and an acceleration input transfer function for the plurality of input points of the acceleration input are calculated, and a contribution calculating step includes a force input value of the structure and the force input value The force input contribution to the response of the force input is calculated based on the force input transfer function, and the acceleration input contribution to the response of the acceleration input is calculated based on the acceleration input value and the acceleration input transfer function. In order to calculate, a transfer function related to force input and a transfer function related to acceleration input can be calculated while formulating input points into force input or acceleration input in advance, and the contribution can be obtained.
Therefore, it is possible to calculate the contribution degree of the transmission path by arbitrarily combining the force input and the acceleration input.
If it is possible to calculate the contribution of the transmission path by arbitrarily combining force input and acceleration input, if the designer specifies in advance the types and positions of measures that can be applied to the input points, the measures can be applied. The degree of contribution that is directly connected can be calculated.
In the present invention, when the unit of response at the evaluation point is acceleration, for example, the force input transfer function and the acceleration input transfer function play a role of converting the input value into the unit of acceleration, and the force input contribution degree and the acceleration input contribution Degree is an additivity in units of acceleration, and the sum of all these contributions is the response at the evaluation point.

  [Operation Effect 2 of the Invention] The contribution calculation step is based on the force input value or the acceleration input value after the countermeasure for the force or acceleration, and the force input transfer function and the acceleration input transfer function before the countermeasure. Thus, in order to calculate the force input contribution and the acceleration input contribution after the countermeasure, it is possible to use the same transfer function before and after the countermeasure to quantify the usefulness of the countermeasure with high accuracy. it can. As described above, in the present invention, the transfer function used for the calculation can be made the same before and after the countermeasure is given, so that the analysis that can clearly determine the effectiveness of the countermeasure can be performed.

It is a flowchart which shows the structural example of one Embodiment of this invention. (Examples 1 to 3) It is explanatory drawing which shows the example of a relationship between the input point in this embodiment, force input, acceleration input, and an evaluation point. (Examples 1 to 3) It is explanatory drawing which shows an example of the model which makes a four-wheeled vehicle interior sound the object of contribution analysis in this embodiment. (Examples 1 to 3) It is explanatory drawing which shows an example which calculates | requires a transfer function on the basis of force input with the model shown in FIG. (Examples 1 to 3) It is explanatory drawing which shows an example which calculates | requires a transfer function on the acceleration input base with the model shown in FIG. (Examples 1 to 3) It is explanatory drawing which shows an example which calculates | requires a transfer function by the hybrid input of force input and acceleration input in the model shown in FIG. (Examples 1 to 3) It is explanatory drawing which shows the structural example of Example 1 of this invention. (Examples 1 to 3) 3 is a flowchart illustrating an example of a processing process according to the first embodiment. (Examples 1 to 3) It is explanatory drawing which shows an example of the engine mount model made into the object of contribution analysis in Example 2 of this invention. (Examples 1 to 3) It is explanatory drawing which shows an example of the mass spring model made into the object of contribution analysis in Example 3 of this invention. (Examples 1 to 3) FIG. 11A shows an example of the transfer function of the model shown in FIG. 10, FIG. 11A shows the transfer function from the input point 12A to the response, and FIG. 11B shows the transfer function from the input point 12B to the response. . (Examples 1 to 3) It is a wave form diagram which shows the spectrum of the actual input to the model shown in FIG. (Examples 1 to 3) It is a wave form diagram which shows the spectrum of the corresponding input corresponding to the spectrum shown in FIG. FIGS. 14A and 14B are waveform diagrams showing examples of contributions obtained on a force input basis in the model shown in FIG. (Examples 1 to 3) FIGS. 15A and 15B are waveform diagrams showing an example of contributions obtained on an acceleration input basis in the model shown in FIG. (Examples 1 to 3) FIGS. 16A and 16B are waveform diagrams showing examples of contributions obtained on a hybrid input basis in the model shown in FIG. (Examples 1 to 3) FIGS. 17A and 17B are waveform diagrams showing examples of contributions obtained on the other hybrid input base in the model shown in FIG. (Examples 1 to 3) It is a wave form diagram which shows an example of the effect prediction in the example shown in FIGS. (Examples 1 to 3)

<1 Contribution analysis method>
<1.1 Force input contribution and acceleration input contribution>
Three embodiments are disclosed as modes for carrying out the invention. Example 1 is a contribution analysis method and apparatus. In the second embodiment, a method for selecting an optimum combination of countermeasures from among a plurality of combinations using the contribution analysis method or apparatus of the first embodiment is disclosed. In the third embodiment, the transfer function used in the contribution analysis method and apparatus of the first embodiment and the nature of the contribution are disclosed.
Embodiments including Examples 1 to 3 are referred to as embodiments.

  As an object of vibration analysis and its contribution analysis, for example, there is a solid propagation sound of a four-wheeled vehicle interior sound. The cause of this solid-propagating sound is that the vibration of the engine 40 transmitted to the vehicle body via the engine mount 42, the muffler vibration transmitted to the vehicle body via the attachment portion of the muffler 54 to the vehicle body, and the road surface transmitted to the vehicle body via the suspension 48. There are irregularities. As measures against these solid propagation sounds, a method for improving the vibration transmission characteristics of the vehicle body by changing the vehicle body structure and a method for reducing the input to the vehicle body part without adjusting the vehicle body can be assumed. However, in the later stage of the vehicle development stage, it becomes difficult to change the vehicle body structure, and in order to adjust the solid propagation sound, rather, a countermeasure plan to reduce the input to the vehicle body is sought.

  As a specific input reduction measure, a typical measure is to change the coupling rigidity (for example, engine mount rigidity, suspension body mounting bushing of the suspension) at the coupling point between the vehicle body and the input side member, and to reduce the force transmitted to the vehicle body itself. This is a method of suppressing the vibration of the bonding point itself by changing or adding a mass or a dynamic damper to the bonding site.

  In this embodiment, in a transmission system having a plurality of vibration sources, which are responsible for the sound and vibration of the evaluation point, “what measures to reduce to which part (the transmission force is reduced, the coupling point It is related to a contribution analysis that gives an index of whether sound or vibration can be effectively reduced if the vibration of itself is suppressed.

Conventionally, a force-based method for formulating force as an input has been used as a method for clarifying the contribution of input to each part of the vehicle body with respect to the solid propagation sound and vibration at the evaluation point. Furthermore, in recent years, an acceleration-based method for formulating acceleration as an input has also been proposed. Both have been commercialized as computer software systems.
Force-based systems: LMS (TPA), B & K (SPC)
Acceleration based method system: Muller-BBM (PAK Binaural TPA)
Patent Document 2 and Non-Patent Document 1 can be considered to have proposed an acceleration-based method.

In the example shown in FIG. 2, force or acceleration is input to the plurality of input points 12 of the structure 10, and these inputs cause a response α of the evaluation point 14. In the contribution analysis by the transmission path analysis, the contribution of each input point 12 is obtained with respect to this response α.
In the example shown in FIG. 3, the input point 12 is set for the vehicle that is the structure 10, and the contribution analysis is performed with the vicinity of the driver's outer ear as the evaluation point 14.

○ Force-based transmission path analysis When the acceleration of the target evaluation point or the sound pressure of the solid-propagating sound is α, in a system that uses force as an external input, the force of the following equation (1a) by using a transfer function H _i from _i to alpha, degrades response alpha in the frequency domain the following equation (1b). In this force-based transmission path analysis, the acceleration a _i is a response determined by the force.
At this time, the frequency omega, contribution Cf _i responses alpha (acceleration or sound pressure) force input f _i to become the following equation (1c).

By comparing these contributions Cf _i, it is possible to identify a large input force contribution Cf _i at frequency omega. Then, for large parts of the contribution Cf _i, and thus to consider measures to reduce the input force, such as lowering the bond rigidity. Note that the adding the contribution Cf _i for all input points 12 and response alpha.
The position of the input point 12 is usually about 15 or more even in a simple analysis. Then, assuming that the input to the position of one input point 12 is three axes orthogonal to each other, there are 45 input points 12 for each axis at 15 locations. Hereinafter, the input is represented by the position of the input point 12 and the number of axes at the position. In the example shown in FIG. 2, for simplicity, the degree of freedom of one axis is set at each position of the input point 12, and the total number of input points is p.

In the example shown in FIG. 4, there are inputs f ₁ and f _{2 at} the position of the input point 12 for two force inputs at the input point 12. Also shows the other forces input is not shown in the f _i. The force inputs f ₁ , f ₂ to these input points 12 and the other force inputs f _i cause a response α at the evaluation point 14. The relationship between the force inputs f ₁ , f ₂ and f _i and the response α is given by transfer functions H ₁ , H _i and H ₂ with each force input as a unit.

