JP5446812B2 - Response measurement point determination method in experimental modal analysis - Google Patents

Description

  The present invention relates to a response measurement point determination method in experimental modal analysis.

When the structure receives a certain external force, vibration and noise may occur. This is because a phenomenon such as occurrence of large vibration (resonance) occurs when the natural frequency of the structure and the frequency of the external force coincide with each other. Therefore, when developing and designing a structure, it is assumed that the structure is composed of a finite mass, a spring, etc., and the natural frequency (resonance frequency) and vibration acceleration of the structure are then calculated. Understand the vibration characteristics of the structure such as natural vibration mode, and if necessary, change the shape and material of the structure to move the natural frequency out of the actual frequency range. It is necessary to take measures such as preventing resonance.
In order to grasp the vibration characteristics of the structure, a method of making a prototype of the structure and measuring it using an experimental modal analysis technique is often used.

  FIG. 3 is a flowchart showing the procedure of a conventional experimental modal analysis.

  In the prototype process 301, a structure is actually prototyped.

  In the numerical analysis model creation step 311, shape data divided into finite elements such as shell elements and solid elements of the structure, material data such as elastic modulus, Poisson's ratio, density, excitation force, excitation position, fixed position, etc. The boundary condition data is input to the auxiliary storage device of the computer. In the case of a plate-like structure whose thickness is sufficiently smaller than the typical dimensions of the structure, such as an injection molded product, a shell element is often used as a finite element.

  In the eigenvalue analysis step 312, vibration characteristics such as natural frequency and mode shape of the structure are analyzed using commercially available vibration analysis software such as “MSC NASTRAN (registered trademark)” manufactured by MSC Software Corporation.

  In the response measurement point / excitation point determination step 302, the position and number of response measurement points and excitation points are determined based on past knowledge and the like.

  Next, in the correlation analysis step 303, the vibration characteristics analyzed in the eigenvalue analysis step 312 are input by using commercially available experimental modal analysis software such as “I-DEAS (registered trademark)” manufactured by UG Corporation, and response measurement is performed. The MAC value (MAC: Modal Assistance Criteria) between natural vibration modes using only the displacement of the response measurement point determined in the point / excitation point determination step 302 is analyzed as shown in Patent Document 1, and as shown in FIG. By creating a simple MAC matrix, it is quantitatively determined which mode of the numerical analysis model is highly correlated. The MAC value quantitatively indicates how much the two mode shapes being compared match, and takes a value of 0 to 1. “0” indicates that the modes do not match at all, and “1” indicates that the modes match completely. At this time, the MAC values of the same natural vibration modes have the same shape, and thus always have a value of 1, and should be a value close to 0 in combination with other modes. For example, consider measuring responses at three points at response measurement points 1602, 1603, and 1604 for a beam structure 1601 as shown in FIG. When a primary mode mode shape 1701 as shown in FIG. 17 and a tertiary mode mode shape 1801 as shown in FIG. 18 exist, response measurement points 1702, 1703, and 1704 in the primary mode mode shape 1701 exist. In the third mode mode shape 1801, the response measurement points are displaced as 1802, 1803, and 1804. Since only the response (displacement, velocity, acceleration, etc.) of the response measurement point can be grasped, the mode shape 1801 of the third-order mode is observed as an apparent 1807 as is apparent from the figure. Therefore, the mode shape 1701 in the first mode and the mode shape 1801 in the third mode cannot be distinguished. In this case, when the MAC value is calculated, a value close to 1 is calculated. In addition, when two response measurement points 1605 and 1606 are added to the structure of FIG. 16 and five responses are measured, the mode shape of the primary mode is observed as shown by 1701 in FIG. The mode shape of the third mode is observed as indicated by 1801 in FIG. As is apparent from the figure, the mode shape 1701 of the first order mode and the mode shape 1805 of the third order mode can be confirmed as completely different shapes. In this case, when the MAC value is calculated, a value close to 0 is calculated. In this way, in order to avoid that the mode shape is apparently indistinguishable depending on the position and number of response measurement points, it is set to a value close to 0 in combination with other modes. The fact that mode shapes cannot be distinguished means that the mode shape characteristics of each mode cannot be correctly grasped. In the MAC threshold determination step 304, it is determined whether or not the MAC value between different modes is equal to or greater than a determination criterion determined based on past knowledge, and a response is made with reference to the natural vibration mode obtained by numerical analysis The position and number of measurement points are changed, the MAC value is analyzed again, and the above steps 302 to 304 are repeated to determine an appropriate response measurement point.

  In the transfer function measurement step 305, as shown in Non-Patent Document 1, vibration is applied by applying an external force to a predetermined position of the prototype with an impact hammer or a vibrator, and responses at a plurality of positions on the prototype are accelerated. The frequency transfer function between the excitation point and the response point is obtained by measuring with a meter. Further, according to Maxwell's reciprocity theorem, the frequency response function does not change even if the excitation point and the response point are interchanged. Therefore, there is a case where the response point is fixed and the excitation point is moved.

  In the modal parameter identification step 306, as shown in Non-Patent Document 2, by extracting a modal parameter from a plurality of transfer functions obtained in the transfer function measurement step 305 using a technique such as a polyreference method, the natural frequency, Vibration characteristics 307 such as a damping coefficient for each mode and a natural vibration mode can be measured. Once the vibration characteristics are obtained, the behavior of the prototype at that time can be simulated by a computer no matter what external force acts on which position.

  However, according to the knowledge of the present inventors, in such a conventional method, the response measurement point / excitation point is determined by trial and error based on the knowledge, etc., for beginners with little experience in experimental modal analysis. First, when deciding the response measurement point / excitation point, or when the MAC value between different modes exceeds the criterion, which response measurement point is changed or deleted, and at which position the response measurement point is added There is a problem that it is difficult to determine what to do. In particular, it is difficult to judge when the shape of the structure is complicated. If the response measurement point cannot be set appropriately, the mode shape may not be correctly grasped, and there is a possibility that an erroneous vibration countermeasure is taken.

  If the response measurement points are increased, the MAC value between different modes often approaches 0. Therefore, there are cases where the response measurement points are increased, but there is also a problem that the experiment time becomes longer because the measurement points increase.

  Therefore, the conventional method cannot quantitatively determine the response measurement point in the experimental modal analysis for measuring the vibration characteristics of the structure.

JP 2001-311659 A

Nobuyuki Okubo, “Modal Analysis of Machines”, Chuo University Press, May 1982, p. 47-82 Nobuyuki Okubo, “Modal Analysis of Machines”, Chuo University Press, May 1982, p. 82-118

  An object of the present invention is to provide a method for quantitatively determining response measurement points in an experimental modal analysis for measuring vibration characteristics of a structure.

In order to achieve the above object, the present invention obtains an eigenvalue analysis step for obtaining a mode shape in a predetermined frequency range and an autocorrelation coefficient between each mode by eigenvalue analysis for a numerical analysis model of a structure. A response measurement point determination method of an experimental modal analysis having a response measurement point determination step for determining a response measurement point,
A mode separation index analysis step of analyzing a mode separation index indicating the magnitude of the influence on the autocorrelation coefficient for each node;
In the response measurement point determination step, a response measurement point determination method in experimental modal analysis is provided in which a response measurement point is determined from the mode separation index calculated in the mode separation index analysis step.

According to a preferred embodiment of the present invention, in the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (1),

(D) Subsequently, the mode separation index Sens _± ⁽ⁱ⁾ of the node i is calculated by the equation (2),

(E) Find the mode separation index Sens _± for all n nodes.
The response measurement point determination method in the experimental modal analysis according to claim 1, further comprising a mode separation index analysis step.

According to a preferred embodiment of the present invention, in the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (3),

(D) Subsequently, the mode separation index Sens ₊ ⁽ⁱ⁾ of the node i is calculated by the equation (4),

(E) Find the mode separation index Sens ₊ for all n nodes.
The response measurement point determination method in the experimental modal analysis according to claim 1, further comprising a mode separation index analysis step.

According to a preferred embodiment of the present invention, in the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (5),

(D) Subsequently, the mode separation index Sens node i _- calculates ⁽ⁱ⁾ in equation (6),

(E) Find the mode separation index Sens ₋ for all n nodes.
The response measurement point determination method in the experimental modal analysis according to claim 1, further comprising a mode separation index analysis step.

Further, according to a preferred embodiment of the present invention, for the numerical analysis model of the structure, by eigenvalue analysis, an eigenvalue analysis step for obtaining a mode shape in a predetermined frequency range, and an autocorrelation coefficient between each mode are obtained, A numerical analysis device for determining a response measurement point of an experimental modal analysis having a response measurement point determination step for determining a response measurement point;
A mode separation index analysis step of analyzing a mode separation index indicating the magnitude of the influence on the autocorrelation coefficient for each node;
A numerical analysis apparatus for determining a response measurement point in an experimental modal analysis, wherein the response measurement point is determined from the mode separation index calculated in the mode separation index analysis step in the response measurement point determination step.