○ Acceleration-based transfer path analysis In a system that uses acceleration as an external input, the following equation (2a) is used as an independent external input, and the transfer function G _i from a _i to α is used. Decomposes with equation (2b). The force f _i is a response determined by the acceleration. At this time, the contribution degree Ca _i of the acceleration input a _i to the acceleration (or sound pressure) α at the frequency ω is expressed by the following equation (2c).

By comparing these contribution levels Ca _i , an acceleration input having a large contribution level Ca _{i at} the frequency ω can be specified. Then, measures for reducing acceleration, such as adding a mass or a dynamic damper, will be examined for a portion having a large contribution degree Ca _i .

For example, in the example shown in FIG. 5, there are acceleration inputs a ₁ and a ₂ and other force inputs a _i at the input point 12, and a response α at the evaluation point 14 is generated. The relationship between the acceleration inputs a ₁ , a ₂ and a _i and the response α is given by transfer functions G ₁ , G _i and G ₂ with each force input as a unit.

○ Analysis of problems When taking measures against sound and vibration, force input can be controlled by changing the coupling rigidity, etc., in areas with external input points, and acceleration input can be controlled by adding mass in certain areas. Thus, it is normal that the improvement measures assumed for each part are different. It is necessary to determine an effective countermeasure guideline from these possible improvement measures.
However, in the conventional power-based scheme, under the premise that "acceleration independent all forces input is determined according to the force input" contribution Cf _i of each force input is calculated. In the conventional acceleration-based method, the contribution degree Ca _i of each acceleration input is calculated under the premise that “all acceleration inputs are independent and the force is determined according to the acceleration input”.

Therefore, the contribution decomposition of the force-based method and the contribution decomposition of the acceleration-based method are performed independently, the part where the force contribution Cf _i is large is identified by the force-based method, and the acceleration contribution Ca _i is determined by the acceleration-based method. If you specify a large part and take measures to control the force and acceleration for each part, the premise of the force-based method (all force inputs are independent, acceleration depends on the force input) and acceleration The premise of the base method (all acceleration inputs are independent and the force is determined according to the acceleration input) is incompatible, resulting in contradiction, and the expected effect of each measure will not be obtained . (See Example 3)

Configuration of the present embodiment The contribution analysis method according to the present embodiment includes an input setting step S1, a function calculation step S2, and a contribution calculation step S3.

Referring to FIG. 1, in the contribution analysis method of the present embodiment, first, a physical quantity transmitted at the input point 12 of the structure 10 is set as a force input f _f or an acceleration input a _a (step S1, input setting step). ). One input point 12 to be subjected to contribution analysis is set to one of force input and acceleration input. The designer who uses this method determines which input point 12 is used as which input. In this specification, the setting in which the input to the input point 12 is one of force input and acceleration input is referred to as “formulation”.
The input point 12 is a contact point between the vibration source side and the elastic body (structure 10) to be analyzed. The designer of the structure 10 formulates the input point 12 that can control the force by some measure as the force input f _f for each input point 12, and the input point that can control the acceleration a _a by other measures. 12 may be formulated as an acceleration input a _a .
The input point 12 for which any countermeasure can be taken may be one that is more significant at the input point 12, and contributes individually to the example of the force input f _f and the example of the acceleration input a _a. Analysis may be performed and results may be compared. In addition, for the input point 12 for which any countermeasure is assumed to be impossible, it is preferable to select the input point 12 that is assumed to have less change as an input to the input point 12. In other words, if neither force countermeasures nor acceleration countermeasures are possible, it is better to allocate physical quantities that are assumed to be less affected by other countermeasures.
This selection is not based on the true input, but is preferably based on measures that can be applied to the input point 12. For example, even if it is clear that a true input is a force in actual operation with respect to a certain input point 12, no matter how much force is applied to the input point 12, the force can be reduced. Suppose that there is a limit. In such a case, even if the true input is a force, it is possible to perform an unprecedented new useful contribution analysis by deliberately setting the acceleration input.
If the position of a certain input point 12 has three degrees of freedom, the three axis directions are determined in consideration of the actual input direction and the influence on the evaluation point 14, and the force input f _f or acceleration input a for each axis. It is set to _a. For example, at the input point 12 at the same position, there can be a formulation in which the x direction is the force input f _f and the y direction is the acceleration input a _a . On the other hand, in the present embodiment, the same input point 12 and the same axial direction are allocated to a single physical quantity, and the force input f _f and the acceleration input a _a are not divided.

Following this input setting step S1, a force input transfer function P from a plurality of the input points 12 of the force input f _f to a response α of the evaluation point 14 of the structure 10 and a plurality of the inputs of the acceleration input The acceleration input transfer function Q from the point 12 to the response α of the evaluation point 14 is calculated (step S2, function calculation step). There are many methods for calculating the force input transfer function P and the acceleration input transfer function Q, such as a method of developing an inertance matrix and a method of using a cross spectrum. In the present embodiment, the function from the group of input points 14 formulated to force input to the response α and the function from the group of input points 12 formulated to acceleration input to the response α are separated as different functions. ing.
In order to obtain the inertance matrix, for example, for each input point 12 of the structure separated from the input, the input point 12 is hit with a hammer having a force sensor, and the acceleration of all the input points and the response of the evaluation point 14 are obtained. By measuring with the acceleration pickup, the acceleration at all input points and the transfer function up to the evaluation point 14 can be calculated from the input force. If this is repeated for all input points, an inertance matrix can be obtained.
Also, the transfer function can be calculated by simultaneously applying uncorrelated force to each input point of the structure and measuring the acceleration of each input point and the response point.
Further, the transfer function may be obtained by simulation of a model such as FEM.

Following the function calculation process, and calculates the force input contribution Cp _i to the response α of the force input f _f based on the force input value and said force input transfer function P of the structure 10, the acceleration input Based on the value and the acceleration input transfer function Q, an acceleration input contribution Cq _j to the response α of the acceleration input a _a is calculated (step S3, contribution calculation step). This not only determines which input point 12 contribution Cp _i , Cq _j is large with respect to the vibration or sound pressure of the response α, but also the contribution Cp _i , Cq _{j of} the input point 12 formulated to which. Is found to be large. Therefore, it is possible to execute a countermeasure to be applied to the input point 12 having a large contribution degree Cp _i , Cq _j according to the formulation. For this reason, although the contribution degree analysis is performed, it is possible to prevent an inconvenience that an effective measure cannot be actually applied to the input point 12.

Thus, in this embodiment, the contribution Cp _i of the plurality of external input to the vibration or sound pressure of the evaluation points, in analyzing Cq _j, at each input point in order to reduce the vibration or sound pressure The external input is defined as a force input or an acceleration input according to an assumed improvement measure (formulation). Then, input contributions Cp _i and Cq _j are obtained based on transfer characteristics from force and acceleration defined as input to vibration or sound pressure at the evaluation point. Thereby, the response of the evaluation point 14 when the input is changed can be predicted.

Specifically, for example, out of p external inputs, r force inputs assumed to be force controlled are assumed to be force vectors f _f of the following equation (3a), and acceleration control is assumed (p − r) Acceleration input _a is an acceleration vector a _a in the following equation (3b). Using the transfer function P _i from f _fi to α and the transfer function Q _j from a _aj to α in a hybrid input system that defines all external inputs of this force vector f _f and acceleration vector a _a Is decomposed into the following equation (3c) in the frequency domain.

At this time, the acceleration a _fi corresponding to the force input f _fi and the force f _aj corresponding to the acceleration input a _aj are responses determined by the input.
In the example shown in FIG. 6, there are p force inputs or acceleration inputs, of which r are force inputs. Of these, force input f _f1 , force input f _fi and acceleration input a _{a (r + 1)} are illustrated, and description of other inputs is omitted. The relationship between the force input f _f1 and other force input f _fi and the response α is given by force input transfer functions P ₁ and P _i , while the acceleration input a _{a (r + 1)} and the other acceleration input a _{a (r + j)} is given by acceleration input transfer functions Q _{(r + 1)} and Q _{(r + j)} .

Depending on the formulation of the input points, the transfer functions will be different for the same type of input at the same site. For example, the transfer function H ₁ in FIG. 4 and the force input transfer function P ₁ shown in FIG. 6 are different functions. Further, the transfer function G ₂ shown in FIG. 5 and the acceleration input transfer function Q _{(r + 1)} shown in FIG. 6 are different functions. Therefore, the degree of contribution will inevitably differ.