  According to another aspect of the present invention, there is provided a program for causing a computer to execute the response measurement point determination method in the experimental modal analysis described above.

  Moreover, according to another form of this invention, the computer-readable recording medium which recorded said program is provided.

  In the present invention, the response measurement point refers to a place where a sensor such as a displacement meter, a speedometer, or an accelerometer for measuring a transfer function of an actual structure is attached in an experimental modal analysis.

In the present invention, the mode shape refers to a vibration mode for each mode. Although the displacement direction is usually three-dimensional, it may be expressed in two dimensions or one dimension. In general, the displacement of the mode shape is normalized so that the maximum displacement is 1. A vector notation of the displacement information of the mode shape is called a mode shape vector, and the mode shape vector of the m-th order mode is represented as {φ _m }.

  In the present invention, the autocorrelation coefficient means a value that quantitatively indicates how much the two mode shapes being compared between the same analysis target (for example, a numerical analysis model of a structure) match. For example, in the case of MAC value,

Is required. The subscript T indicates transposition. {φ _A } and {φ _B } represent mode shape vectors, respectively, and when comparing the Ath order mode and the Bth order mode, the mode shape vector {φ _A } and the Bth order mode of the Ath order mode Mode shape vector {φ _B } is substituted into equation (7). The MAC value ranges from 0 to 1, and the closer to 1, the higher the correlation between the two mode shapes, and the closer to 0, the lower the correlation between the two mode shapes. By confirming the correlation quantitatively, it is possible to quantitatively determine which mode of the numerical analysis model the correlation is high.

  In the present invention, the autocorrelation matrix refers to a matrix that represents autocorrelation coefficients. For example, when autocorrelation coefficients are calculated for all combinations of the primary mode, the secondary mode, and the tertiary mode, nine autocorrelation coefficients are calculated. These are expressed as a 3 × 3 autocorrelation matrix.

In the present invention, the sensitivity matrix refers to a matrix that shows changes in two autocorrelation matrices and quantitatively represents the degree of influence on the autocorrelation matrix for a node of interest. For example, consider a numerical analysis model 1900 of a beam structure including nodes 1 (1911) to 5 (1915) and elements 1 (1921) to 4 (1924) as shown in FIG. Here, each node is a candidate for a response measurement point. FIG. 20 shows the mode shape of the first-order mode of the numerical analysis model 1900, which is displaced as nodes 1 (2011) to 5 (2015) and elements 1 (2021) to 4 (2024). FIG. 21 shows the mode shape of the second-order mode of the numerical analysis model 1900, which is displaced as nodes 1 (2111) to 5 (2115) and elements 1 (2121) to 4 (2124). FIG. 22 shows a mode shape of the third-order mode of the numerical analysis model 1900, which is displaced as nodes 1 (2211) to 5 (2215) and elements 1 (2221) to 4 (2224). Here, the sensitivity matrix is obtained for all the nodes. Here, for example, the sensitivity matrix for the node 4 is obtained. Here, it is assumed that a MAC value is used as the autocorrelation coefficient. First, the autocorrelation matrix [MAC _ALL ] is calculated from the mode shape vectors of the first, second, and third modes having the displacement information of the nodes 1 to 5. The autocorrelation matrix [MAC _ALL ] is shown in FIG. Next, the autocorrelation matrix [MAC _not ⁽⁴⁾ ] is calculated from the mode shape vectors of the first, second, and third modes having the displacement information of the nodes 1, 2, 3, and 5 excluding the node ⁴ . The autocorrelation matrix [MAC _not ⁽⁴⁾ ] is shown in FIG. The mode shape of the primary mode excluding the node 4 is expressed by complementing the element 3 (2023) and the element 4 (2024) with 2025. Similarly, the mode shape of the second-order mode excluding the node 4 is expressed by complementing the element 3 (2123) and the element 4 (2124) with 2125. Similarly, the mode shape of the third-order mode excluding the node 4 is represented by complementing the element 3 (2223) and the element 4 (2224) with 2225. Therefore, [MAC _ALL ] compares the correlations between the modes of the numerical analysis model using the five nodes 1 to 5, whereas [MAC _not ⁽⁴⁾ ] has no node 4. , The correlation between the modes of the numerical analysis model is compared only at the four nodes of nodes 1-3, and [MAC _not ⁽⁴⁾ ] reduces the characteristic displacement information of each mode shape, It becomes difficult to distinguish mode shapes. Therefore, the MAC value between other modes of [MAC _not ⁽⁴⁾ ] tends to increase. Next, a sensitivity matrix [Sens ⁽⁴⁾ ] is obtained by subtracting [MAC _ALL ] from [MAC _not ⁽⁴⁾ ]. The sensitivity matrix [Sens ⁽⁴⁾ ] is shown in FIG. Therefore, the sensitivity matrix is a matrix that quantitatively represents the degree of influence of the node 4 on the autocorrelation matrix. Each element of the sensitivity matrix [Sens ⁽⁴⁾ ] takes a value in the range of −1 to 1, and the closer to 1, the larger the MAC value between the other modes of [MAC _not ⁽⁴⁾ ]. The absence of 4 indicates that it is difficult to distinguish between the mode shapes. Since the MAC value between other modes of [MAC _not ⁽⁴⁾ ] becomes smaller as the element is closer to -1, the absence of node 4 It shows that each mode shape can be easily distinguished. Since the values of the primary mode and the tertiary mode of the sensitivity matrix [Sens ⁽⁴⁾ ] are 0.00, the presence or absence of the node 4 is used to distinguish the mode shape of the primary mode and the tertiary mode. Indicates that it is not important. Further, since the values of the second order mode and the third order mode of the sensitivity matrix [Sens ⁽⁴⁾ ] are 0.50, the mode shape of the node 4 is used to distinguish the mode shape of the second order mode and the third order mode. It shows that the presence or absence affects.