The formula (3c), at a frequency omega, the acceleration (or sound pressure) contribution Cp _i force input to the α following formula (4a), and the contribution degree Cq _j of the acceleration input to the acceleration α equation (4b ).

Thus, contributions Cp _i and Cq _j to the input assuming control are accurately obtained, and it is possible to predict a change in acceleration (or sound pressure) α when the respective inputs are changed simultaneously.

1.1 Effects of force input contribution and acceleration input contribution As described above, in the first embodiment, the input setting step S1 sets the physical quantity transmitted at the input point of the structure as force input or acceleration input, calculating step S2 is to calculate the force input transfer function P, and an acceleration input transfer function Q, the contribution degree calculating step S3 is input force contribution Cp _i, and, in order to calculate the acceleration input contribution Cq _j, input The respective contributions Cp _i and Cq _j can be obtained by calculating the transfer function related to force input and the transfer function related to acceleration input while formulating the point 12 into force input or acceleration input in advance. Accordingly, it is possible to calculate the transmission path contributions Cp _i and Cq _j by arbitrarily combining the force input and the acceleration input. Then, if the designer specifies in advance the types and positions of measures that can be applied to the input points, contributions Cp _i and Cq _j that are directly related to the applicable measures can be calculated.
That is, if an input point 12 with high contributions Cp _i and Cq _j is specified, the type of countermeasure becomes clear. For this reason, in the conventional example, there is an inconvenience that even if a preferable countermeasure can be proposed, an analysis result in which the countermeasure cannot be actually performed is given, but in the present invention, the countermeasure by the designer is present. By making a preset, it is possible to analyze the contributions Cp _i and Cq _j that are immediately linked to applicable measures.
Thus, by calculating the force input contribution Cp _i and the acceleration input contribution Cq _j, it is possible to quantitatively comparable to calculate the effect of the impact force and acceleration.

○ Conversion to acceleration input system Furthermore, Non-Patent Document 1, which is the original paper on the acceleration-based method, suggested a contribution decomposition using acceleration near the input point, not the acceleration at the force input point itself. In addition, it is said that the excitation input at the time of transmission rate acquisition may be given to any point, and when these use the response-response relationship, various discussions have been called. However, by considering the acceleration at the force input point as an acceleration input, the acceleration-based method can be regarded as a method equivalent to the conventional force-based method.
Generally, a forced acceleration input can be assumed in addition to a force input as a dynamic external input. A typical example of such an input is an acceleration that is forcibly given to a contact point by a contact motion with a rigid body that performs a predetermined motion. In acceleration input, the force acting on the elastic body at the input point is obtained as a response.

The equation of motion obtained by approximating the elastic body model of FIG. 2 with finite degrees of freedom is represented by the following equation (5a).
Here, the vector xf (t) is a displacement vector of an external force input point, and the vector x0 (t) is a displacement vector of a node (including a focused response point) to which no external force works.
When the acceleration vector a (t), which is the second derivative of the vector xf (t) of the equation (5a), is input, and the second derivative of the vector x0 (t) and the force vector f (t) are output, The state and output equations of the following equations (5b) and (5c) are obtained. The vector ξa (t) in the equations (5b) and (5c) becomes the following equation (5d).

  Here, assuming that O and I are zero matrices and unit matrices of appropriate sizes, the matrices of equations (5b) and (5c) are expressed by the following equations (6a), (6b), (6c) and (6d) .

As described above, the system expression using the acceleration at the force input point as an input is possible. The order of the acceleration input system is not different from the order of the force input system.
Thus, the acceleration-based method is also a method based on a transfer function with acceleration as an external input, and it has become clear that the method is the same as the conventional transfer path analysis based on force. However, the degree of contribution obtained is generally not the same.
In the conventional force-based method, it can be seen from the obtained contribution level which external force can be reduced to most effectively reduce the acceleration at the response point. That is, it can be said that the analysis method is based on the premise that the magnitude of the force input is controlled by changing the rigidity of the bush or the like. Similarly, in the acceleration-based method, it can be seen from the obtained contribution degree which acceleration input can be reduced most effectively to reduce the acceleration at the response point. In other words, it can be said that the analysis method is based on the assumption that the magnitude of acceleration input is controlled. For controlling the acceleration, it is conceivable to add a mass damper or the like to the input point.

As described above, the two methods have an equal relationship. When assuming a measure for controlling force input, a force-based method is used. When a measure for controlling acceleration input is assumed, an acceleration-based method is used. It can be said.
As described above, in this embodiment, it is possible to calculate the contributions Cp _i and Cq _j of the transmission path by arbitrarily combining the force input and the acceleration input. That is, calculation of force input and acceleration input contributions Cp _i and Cq _j according to an assumed measure, which cannot be obtained by performing the contribution decomposition of the force-based method and the contribution decomposition of the acceleration-based method independently. Is possible.

<1.2 Use the same transfer function before and after countermeasures>
In the present embodiment, more preferably, the contribution calculation step S3 shown in FIG. 1 includes the force input value or the acceleration input value after the countermeasure for the force or acceleration and the force input transfer function P or the countermeasure before the countermeasure is taken. wherein based on the acceleration input transfer function Q, may comprise a step S7 to calculate the force input contribution Cp _i and the acceleration input contribution Cq _j after the measures. That is, in the example shown in FIG. 1, performs initial contribution calculation (step S3), and thereafter, the contribution Cp _i, the larger the input point 12 of Cq _j, the measures according to the type of the input (force or acceleration) Apply. Subsequently, analysis and countermeasures are continued (step S5), and the process returns to step S3 again. In step S3, as a result of the countermeasure being taken, the value of the input point 12 where the countermeasure was taken (force or acceleration depending on the formulation) is changing.

On the other hand, in the present embodiment, the transfer function does not change before and after the countermeasure as a feature of its function / action. This is the same for both force input and acceleration input. Therefore, the contribution calculation step S3 is based on the force input value after the countermeasure against the force and the force input transfer function P before the countermeasure in the contribution analysis after the countermeasure in the case of force input, for example. , and it calculates the force input contribution Cp _i after the measures. In this way, the contributions Cp _i , Cq _j and response α can be calculated and compared before and after the countermeasure using the same transfer function, so that the prediction accuracy of the response change due to the countermeasure can be increased.

1.2 Effect of using the same transfer function before and after the countermeasure In this example, the contribution calculation step includes the force input value or the acceleration input value after the countermeasure for the force or acceleration and the force input transfer function before the countermeasure. And the acceleration input transfer function Cq _i and the acceleration input contribution Cq _j after the countermeasure are calculated based on the acceleration input transfer function and the acceleration input transfer function. The usefulness can be quantified with high accuracy in a comparable manner.
In this way, it is possible to analyze the contributions Cp _i and Cq _{j on} the premise of the types and positions of applicable measures. That is, while one formulation to the said input point input force or acceleration input assumption applicable measures, contribution Cp _i, it is possible to identify the portion of high Cq _j, contribution Cp _i, Cq _j It is possible to surely take measures that are preliminarily assumed in the high portion.
Furthermore, in the present invention, the transfer function used for the calculation can be made the same before and after the countermeasure is given, so that the analysis that can clearly determine the effectiveness of the countermeasure can be performed.
Therefore, it is possible to predict the effect when the assumed input reduction is realized.
Thus, in the present embodiment, it is possible to quantitatively evaluate the measures that can be adopted with high accuracy.

<1.3 Encourage the formulation of physical quantities at input points>
The input setting step S1 prompts the user to set the force input f _f for the input point 12 capable of dealing with force, and sets the acceleration input a _a for the input point 12 capable of dealing with acceleration. It is good to provide the prompting step S6. As a method for prompting input, the user interface of the computer realizing this method should match the type of measures that can be adopted and the type of input (force or acceleration) when formulating the input point 12 It is good to display. Moreover, you may make it explain beforehand as the usage of the contribution analysis method or apparatus by this invention.
As a specific countermeasure, for example, if there is a space for attaching a dynamic damper, the input point 12 can control the acceleration. If the mount stiffness value can be changed, the force can be controlled. In addition, there is an input point 12 for only one countermeasure, and there are input points for which both countermeasures are possible. For this reason, for example, it is preferable to encourage the input point 12 where the dynamic damper is effective to be an acceleration input and to use a force input in a place where the rigidity can be changed.