  In the present invention, the mode separation index refers to a scalar value calculated from a sensitivity matrix. The value represented by one element of the sensitivity matrix is the sensitivity between two mode shapes among many modes of the sensitivity matrix. However, if the overall mode represented by the sensitivity matrix is not evaluated comprehensively, mode shapes between some modes can be distinguished, but mode shapes between other modes may not be distinguished. Further, since the information held by each node is enormous in the matrix state, the information held by the sensitivity matrix can be simply expressed by using a scalar value that comprehensively represents the information of each element of the sensitivity matrix. In order to separate the mode shapes between the target modes by evaluating the distribution of the mode separation index of the structure, i.e., to avoid apparently indistinguishably distinguishing the mode shapes between the modes, It is understood that the region that should be performed and the region that should not be used as the response measurement point are recognized.

For example, the mode separation index Sens _± ⁽ⁱ⁾ may be obtained by adding all the elements of the sensitivity matrix. At this time, the mode separation index Sens _± ⁽ⁱ⁾ represents the magnitude of the effect of increasing or decreasing the autocorrelation coefficient by eliminating the node i. When the MAC value is used as the autocorrelation coefficient, the mode separation index Sens _± is increased when there are many combinations in which the MAC value approaches 1 in combination with other modes when the node i is not used as a response measurement point. When there are many combinations in which the MAC value approaches 0 in combination with other modes, the mode separation index Sens _± becomes small. Therefore, in the mode separation index Sens _± distribution, by selecting a place where the mode separation index Sens _± has a large value, the MAC value of the same natural vibration mode has the same shape, so it is always 1, and in combination with other modes The position of the response measurement point that tends to be a value close to 0 can be selected. In other words, in order to avoid that the mode shapes between the target modes are apparently indistinguishable, it is better to set a place where the mode separation index Sens _± has a large value as a response measurement point. On the other hand, it is better not to use a response measurement point for small values (negative values).

Alternatively, only the positive elements of the sensitivity matrix elements may be added to obtain the mode separation index Sens ₊ ⁽ⁱ⁾ . At this time, the mode separation index Sens ₊ ⁽ⁱ⁾ represents the magnitude of the effect of increasing the autocorrelation coefficient by eliminating the node i. When the MAC value is used for the autocorrelation coefficient, the mode separation index Sens ₊ becomes large when there are many combinations in which the MAC value approaches 1 in combination with other modes when the node i is not a response measurement point. When there are few combinations whose MAC value approaches 1 in combination with other modes, the mode separation index Sens ₊ becomes small. Therefore, in the mode separation index Sens ₊ distribution, by selecting a place where the mode separation index Sens ₊ has a large value, the MAC value of the same natural vibration mode is always the same shape, and in combination with other modes. The position of the response measurement point that tends to be a value close to 0 can be selected. In other words, in order to avoid that the mode shapes between the target modes are apparently indistinguishable, it is better to set a place where the mode separation index Sens ₊ has a large value as a response measurement point.