・ Effects for promoting formulation of physical quantities at input points Prompt to set the force input for the input points that can take measures against force, and set the acceleration input for input points that can take measures against acceleration Can be used to analyze the contributions only for applicable measures, and analyze the contributions Cp _i and Cq _j based on the types and positions of applicable measures. Can do. In other words, the advance measures where possible as input points, while further one formulation to the said input point input force or acceleration input assumption applicable measures to identify the portion of high contribution Cp _i, Cq _j Therefore, it is possible to reliably take measures that are preliminarily assumed in the portions where the contributions Cp _i and Cq _j are high.
As described above, in the present embodiment, the result of the contribution analysis can be directly linked to the selection of the countermeasure, and the design support for selecting the countermeasure can be clarified.

<1.4 Transfer function calculation method>
As shown in FIG. 7, the first embodiment employs a hybrid input that formulates a force input and an acceleration input for a plurality of input points 12. The relationship between the force input and the response α is represented by a force input transfer function P, and the relationship between the acceleration input and the response α is represented by an acceleration transfer function Q.

  Referring to FIG. 8, in this embodiment, first, the passive unit 16 and the input unit 18 are defined (step S11). In this step S11, the entire acoustic structure is divided into a passive part including the evaluation point 14 of acceleration and sound pressure and the other input part 18. This separation is performed at a site where the parts are in contact with each other within a narrow range and are regarded as point contacts.

  Next, the input and response of the passive unit 16 are defined (step S12). In this step S12, first, let p be the degree of freedom of the force that the passive unit 16 receives from the input unit 18. Among them, r force inputs that are assumed to be controlled are put together into the following equation (7a), and the corresponding acceleration response is expressed as the following equation (7b). Expression (7a) is the same as Expression (3a). Further, acceleration inputs assuming (p-r) controls are collectively expressed as the following equation (7c), and the corresponding force response is expressed as the following equation (7d). Expression (7c) is the same as Expression (3b).

The corresponding inputs a _f and f _a corresponding to the actual inputs f _f and a _a are responses at the input point 12. For example, when a force input f _f1 that is an actual input is given to the input point 12, an acceleration response to the force input f _f1 occurs. In this acceleration response, a component in the same direction as the axial direction of the force input f _f1 is set as a corresponding input a _f1 . In this way, the corresponding inputs a _f and f _a corresponding to the actual inputs f _f and a _a are in the same direction as the axis of the actual input (direction of the vector of the actual input) with the position of the input point 12 of the actual input as the reference position. Of the ingredients. Thus, the actual inputs f _f , a _a and the corresponding inputs a _f , f _a share the axial direction. The magnitudes of the corresponding inputs a _f and f _a are determined by taking out components in the axial direction of the actual inputs from the responses of the actual inputs f _f and a _a .
In addition, since the force and acceleration assumed corresponding to an actual input are used only for defining an inertance matrix and are not used in an actual calculation, it is not necessary to calculate an actual value using mass or the like.

  Next, the input unit 18 is removed (step S13). In step S13, in order to calculate a transfer function matrix, the input unit 18 defined in step S11 is removed from the entire acoustic structure.

Further, a transfer function matrix is obtained by experiment (step S14). In step S14, providing a force vector f _f and the force vector f _a is the force input f to the passive portion 16 has been removed the input section 18. Then, the acceleration vector a _{f, the} acceleration vector a _a , and the acceleration (or sound pressure) α are measured. Thereby, the transfer function matrix H (ω) of the following equation (8) is acquired. In particular, when the response α is acceleration, H (ω) is called an inertance matrix.

Next, hybrid input transfer function matrices P (ω) and Q (ω) are calculated (step S15). In step S15, the transfer function matrix H (ω) is organized, and the following equation (9a) is derived, in which the force vector f _f and the acceleration vector a _a are input and the acceleration α is output. Further, as defined in the following equation (9b), the parenthesis in the first term on the right side of the equation (9a) is defined as a transfer function matrix P (ω), and as defined in the following equation (9c), the equation (9a ) Is the transfer function matrix Q (ω).

By this equation (9a), two methods with different properties of force input and acceleration input can be included, and the contributions Cp _i and Cq _j to the response α of force input and acceleration input can be directly compared. it can.

As described above, in the first embodiment, on the assumption of the inertance matrix H (ω) represented by the equation (8), the inertance matrix H (ω) is expanded as in the equation (9a), so that the equation (9b) A force input transfer function P (ω) shown in FIG. 5 and an acceleration input transfer function Q shown in equation (9c) are calculated. As described above, the inertance matrix H (ω) is a transfer function matrix having the force input f _{f and} the force corresponding to the acceleration input as inputs, and the acceleration input acceleration and the acceleration input It is a transfer function matrix that outputs the acceleration corresponding to the force input and the response of the evaluation point.

In the method of developing this inertance matrix H (ω), the acceleration response a _f corresponding to the force input f _f and the force response f _a corresponding to the acceleration input a _a are defined in order to establish the inertance matrix The corresponding acceleration a _f and the corresponding force f _a are not used in subsequent calculations. Further, it is not necessary to actually measure the mass and rigidity of each part in order to correspond the force and the acceleration. That is, only the inertance matrix needs to be obtained by actual measurement in order to calculate the transfer function of the hybrid input.

In this way, whether force is regarded as input or acceleration is regarded as input, the basis is a common equation of motion, and a relationship connected by an inertance matrix is established between force and acceleration. In the first embodiment, what is considered as an input from this equation is devised to obtain a transfer function up to the response of interest, a hybrid transfer function is obtained, and the contributions Cp _i and Cq _{j of both} are added. I was able to organize it as possible.
In particular, since the physical quantity is formulated for each axis at the position of the input point 12 and the input for each axis of the input point 12 is not apportioned between force and acceleration, it is always distributed to one of the axes. The relationship between the force and acceleration in the direction can be organized as an input and a response, and can be correlated by equation (7). Given this equation (7), the inertance matrix of equation (8) can be established. Then, by expanding the expression (8), the expression (9a) is derived, and by using this transfer function, the force contribution and the acceleration contribution can be calculated in a comparable manner. Also, based on the theory of Equations (8) and (9a) that presupposes a mechanism that always distributes to one side, the cross-spectrum method described below can be used to further improve the accuracy of the transfer function. it can.

In the first embodiment, the transfer function may be calculated by a method using a cross spectrum instead of a method by developing the inertance matrix H (ω).
Here, the acceleration input transfer function Qk is a transfer function from a _ak to α. In principle, acceleration input other than a _ak is smoothly constrained to 0, the full power input is set to 0, and broadband acceleration input to a _ak And can be obtained by measuring the response of α. However, it is not easy to smoothly constrain the acceleration to zero as compared to setting the force to zero. It is realistic to obtain by multi-point input such that the cross spectrum matrix is regular.
In the example using the cross spectrum, the force input f _f and the acceleration input a _a are given as the input w to measure the response, and the force input transfer function P and the force input function P and the response α based on the cross spectrum of the input w and the response α. Acceleration input transfer function Q is calculated.
That is, an input is given by the following equation (10a) so that the cross spectrum matrix Sww of the input vector w is regular, and the response α at that time is measured. Then, a cross spectrum Swα (column vector) between the vector w and the response α is obtained, and transfer function matrices P (ω) and Q (ω) are obtained by the following equation (10b). In this method, the multi-input excitation of force and acceleration is performed so that the cross spectrum matrix becomes regular, and the response α is obtained, so that the transfer function matrices P (ω) and Q (ω) of the hybrid input are directly obtained. Can be identified.

1.4 Effects of Transfer Function Calculation Method As described above, in this embodiment, the transfer function can be experimentally obtained by a method of deforming from inertance or a method using a cross spectrum. Then, by obtaining inertance H (ω) or examining the cross spectrum, it is possible to calculate the contributions Cp _i and Cq _j of each part by changing the combination of inputs to be controlled in various ways. Can consider appropriate countermeasure guidelines.
In principle, it is possible to obtain transfer functions one by one by giving only one input, setting the other inputs to 0, and taking the ratio of the response to the input. However, to make the force input zero, it is only necessary to make the point free. However, it is practically difficult to make the acceleration input zero because the movement of the point needs to be restrained smoothly. For this reason, the transfer function may be calculated by one of the above two methods.
If the inertance matrix H (ω) is deformed, a phenomenon that cancels the pole of the inertance occurs, and there is a possibility that an error increases in numerical calculation. For this reason, as a precision, a method using a cross spectrum is preferable.

<1.5 Contribution and response calculation methods>
First, the input during actual operation is estimated or measured (step S16). For example, in the case of a vehicle body, the input during actual operation is a force or acceleration applied to each input point using vibration from the road surface or engine vibration as a vibration source. In step S16, force input during actual operation is estimated by, for example, the dynamic spring method. In the dynamic spring method, a frequency characteristic for converting a displacement into a force is measured in advance in the frequency domain as a spring characteristic of a vibration transmitting portion. Then, the dynamic displacement is recorded using an acceleration sensor during actual operation. A dynamically changing force is calculated based on the dynamic displacement and the frequency characteristic of the vibration transmitting portion modeled on the dynamic spring.
The acceleration input is measured by an acceleration pickup.

  Next, short-time Fourier analysis of the input at time t at which contribution analysis is desired is performed (step S17). In this step S17, the region of time width T at time t of the input data is cut out, and the frequency spectrum of the force input of the following equation (11a) and the acceleration input frequency spectrum of the following equation (11b) are obtained by FFT processing. Ask.

そして、上記時刻tにおける応答αへの各入力の寄与度Cp_i, Cq_jを算出する(ステップS18)。このステップS18では、そして、力入力の寄与度Cp_i,を次式(12a)により求める。さらに、加速度入力の寄与度Cq_jを次式(12b)により求める。全ての寄与度Cp_i, Cq_jを加算すると、式(9d)より、応答αとなる。

The contribution Cp _i of each input to the α response in the time t, and calculates the Cq _j (step S18). In the step S18, and determines the contribution degree Cp _i force _input, a by the following equation (12a). Further, the contribution Cq _j of the acceleration input is obtained by the following equation (12b). When all the contributions Cp _i and Cq _j are added, the response α is obtained from the equation (9d).

1 and FIG. 8, first, step S1 in FIG. 1 corresponds to step S12 in FIG. Next, step S2 in FIG. 1 corresponds to steps S13, S14 and S15 in FIG. Step S3 in FIG. 1 corresponds to steps S16, S17, and S18 in FIG. In particular, in the present embodiment, the step S3 for calculating the contributions Cp _i and Cq _j includes the following steps.
Calculating a frequency spectrum f _f (ω; t) of the force input f _f and _a frequency spectrum a _a (ω; t) of the acceleration input a _a (step S17);
The frequency spectrum f _f of the force input transfer function P and the force input f _f; calculating a (omega t) and the force input contribution Cp _i based on (step S18).
A step of calculating the acceleration input contribution Cq _j based on the acceleration input transfer function Q and the frequency spectrum a _a (ω; t) of the acceleration input a _a (step S18).
Step of calculating the response α of the evaluation points 14 by adding the said acceleration input contribution Cq _j and the force input contribution Cp _i (step S19).

○ Qualitative properties of contribution peaks
(1) Spectrum of force input f _fi and acceleration input a _{aj In} the transfer path analysis, the entire system exposed to the true external input is divided into two, the elastic body containing the response of interest is the passive part 16, and the vibration source side is the input part. 18, and consider the input from the input unit 18 to the passive unit 16. In this case, the force input f _fi or the acceleration input a _aj to the passive unit 16 side is not a true external force, but is normally a response of the entire system of the input unit 18 and the passive unit 16 affected by the external force. is there. The frequency spectrum of the response that is regarded as an input to the passive unit 16 generally has peaks at the resonance frequency of the entire system and the spectrum peak position of the true external input.

(2) poles of the transfer function P _i, the transfer function P _i from each input the poles of Q _j to respond alpha, Q _j is a part of the eigenvalues of the system. The eigenmode is the zero input response of the system, and the degree of freedom defined as the acceleration input is given a constant speed at the time of zero input, but is restricted when focusing on the elastic mode. Therefore, it has an eigenmode in which the points defined as acceleration inputs are constrained, and the poles of the transfer functions P _i and Q _j differ depending on the input formulation differences.

(3) contribution Cp _i, spectrum Cq _j (1), from the discussion of (2), Equation (11), the spectral contribution Cp _i, Cq _j calculated by (12) is generally true The total system resonance frequency formulated for the external input, the spectral peak position of the true external input, and the input formulation will have peaks at the pole positions of the different transfer functions P _i and Q _j .

The contribution analysis apparatus according to the first embodiment includes a data input unit 20, a transfer function storage unit 22, and a contribution calculation unit 26.
In the example illustrated in FIG. 7, a Fourier transform unit 24 and a response calculation unit 28 are further provided.

The transfer function storage unit 22 transmits the force input transfer function P from the force input f _f to the input point 12 capable of countermeasures against force to the response α at the evaluation point 14 and the input point 12 capable of countermeasures against acceleration. An acceleration input transfer function Q from the acceleration input a _a to the response α is stored in advance.

The data input unit 20 estimates or measures force input and acceleration input during actual operation of the structure 10. Specifically, in response to a force input or acceleration input preset as a physical quantity transmitted at the input point 12 of the structure 10, the input point 12 set to the force input is the actual value of the structure 10. The force input value during operation is estimated or measured by the dynamic spring method or the like. The data input unit 20 measures an acceleration input value using an acceleration pickup or the like for the input point 12 set to the acceleration input.
Contribution calculation unit 26 calculates the power input contribution Cp _i, to the response of the power input based on production at the force input value and said force input transfer function P of the structure 10. The contribution calculation unit 26 calculates the acceleration input contribution Cq _j to the response of the acceleration input based on the acceleration input value and the acceleration input transfer function Q.

The force input value and the acceleration input value are data in the frequency domain, for example, a frequency spectrum, in order to obtain the contributions Cp _i and Cq _j by the product of the transfer functions P and Q.
In this example, the contribution analysis apparatus includes a Fourier transform unit 24. The Fourier transform unit 24 calculates a frequency spectrum f _f (ω; t) of the force input f _f and _a frequency spectrum a _a (ω; t) of the acceleration input a _a . The contribution calculation unit 26, the frequency spectrum f _f of the force input transfer function P and the force input f _f; to calculate the force input contribution Cp _i on the basis of the (omega t). Similarly, the contribution degree calculating unit 26, the frequency spectrum a _a of the said acceleration input transfer function Q acceleration input a _a; calculating the (omega t) and the acceleration input contribution Cq _j based on.
Moreover, as is clear by the formula (9a), a force input contribution Cp _i, there is additivity is an acceleration input contribution Cq _j, all of the two contributions Cp _i, when adding Cq _j, the response α Become. Therefore, the response calculation unit 28 can calculate the response α of the force input contribution Cp _i, and the acceleration input contribution Cq _j and the evaluation point 14 by adding the.
As described above, the contribution analysis apparatus executes the calculation of the transfer function in steps S13, S14 and S15 shown in FIG. 8 in advance and stores it in the transfer function storage unit 22 shown in FIG. And each part 20, 24, 26, 28 of a contribution analysis apparatus performs the process corresponding to step S12, S16, S17, and S18 shown in FIG. The processing shown in FIG. 8 and the processing of each unit shown in FIG. 7 can be realized by executing a contribution analysis program on a computer having a CPU and a memory.
Note that this contribution analysis program preferably includes only codes (commands) specific to the contribution analysis of the present invention, depending on the functions of an operating system used on a computer and a commercially available application system. For example, since the input / output of data and the Fourier transform itself can be realized by the functions of an operating system and a commercially available application system, the contribution analysis program does not include a code for processing the input / output of data itself.

-1.5 Effects of the contribution and response calculation method As described above, according to the present embodiment, how vibrations at a plurality of input points arbitrarily combining force input and acceleration input change to vibration at the evaluation point. It is possible to quantitatively evaluate whether it contributes. For this reason, if the contributions Cp _i and Cq _j are calculated by artificially relating the assumed measures to the structure and the input type (force or acceleration), measures with large contributions Cp _i and Cq _j Can be selected easily. Further, there is no deviation from the actual when separately evaluating force and acceleration.
For example, a large portion of the contribution Cp _i force input and guidance of reducing the input drop the bond rigidity, a large part of the contribution Cq _j of the acceleration input, set the dynamic damper, the vibration input point Specific countermeasure guidelines such as guidelines for reduction can be obtained.
Further, in this embodiment, since a transfer function directly related to a physical measure is obtained, it is easy to actually reflect the calculation measure effect.
Furthermore, it is possible to narrow advance according feasibility measures a combination of measures, to calculate the contribution of Cp _i, the Cq _j and their possible countermeasures assumption, adopted the contribution Cp _i, is high Cq _j measures Compared with the conventional method where input points that cannot be used and countermeasures that can be taken but input points with low contributions Cp _i and Cq _j are inevitably mixed, transfer path analysis and countermeasures are considered to be significantly more effective. can do.
As a result, the time required for drafting and considering countermeasures can be shortened. That is, it contributes to the shortening of the design period, which can shorten the model cycle and reduce the cost.
In particular, for example, an extremely high effect can be obtained for noise countermeasures in the interior of a four-wheeled vehicle.
Furthermore, in the latter stage of development, the examination of countermeasures is limited to the connection point, and according to the present embodiment, a guideline for optimum countermeasures can be obtained. And since it is based on the transfer function obtained not experimentally but FEM, prediction accuracy can be improved.
The acceleration-based method itself is disclosed in Non-Patent Document 1 and the method used in combination is disclosed in Patent Document 4 and the like. However, in the present invention, the acceleration-based method is based on the theoretical analysis based on Example 3 described later. The method is based on the true nature of the analysis method. For example, in the conventional understanding of the acceleration-based method, it is arranged that acceleration is used instead of force, and the force and acceleration are regarded as equivalent, and the contribution of acceleration Cq according to the simple idea of force = mass × acceleration _j even for large sites, treat the same as the site contribution Cp _i, a large force, had adopted measures to reduce the force. However, in this embodiment, the idea is shifted to the idea that a measure to reduce acceleration with a dynamic damper should be taken for a portion where the contribution Cq _{j of} acceleration is large.
Furthermore, compared with the conventional example that prompts the selection of the rigidity countermeasure and the mass countermeasure according to the analysis result, in this embodiment, the analysis can be performed after assuming the countermeasure in advance. An effective contribution analysis can be performed even when it is limited. Furthermore, in this embodiment, if the countermeasure is applied to the input point based on the assumed countermeasure, the transfer function after the countermeasure is unchanged, and if the acceleration input and the force input after the countermeasure are obtained, the contribution analysis after the countermeasure is immediately performed. It is easy to verify the effectiveness of the measures and provide clear quantification of the effectiveness of the measures.