Further, only the summed negative elements among the elements of the sensitivity matrix, mode separation index Sens - may be ^_(i). At this time, the mode separation index Sens - ^_(i) is the autocorrelation coefficient represents the magnitude of the effect of reduction by eliminating nodes i. When the MAC value is used as the autocorrelation coefficient, the mode separation index Sens ₋ is small when the node i is not used as the response measurement point, and when there are many combinations whose MAC value approaches 0 in combination with other modes. The mode separation index Sens ₋ increases when there are few combinations whose MAC value approaches 0 in combination with the mode. Therefore, by selecting a mode separation index Sens ₋ distribution other than the one where the mode separation index Sens ₋ has a small value, the MAC values of the same natural vibration modes are always the same shape, so that the combination with other modes is always 1 Then, the position of the response measurement point that tends to be a value close to 0 can be selected. That is, in order to avoid that the mode shapes between target modes are apparently indistinguishable, it is better not to set the mode separation index Sens _{− to} have a small value as a response measurement point.

Further, among the elements of the sensitivity matrix, the positive element may be added only elements having a positive threshold value or more, and the negative element may be added only elements having a negative threshold value or less to obtain the mode separation index Sens _th ^(i). . At this time, the mode separation index Sens _th ⁽ⁱ⁾ represents the magnitude of the effect of increasing or decreasing the autocorrelation coefficient by eliminating the node i. When the sensitivity matrix change uses the MAC value for the autocorrelation coefficient, the mode separation index Sens when there are many combinations in which the MAC value approaches 1 in combination with other modes when the node i is not used as a response measurement point _{When th} increases and there are many combinations in which the MAC value approaches 0 in combination with other modes, the mode separation index Sens _th decreases. Therefore, in the mode separation index Sens _th distribution, by selecting a place where the mode separation index Sens _th has a large value, the MAC values of the same natural vibration modes are always the same shape, and in combination with other modes The position of the response measurement point that tends to be a value close to 0 can be selected. In other words, in order to avoid that the mode shapes between the target modes are apparently indistinguishable, it is better to set a place where the mode separation index Sens _th has a large value as a response measurement point. On the other hand, it is better not to use a response measurement point for small values (negative values).

  There are various calculation methods for the mode separation index, but the response measurement point may be selected using various mode separation indices, or the response measurement point may be selected using one type of mode separation index. Good. Further, when a tendency cannot be grasped with one type of mode separation index, other mode separation may be referred to.

  According to the present invention, by calculating the mode separation index at each node of the numerical analysis model, it is possible to quantitatively determine the response measurement point in the experimental modal analysis for measuring the vibration characteristics of the structure. It is possible to improve the accuracy and efficiency of the experimental modal analysis.

It is a block diagram which shows an example of embodiment of this invention. It is a block diagram which shows an example of the procedure of implementation of this invention. It is a block diagram of the example of a procedure of experimental modal analysis. It is a block diagram which shows an example of an autocorrelation matrix of 5x5. It is a block diagram which shows an example of an autocorrelation matrix of 5x5. It is a block diagram which shows an example of a sensitivity matrix of 5x5. FIG. 3 is a tilt diagram illustrating a numerical analysis model of a flat plate in Example 1. 4 is a distribution diagram of a mode separation index Sens _± of a flat plate in Example 1. FIG. 6 is a distribution diagram of a mode separation index Sens ₊ of a flat plate in Example 1. FIG. It is an inclination figure which shows the position of the response measurement point calculated | required from distribution of the mode separation index | exponent Sens _± of the flat plate in Example 1. It is an inclination figure which shows the position of the response measurement point calculated | required from the distribution of the mode separation index | index Sens ₊ of the flat plate in Example 1. It is an inclination figure which shows the position of the general response measurement point of a flat plate in the comparative example 1. FIG. The MAC matrix in the response measurement point selected from the distribution of the mode separation index Sens _± is shown. The MAC matrix in the response measurement point selected from the distribution of the mode separation index Sens ₊ is shown. The MAC matrix in arrangement | positioning of the general response measurement point of a flat plate in Example 1 is shown. An example of a beam structure is shown. An example of the mode shape of the primary mode of a beam structure is shown. An example of the mode shape of the 3rd mode of a beam structure is shown. An example of a numerical analysis model of a beam structure is shown. An example of the mode shape of the primary mode of the numerical analysis model of a beam structure is shown. An example of the mode shape of the secondary mode of the numerical analysis model of a beam structure is shown. An example of the mode shape of the third mode of the numerical analysis model of a beam structure is shown. An example of an autocorrelation matrix [MAC _ALL ] is shown. An example of an autocorrelation matrix [MAC _not ⁽⁴⁾ ] is shown. An example of a sensitivity matrix [Sens ⁽⁴⁾ ] is shown. It is an inclination figure which shows the position of the response measurement point of the flat plate examined in Comparative Example 1 for the first time. It is an inclination figure which shows the position of the response measurement point of the flat plate examined in Comparative Example 1 for the second time. The MAC matrix in arrangement | positioning of the response measurement point of the flat plate examined in Comparative Example 1 for the first time is shown. The MAC matrix in arrangement | positioning of the response measurement point of the flat plate examined 2nd time in the comparative example 1 is shown.