<2.1 Engine mount model>
Next, Example 2 of this embodiment is disclosed. In the second embodiment, a method for selecting an optimum combination when a combination of a plurality of countermeasures is assumed using the contribution analysis method and apparatus of the first embodiment, taking an engine mount model as an example.

  In recent years, there has been a tendency to lock up AT and CVT from low rotation to improve fuel efficiency, and vibration of low-frequency engine 40 is transmitted to the vehicle body, and there is a case where a booming noise of about 40 Hz is generated at the driver's ear position . Regarding this problem, the engine mount 42, the suspension mounting portion of the front wheel (driving wheel), and the muffler mounting portion are assumed as the main transmission paths of the vibration of the engine 40 to the vehicle body.

  FIG. 9 shows an example of an engine mount model. This model includes an engine mount 42 that supports the engine 40 and McPherson strut type front suspensions 48A and 48B. The front suspensions 48A and 48B include lower arms 44A and 44B and suspension struts 46A and 46B. The lower arms 44A and 44B connect the engine mount 42 and the drive wheels 50A and 50B. Also, four muffler attachment points 52 are provided.

For the example shown in FIG. 9, a specific input point 12 is set as follows. In the example shown in FIG. 9, each input point 12 is represented by a combination of a symbol IN and a number. When all the input points 12 shown in FIG. 9 are expressed, they are expressed as INxx.
Regarding the engine mount 40, the input points IN01, IN02, and IN03 are in total three points, each in the direction of three axes. The attachment points of the lower arms 44A and 44B to the engine mount 42 are input points IN04 and IN05 on the left side, and input points IN06 and IN06 on the right side, and the left and right points are in three axis directions. The suspension struts 46A and 46B have one left and one right input point IN08 and one right input point IN09, and three left and right axis directions. Furthermore, it is assumed that the muffler attachment points 52 are four points and receive inputs in three axial directions at the respective input points IN10, IN11, IN12, and IN13.

A specific countermeasure plan that can be applied in advance to the configuration shown in FIG. Here, it is assumed that the coupling stiffness is changed at all input points INxx. Further, it is assumed that a vertical dynamic damper can be added to the input points IN01, IN02, and IN03, which are coupling points of the engine mount 42.
The evaluation point 14 is the outer ear position of the driver (not shown), and the specific response to be taken as a countermeasure at the evaluation point 14 is the sound pressure, and the 40 [Hz] component is the target.

Here, the contribution degree analysis is performed three times.
(1) Analysis of contribution to the target sound pressure at the evaluation point 14 with the input of all input points INxx as force
(2) Analysis of contribution to the target sound pressure at the evaluation point 14 using acceleration as the vertical input at the input point IN03 of the engine mount 42 and force as the other input
(3) Analysis of contribution to the target sound pressure using acceleration as the vertical direction input at the input points IN01 and IN02 of the engine mount 42 and other inputs as forces

Assume that the following example is obtained for the input point IN with the highest contribution exceeding the cumulative contribution of 50% as a result of the three contribution analysis.
(1) Higher contribution when all inputs are force inputs: Front / rear direction input at input points IN04 and IN06 of lower arms 44A and 44B, and vertical input at input points IN05 and IN07.
(2) Higher contribution when the vertical input at the input point IN03 of the engine mount 42 is acceleration and the other input is the force: Vertical acceleration at the input point IN03 of the engine mount and the input points IN04 and IN06 of the lower arm Forward / backward input
(3) Higher degree of contribution when the vertical input at the input points IN01 and IN02 of the engine mount 42 is acceleration and the other input is force: Vertical acceleration at the input points IN01 and IN02 of the engine mount 42 and the lower arm 44A, 44B input points IN05 and IN07 input in the front-rear direction

2.1 Effects of engine mount model From the above results, for example, if you want to minimize the number of changes, set a dynamic damper that reduces vibrations of 40 Hz in the vertical direction of engine mount IN03 based on the result of (2). Thus, it can be seen that if the vibration level is reduced and the bushing spring constant at 40 Hz in the front-rear direction of the lower arm input points IN04 and IN06 is reduced, the 40 Hz sound pressure can be effectively reduced.
In addition, based on the above results, designers can realize multiple objectives such as multiple countermeasures under conditions that minimize the number of changes, multiple countermeasures at the same level of cost, and the response α reduction rate. It is possible to propose a number of measures that are assumed to be. Then, the designer must select an optimum measure from among a plurality of measures. The contribution analysis method or apparatus according to the first embodiment can provide the above-described effect, and can assist the designer in selecting an optimum measure.
Based on the above result, the designer selects an input point for which a countermeasure is to be taken and a countermeasure for reducing the input value to the input point by, for example, 20%. Such countermeasures can be assumed in multiple types. Then, a contribution analysis after the reduction of the input value is performed using the same transfer function, and a response α is obtained. This response α can be calculated for each of a plurality of types of countermeasures. Then, the countermeasure that most reduces the value of the response α among the plurality of kinds of countermeasures can be specified by simulation.
In addition, if the cost of measures can be determined in advance and multiple measures that can reduce the response α below a predetermined target value can be extracted by simulation, the lowest cost measure is selected from the group of useful measures. can do.
Moreover, in the contribution analysis method and apparatus according to the present embodiment, the force input and the acceleration input can be evaluated on an equal basis. Therefore, the countermeasure according to the force input and the countermeasure according to the acceleration input are the same. It is possible to provide useful information for selection by a designer by comparing with a standard.
For example, in the conventional method, only the reduction of the force applied to the input point was considered as a countermeasure. In this embodiment, instead of reducing the force, a countermeasure for extracting acceleration with respect to the force input was examined, and the response α can be calculated. Then, it is possible to quantitatively compare the response α before the countermeasure, the response α when the countermeasure is taken with the force, and the value of the response α when the countermeasure is taken against the acceleration.

  Next, the properties and contribution of acceleration input will be described using a three-mass spring mass model that performs planar motion. In this example, the effect cannot be predicted even if the force-based method and the acceleration-based method are applied separately, and the degree of contribution generally differs depending on how to select whether to apply force or acceleration to the input point 12. Make it clear.

  First, as a preparation, consider the following equation of motion (13).

Here, the vector xf (t) is the displacement vector of the force input point 12, xa (t) is the displacement vector of the input point 12 of the acceleration input, and x0 (t) is a node to which no external force acts (the evaluation point 14 to be focused on). Displacement vector). These displacement vectors are displacement, corresponding to the force vector f _f (t), a displacement component in the axial direction of the force vector _f f (t).
The force vector f _f (t) is an external force acting on the input point 12 of force input, and the force vector f _a (t) is an external force acting on the input point 12 of acceleration input.
This equation (13) is transformed so that the force vector f _f (t) and the acceleration vector a _a (t) which is the second derivative of the displacement vector xa (t) are input, and the displacement vector xf (t) Are the second derivative of, the second derivative of the displacement vector x0 (t), and the force vector f _a (t). By changing the equation (13), the state / output equations of the following equations (14a) and (14b) are obtained. The vector ξh (t) in the equations (14a) and (14b) becomes the following equation (14c).