  Hereinafter, an example of the best mode of the present invention will be described with reference to the drawings.

  FIG. 1 is a block diagram showing a configuration of an example of an embodiment of the present invention. In this embodiment, as shown in FIG. 1, (100) is a computer such as a computer or workstation, (101) is a keyboard, (102) is a mouse, (103) is a display, and (104) is an auxiliary storage device. . The auxiliary storage device (104) includes a hard disk device, a tape, an FD (flexible disk), an MO (magneto-optical disk), a PD (phase change optical disk), a CD (compact disk), a DVD (digital versatile disk). ) Etc., removable media such as USB (Universal Serial Bus) memory, memory cards, etc. can also be used.

  The auxiliary storage device 104 includes a program 105 for analyzing the vibration characteristics of the structure, shape data 106, material data 107 such as an elastic coefficient, Poisson's ratio, density, and constraint conditions such as a constraint node number and a constraint direction. In addition, boundary condition data 108 of load conditions such as the position, magnitude, and direction of the excitation force is stored.

  A computer 100 such as a computer or a workstation includes data reading means 110 that can read a program 105, shape data 106, material data 107, boundary condition data 108, and the like from the auxiliary storage device 104. Further, it comprises an eigenvalue analysis means 112, a mode separation index analysis means 113, a response measurement point determination means 114, and an output means 111. Each of these means is implemented as a module such as a subroutine of a program stored in a storage means such as a main storage device of the computer 100. Similarly, data handled by these means is volatile or nonvolatile in the storage means. Remembered.

  The shape data 106 can be created by a general-purpose structural analysis preprocessor such as UNV format of “I-DEAS (registered trademark)” manufactured by UG Corporation, and is expressed by shell elements, solid elements, and the like. Of course, the format of the shape data 106 is not limited as long as the format of the file storing the model data is data in which nodes, elements, element properties, material properties, and the like are described.

  FIG. 2 is a flowchart showing an example of an implementation procedure in the present embodiment.

  Hereinafter, an embodiment of the present invention will be described with reference to FIG. The embodiment of the present invention relates to the eigenvalue analysis step 210 for obtaining the natural frequency and mode shape in a predetermined frequency range by eigenvalue analysis for the numerical analysis model of the structure, and the mode shape calculated in the eigenvalue analysis step. A mode separation index analysis step 220 for obtaining an autocorrelation coefficient between the modes and analyzing a mode separation index indicating the magnitude of the influence on the autocorrelation coefficient at each node, and a mode calculated in the mode separation index analysis step This is roughly divided into a response measurement point determination step 230 for determining a response measurement point from the separation index. Here, the structure is represented as a numerical analysis model composed of n nodes.

  First, the eigenvalue analysis step 210 will be described.

  In the numerical analysis model capturing means 211, the shape data of the structure divided into finite elements such as shell elements and solid elements, material data such as elastic modulus, Poisson's ratio, density, excitation force, excitation position, fixed position The boundary condition data such as is input to the auxiliary storage device of the computer. In the case of a plate-like structure whose thickness is sufficiently smaller than the typical dimensions of the structure, such as an injection molded product, a shell element is often used as a finite element.

The eigenvalue analysis means 212 analyzes vibration characteristics such as the natural frequency and mode shape of the structure using commercially available vibration analysis software such as “MSC NASTRAN (registered trademark)” manufactured by MSC Software Corporation. In this description, it is assumed that the mode shape is represented by a mode shape vector, and the mode shape vector of the m-th order mode is {φ _m }.