  Here, O and I are respectively a zero matrix and unit matrix of an appropriate size, and Ah, Bh, Ch, and Dh in equations (14a) and (14b) are respectively the following equations (15a), (15b), (15c) and (15d). Further, M and K are represented by the following equations (15e), (15f), (15g), and (15h).

Now, mass m of the mass m _i in the equilibrium state shown in FIG. 10, the mass spring model of the spring stiffness k _i, consider that small vibrations. The mass spring model shown in FIG. 10 is a right triangle having an angle θ, a mass point m ₁ coupled to another mass point at the angle θ, a mass point m ₂ coupled to another mass point at a right angle, and a mass point m _1. And a mass point m ₃ combined with a mass point m ₂ . The spring constant between mass point m ₃ and mass point m ₂ is k ₁ , the spring constant between mass point m ₃ and mass point m ₁ is k ₂ , and the spring constant between mass point m ₁ and mass point m ₃ is k _2. And A direction from the material point m1 to the mass point m ₂ and x-direction, a direction from the mass point m ₂ in mass point m ₃ and y directions. The mass point m ₁ and the mass point m ₂ are set as the input points 12A and 12B, and the mass point m ₃ is set as the evaluation point 14.

The x component, which is the displacement of the mass point m, is x _i , and the y component is y _i . The input of force or acceleration is applied in the y direction of the mass point m _{1 and} the x direction of the mass point m _{2. In} this order, the forces are f ₁ and f ₂ , respectively, and the accelerations are a ₁ and a ₂ , respectively. Further, the response α of interest is the y component of the acceleration at the mass point m ₃ .
Then, equation (16a) is obtained as an equation of motion. Hereinafter, for simplicity, it is assumed that Si = sinθ and Co = cosθ, and the matrix representation follows the Matlab notation. Elements of the equation of motion (16a) are expressed by the following equations (16b), (16c), (16d), and (16e). In the equation (16d), diag means a diagonal matrix.

The state / output equations in each formulation should be as follows in Equation (14).
(1) Formulation by hybrid input (f ₁ and a ₂ are external inputs)

(2) Formulation by force input (f ₁ and f ₂ are external inputs)

(3) Formulation by acceleration input (a ₁ and a ₂ are external inputs)

Transfer function First, consider a situation where a force input f ₁ is applied to the input point 12A as a true external input, an acceleration input a ₂ is applied to the input point 12B, and the mass spring system vibrates due to both. Then, this vibration state is captured by the following three methods. The first is a force-based method, in which external input is regarded as force f ₂ corresponding to force f ₁ and acceleration a ₂ . The second is an acceleration-based method in which external inputs are regarded as acceleration a ₁ and acceleration a ₂ corresponding to force f ₁ . The third is a hybrid input method according to the present embodiment, in which external input is regarded as force f ₁ and acceleration a ₂ . This is hybrid 1 (HB1). An example in which the external input is acceleration a ₁ and force f ₂ is also disclosed as hybrid 2 (HB2).

FIG. 11 shows transfer functions according to the formulation of input points in each method. FIG. 11A shows an example of a transfer function from the input point 12A to the evaluation point 14, and FIG. 11B shows an example of a transfer function from the input point 12B to the evaluation point 14. In FIGS. 11A and 11B, the transfer function H of the force-based method is indicated by a two-dotted line, the transfer function G of the acceleration-based method is indicated by a one-dot chain line, and the hybrid 1 ( f ₁ , a ₂ ) is indicated by a solid line, and hybrid 2 (f ₂ , a ₁ ) is indicated by a broken line.

  In this embodiment, the contributions of the actual input shown in FIG. 12 and the corresponding input shown in FIG. 13 are shown in FIGS. The following is a summary of the method; the transfer function of FIG.

(1) Force-based method (f ₁ , f ₂ ): Fig. 11 Two-dot chain line; Fig. 14
(2) Acceleration based method (a ₁ , a ₂ ): FIG.
(3) Hybrid 1 (f ₁ , a ₂ ): FIG. 11 solid line; FIG.
(4) Hybrid 2 (a ₁ , f ₂ ): broken line in FIG. 11; FIG.

The following parameters were used in the calculation.
m ₁ : 10; m ₂ : 20; m ₃ : 15 [kg]
k ₁ : 60,000; 20,000; 30,000 [N / m]
θ: 60 [deg]

  As shown in FIG. 11, it can be seen that the transfer function for the same input varies depending on the combination (formulation) of what is regarded as the input. That is, the force base, acceleration base, and hybrid 1 in FIGS. 11A and 11B have different transfer functions due to differences in the way of grasping the formulation.

  As shown in FIG. 11, there are three elastic modes in any of the methods. If the acceleration is regarded as an input, the degree of freedom of the mass point is constrained at the time of zero input, so the elastic mode changes. The resonance frequencies are 39.5, 62.0, and 89.1 [rad / s] for hybrid input, 44.2, 70.2, and 89.2 [rad / s] for force input, and 24.2, 59.4, and 87.9 [rad / s] for acceleration input. The resonance frequency differs depending on what is regarded as an input, and the influence of the difference between these resonance points appears in the contribution decomposition.

  Note that the transfer function in the case of acceleration input and hybrid input is the same as that shown in FIG. However, it is easy to get numerical noise due to the calculation that cancels the pole of inertance. On the other hand, it is preferable to use the cross spectrum method according to the equation (12b) because there is no influence of such noise.

○ Time history simulation and contribution analysis conditions The contribution of external input to the response acceleration α in a short time interval is calculated by the above three methods.
Given f ₁ and a ₂ as true external inputs, calculate the contribution in each formulation at that time. f ₁ is the sum of a random signal with a spectral peak at 30 [rad / s] and 75 [rad / s] and a sweep signal that changes from 0 to 30 [rad / s] in 100 seconds, and a ₂ is 50 The response acceleration α was calculated as the sum of a random signal with a spectral peak at [rad / s] and a sweep signal varying from 125 to 95 [rad / s] in 100 seconds. Thereafter, as an example, a section from 50 to 52.56 [s] was cut out, and the contributions of the input points 12A and 12B in each formulation were calculated. FIG. 12 shows the spectra of f ₁ and a _{2 in} this section. Frequency of the sweep signal are each at f ₁ and a _2, about 17 [rad / s], a 110 [rad / s]. FIG. 13 is a spectrum of a ₁ and f ₂ corresponding to the true inputs f ₁ and a ₂ shown in FIG.

○ Contribution calculation in each formulation For the first example, the contributions of the input point 12A and the input point 12B based on each formulation are shown by broken lines in FIGS. 14A to 16B, respectively. Show. The solid line in each figure is the response acceleration α spectrum, which is the same in all figures. Since the true external inputs are f ₁ and a ₂ , the response acceleration α spectrum has peaks due to the resonance of the hybrid input transfer function (39.5, 62.0, 89.1 [rad / s]) and the input f ₁ A peak due to the input (approximately 17, 30, 75 [rad / s]) and a peak due to the input a ₂ (50, approximately 110 [rad / s]) appear.

(1) Contribution based on formulation by force input (f ₁ , f ₂ ) (Fig. 14)
The influence of the input point 12A is obtained by multiplying the spectrum of the external input f1 by a transfer function indicated by a two-dot chain line in FIG.
Effect of the input point 12B will that by multiplying the spectrum of the force response f ₂ to a transfer function indicated by the two-dot chain line in FIG. 11 (B). Since the spectrum shape of the force response f ₂ is almost similar to the response acceleration α (FIG. 13), the influence of the input point 12B is that the resonance peak of the transfer function formulated by the force input is added to the spectrum peak of the response acceleration α. The shape is such that is superimposed.

(2) Contribution based on formulation by acceleration input (a ₁ , a ₂ ) (Fig. 15)
The influence of the input point 12A is obtained by multiplying the spectrum of the acceleration response a _{1 by} the transfer function indicated by the alternate long and short dash line in FIG. Since the spectrum shape of the acceleration response a ₁ is almost similar to the response acceleration α (FIG. 13), the influence of the input point 12A is that the resonance peak of the transfer function formulated by the acceleration input is added to the spectrum peak of the response acceleration α. The shape is such that is superimposed.
The influence of the input point 12B is obtained by multiplying the spectrum of the external input a _{2 by} the transfer function indicated by the alternate long and short dash line in FIG.
A large contribution appears at the input point 12A and the input point 12B in the vicinity of 24.2 [rad / s] indicated by the reference sign c1 in FIG. 15, but these components cancel out as opposite phase components and do not appear in the response acceleration α. Moreover, the contribution of a ₁ is dominant in the entire frequency range. This is probably because a ₁ and α are the same y direction in FIG. 10, but a ₂ is orthogonal to α.