  Next, the mode separation index analysis step 220 will be described. In the present embodiment, a MAC value is used as a correlation coefficient. In the conventional method, there is no mode separation index analysis process. First, the response measurement point / excitation point is determined on a trial and error basis based on knowledge, etc., and the MAC value between different modes exceeds the criterion. It was determined whether to change or delete the response measurement point, and at which position the response measurement point should be added. In particular, when the shape of the structure is complex, it is difficult to judge, and if the response measurement points cannot be set appropriately, the mode shape may not be correctly grasped, and there is a possibility that erroneous vibration countermeasures may be taken. It was. However, in the present invention, by introducing this mode separation index analysis step, quantitative response measurement points can be determined in the experimental modal analysis for measuring the vibration characteristics of the structure.

The all-node autocorrelation matrix calculating means 221 first picks up nodes for analyzing the mode separation index in the numerical analysis model. A mode shape vector {φ ′ _m } is created for all nodes picked up in the m-th order mode mode shape calculated in the eigenvalue analysis step 210. Further, the MAC value (correlation coefficient) between the modes is obtained for the mode shape for all the nodes picked up in the mode calculated in the eigenvalue analysis step. As an example, the MAC values (correlation coefficients) of the A-th order mode and the B-th order mode are shown in the following equations.

MAC values are calculated for all combinations of modes targeting this, and an autocorrelation matrix [MAC _all ] is created in which the MAC values (correlation coefficients) between the modes are summarized. The autocorrelation matrix [MAC _all ] is shown in the following equation.

Here, MAC ₁₂ of the autocorrelation matrix [MAC _all ] indicates the MAC values (correlation coefficients) of the primary mode and the secondary mode. In this case, all the modes calculated in the eigenvalue analysis step 210 may be used as the target of the mode for calculating the autocorrelation coefficient, or only a part of the modes may be used. For example, when the natural frequency and the mode shape from the first mode to the sixth mode are calculated in the eigenvalue analysis step 210, the autocorrelation coefficient is calculated for the combination of the first mode to the fifth mode. 25 autocorrelation coefficients are calculated. These can be expressed as a 5 × 5 autocorrelation matrix as shown in FIG. In matrix expression, it is expressed as follows. (In the matrix, the order of the mode is represented by 1, 2, and 3 in the order from the bottom to the top in FIG. But shows the same thing.)

  Moreover, it is good also as a mode shape vector of only a one-dimensional displacement or a two-dimensional displacement among the three-dimensional displacements of a mode shape.

  In addition, since the autocorrelation matrix has symmetry and the value between modes of the same order is always 1, only non-diagonal components may be calculated.

Each node autocorrelation matrix calculation means 222 creates an _m-th mode mode shape vector {φ _m ⁽ⁱ⁾ } for the nodes excluding the node i from all nodes targeted by the all-node autocorrelation function matrix calculation means 210. To do. Next, the MAC value (correlation coefficient) between the respective modes is obtained in the same manner as the all-node autocorrelation function matrix calculating unit 221. The MAC value is calculated for all the combinations of modes targeted by the all-node autocorrelation matrix calculating means 221 and the MAC values (correlation coefficients) between the modes are summarized. [MAC _not ⁽ⁱ⁾ ] Create For example, for the mode shape of the example of the all-node autocorrelation matrix calculating means, if the autocorrelation matrix for all the nodes other than the node i is calculated using this means, a 5 × 5 autocorrelation matrix is obtained as shown in FIG. Can be represented. In matrix expression, it is expressed as follows.

  Further, since the autocorrelation matrix is symmetric and the value between modes of the same order is always 1, only the off-diagonal component may be calculated.

  When FIG. 4 and FIG. 5 or Expression (10) and Expression (11) are compared, the MAC value (correlation coefficient) between the modes of the autocorrelation matrix is changed by removing the node i. In particular, the MAC values (correlation coefficients) between the primary mode and the secondary mode, between the primary mode and the fifth mode, and between the secondary mode and the fourth mode are extremely increased and changed. The amount is large. Therefore, it can be seen that the displacement of the node i greatly affects (high sensitivity) between these modes.

The sensitivity matrix calculation means 223 calculates the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i by the following equation in order to numerically express the magnitude of the influence of the node i on the autocorrelation coefficient.