(3) Contribution based on formulation with hybrid input 1 (f ₁ , a ₂ ) (Fig. 16)
The influence of the input point 12A is obtained by multiplying the spectrum of the external input f _{1 by} the transfer function indicated by the solid line in FIG.
The influence of the input point 12B is obtained by multiplying the spectrum of the external input a _{2 by} the transfer function indicated by the solid line in FIG.
Since the added input is the hybrid input itself, the contribution decomposition is straightforward.

(4) Contribution based on formulation with hybrid input 2 (a ₁ , f ₂ ) (Fig. 17)
The influence of the input point 12B is obtained by multiplying the spectrum of the external input a _{1 by} the transfer function indicated by the broken line in FIG.
Effect of input points 12A will those in multiplication transfer function shown by a broken line a spectrum of the external input f ₂ in FIG. 11 (B).
Since the spectral shapes of the acceleration response a ₁ and the force response f ₂ are generally similar to the response α, the glory of the input points 12A and 12B is transferred to the formulation of the hybrid input 2 in the spectral peak of the response 痾. The shape is such that the resonance peak of the function is superimposed.
From FIG. 14B and FIG. 17B, it can be seen that even with the same contribution of f _2, a difference occurs due to the formulation. Further, from FIG. 15A and FIG. 17A, it can be seen that there is a difference due to the formulation even with the same a ₁ contribution. These differences are caused by differences in transfer functions shown in FIG.

Therefore, when assuming control of acceleration a ₁ and control of force f ₂ , the effect of reducing acceleration a ₁ with the acceleration-based method is estimated, and the effect of reducing force f ₂ with the force-based method is estimated. be estimated, the effect can not be predicted at the time of controlling the acceleration a ₁ and the force f ₂ at the same time. Rather, it can even have bad results when combined with improvements that seem to be effective alone.

Now, the broken line in FIG. 18 shows the spectrum of α when f ₂ → f ₂ * 0.3 (force f ₁ is unchanged) by the force-based method (external input is regarded as force f ₁ and force f ₂ ). The thick dashed line is the original alpha spectrum. In this case, it can be seen that the level of α is reduced at a frequency where the force f ₂ is dominant.

Next, the spectrum of α in the case of a ₁ → a ₁ * 0.8 (acceleration a ₂ is unchanged) by the acceleration-based method (external input is regarded as acceleration a ₁ and acceleration a ₂ ) is shown by a one-dot chain line in FIG. . In this case, it can be seen that the level of α is reduced at a frequency where the acceleration a ₁ is dominant.

Therefore, by controlling the acceleration a ₁ and the force f ₂ to reduce a ₁ → a ₁ * 0.8 and f ₂ → f ₂ * 0.3, the spectrum of α is hybrid input method (external input acceleration a ₁ And the force f ₂ ) is shown by a solid line in FIG.
It can be seen that the effect expected with the force-based method and the effect expected with the acceleration-based method are not as effective. In particular, at 40 [rad / s], although a large reduction effect is expected by itself, the level of α is increased by combining two measures.
Thus, a result cannot be predicted unless an input is selected according to an assumed measure.

As described above, in the present embodiment, the theoretical validity of the acceleration-based transmission path analysis is considered for the vibration of the elastic body, and the following conclusions are explained. The basic idea is the same when the response is a sound.
(1) It was confirmed that the acceleration-based method can be regarded as a transfer function-based method equivalent to the force-based method by regarding the acceleration at the force input point itself as a forced acceleration input.
(2) It was shown that contributions calculated by force-based method and acceleration-based method are generally different, and the interpretation was clarified as follows.
・ Assuming measures to reduce force input → Force-based method ・ Assuming measures to reduce acceleration input → Acceleration-based method
(3) Based on the above interpretation, we proposed a hybrid input method that mixes force and acceleration as inputs.
(4) The mechanism by which the resonance frequency of the transfer function differs depending on the choice of input was discussed, and the qualitative nature of the contribution peak was clarified.
(5) A simple simulation confirmed the difference in contribution due to formulation.

DESCRIPTION OF SYMBOLS 10 Structure 12 Input point 14 Evaluation point 16 Passive part 18 Input part 20 Data input part 22 Transfer function memory | storage part 24 Fourier transformation part 26 Contribution calculation part 28 Response calculation part 40 Engine 42 Engine mount 44A, 44B Lower arm 46A, 46B Strut 48A, 48B Suspension 50A, 50B Drive wheel 52 Muffler attachment point 54 Muffler
P, P (ω) Force input transfer function
Q, Q (ω) Acceleration input transfer function α Response
C contribution
Cp _i , C _i (ω; t) Force input contribution
Cq _j , C _j (ω; t) Acceleration input contribution
f, f _f force input
a, a _a Acceleration input

Claims (9)

An input setting step for setting a physical quantity transmitted at an input point of the structure as force input or acceleration input;
A force input transfer function from the plurality of input points of the force input to responses of the evaluation points of the structure, and an acceleration input transfer function from the plurality of input points of the acceleration input to the responses of the evaluation points. A function calculation step to calculate,
Calculate the force input contribution to the response of the force input based on the force input value of the structure and the force input transfer function, and the acceleration input value based on the acceleration input value and the acceleration input transfer function A contribution calculation step of calculating an acceleration input contribution to the response;
A contribution analysis method characterized by comprising: The contribution calculation step is based on the force input value or the acceleration input value after the countermeasure for the force or acceleration, the force input transfer function and the acceleration input transfer function before the countermeasure, and the force after the countermeasure. A step of calculating an input contribution and the acceleration input contribution;
The contribution analysis method according to claim 1, wherein: The input setting step includes a step of prompting a setting to be the force input for the input point capable of countermeasures against force and a step of prompting a setting to be the acceleration input for the input points capable of countermeasures for acceleration. ,
The contribution analysis method according to claim 1 or 2, characterized in that: The function calculating step includes
A transfer function matrix having as input the force of the force input and the force corresponding to the acceleration input, the acceleration of the acceleration input, the acceleration corresponding to the force input, and the response of the evaluation point Given an inertance matrix as output,
The force input transfer function and the acceleration input transfer function are calculated by expanding the inertance matrix.
The contribution analysis method according to claim 1, 2, or 3. The function calculating step includes
Measuring the response by giving the force input and the acceleration input as inputs, and calculating the force input transfer function and the acceleration input transfer function based on the cross spectrum of the input and response;
The contribution analysis method according to claim 1, 2, or 3. The contribution calculation step includes:
Calculating a frequency spectrum of the force input and a frequency spectrum of the acceleration input;
Calculating the force input contribution based on the force input transfer function and the frequency spectrum of the force input;
Calculating the acceleration input contribution based on the acceleration input transfer function and the frequency spectrum of the acceleration input;
Calculating the response of the evaluation score by adding the force input contribution and the acceleration input contribution,
The contribution analysis method according to claim 1, 2, 3, 4 or 5.   A contribution analysis program for executing the method according to claim 1, 2, 3, 4, 5 or 6 using a computer. In response to a force input or acceleration input set in advance as a physical quantity transmitted at an input point of the structure, for the input point set to the force input, a force input value in actual operation of the structure is estimated or A data input unit for measuring an acceleration input value for the input point set for the acceleration input,
A force input transfer function from the plurality of input points of the force input to responses of the evaluation points of the structure, and an acceleration input transfer function from the plurality of input points of the acceleration input to the responses of the evaluation points. A transfer function storage unit stored in advance;
While calculating the force input contribution to the response of the force input based on the force input value and the force input transfer function at the time of actual operation of the structure, and based on the acceleration input value and the acceleration input transfer function A contribution calculation unit for calculating an acceleration input contribution to the response of the acceleration input;
A contribution analysis device characterized by comprising: A data input unit for estimating or measuring a force input value and an acceleration input value during actual operation of the structure;
A force input transfer function from a force input to an input point capable of countermeasures against force to a response at an evaluation point, and an acceleration input transfer function from an acceleration input to an input point capable of countermeasures against acceleration to the response in advance A stored transfer function storage unit;
A Fourier transform unit for calculating the frequency spectrum of the force input and the frequency spectrum of the acceleration input;
The force input contribution is calculated based on the force input transfer function and the frequency spectrum of the force input, and the acceleration input contribution is calculated based on the acceleration input transfer function and the frequency spectrum of the acceleration input. A contribution calculation unit to calculate,
A response calculation unit that calculates the response of the evaluation score by adding the force input contribution and the acceleration input contribution;
A contribution analysis device characterized by comprising:

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