  The sensitivity matrix quantitatively represents the degree of influence of the node i on the autocorrelation matrix by subtracting the autocorrelation matrix for the nodes excluding the node i from all the nodes from the autocorrelation matrix for all the nodes. Matrix. For example, when the autocorrelation matrix of the example of the all-node autocorrelation matrix calculation unit and the sensitivity matrix of the autocorrelation matrix of the example of each node autocorrelation matrix calculation unit are calculated, a 5 × 5 autocorrelation matrix is obtained as shown in FIG. Can be expressed as In matrix expression, it is expressed as follows.

  Further, since the sensitivity matrix has symmetry and the value between the modes of the same order is always 0, only the non-diagonal component may be calculated.

  The mode separation index calculation means 224 converts the sensitivity matrix of the node i into a mode separation index that is a scalar value in order to evaluate the degree of influence of the node i on the entire autocorrelation matrix.

First, a method of calculating the mode separation index Sens _± ⁽ⁱ⁾ of the node i shown in claim 2 will be described.

Here, m in the equation (14) indicates the size of the sensitivity matrix. The mode separation index in this claim indicates the sum of all components of the sensitivity matrix. For example, the mode separation index Sens _± ⁽ⁱ⁾ of the sensitivity matrix shown in FIG. 6 is 2.68. This represents the magnitude of the effect of increasing or decreasing the MAC value (autocorrelation coefficient) by eliminating the node i. Further, since the sensitivity matrix has symmetry and the value between the modes of the same order is always 0, only the non-diagonal component may be calculated.

First, a method for calculating the mode separation index Sens ₊ ⁽ⁱ⁾ of the node i shown in claim 3 will be described.

Here, m in Equation (15) indicates the size of the sensitivity matrix. The mode separation index in this claim indicates the sum of positive elements of the sensitivity matrix. For example, the mode separation index Sens ₊ ⁽ⁱ⁾ of the sensitivity matrix in the example of the sensitivity matrix calculation unit is 2.92. This represents the magnitude of the effect of increasing the MAC value (autocorrelation coefficient) by eliminating the node i. Further, since the sensitivity matrix has symmetry and the value between the modes of the same order is always 0, only the non-diagonal component may be calculated.

First, the mode separation index Sens node i indicated in Claim 4 _- describes the calculation method of ^(i).

Here, m in Equation (16) indicates the size of the sensitivity matrix. The mode separation index in this claim indicates the sum of the negative elements of the sensitivity matrix. For example, the sensitivity matrix calculation means example of the sensitivity matrix of the mode separation index Sens _- ⁽ⁱ⁾ becomes -0.24. This represents the magnitude of the effect of reducing the MAC value (autocorrelation coefficient) by eliminating the node i. Further, since the sensitivity matrix has symmetry and the value between the modes of the same order is always 0, only the non-diagonal component may be calculated.

  The target node confirmation unit 225 confirms whether or not the mode separation index is calculated for all the nodes picked up by the all node autocorrelation matrix calculation unit 221. If there is a node for which the mode separation index is not calculated, each node autocorrelation is determined. The matrix calculation means 222, the sensitivity matrix calculation means 223, and the mode separation index calculation means 224 are repeated until the mode separation index is calculated for all nodes picked up by the all nodes autocorrelation matrix calculation means 221.

Finally, the response measurement point determination step 230 will be described. Mode separation index analysis step 220 at the calculated total nodes for mode separation index Sens _±, Sens _+, Sens _- at least one distribution U manufactured by GS Corporation "I-DEAS (registered trademark)" generic structural analysis preprocessor such as Visualize by using contour display or contour display. The mode separation index may be displayed as a numerical value.

  Next, the position of the response measurement point is selected from the displayed mode separation index distribution.

Since the MAC value is used as the autocorrelation coefficient, the mode separation index Sens _± is increased when there are many combinations in which the MAC value approaches 1 in combination with other modes when the node i is not a response measurement point. When there are many combinations in which the MAC value approaches 0 in combination with other modes, the mode separation index Sens _± becomes small. Therefore, in the mode separation index Sens _± distribution, by selecting a place where the mode separation index Sens _± has a large value, the MAC value of the same natural vibration mode has the same shape, so it is always 1, and in combination with other modes The position of the response measurement point that tends to be a value close to 0 can be selected. In other words, in order to avoid that the mode shapes between the target modes are apparently indistinguishable, it is better to set a place where the mode separation index Sens _± has a large value as a response measurement point. On the other hand, it is better not to use a response measurement point for small values (negative values). For example, the number of response measurement points that are absolutely necessary differs depending on the frequency range to be measured and the number of modes. However, when the mode separation index Sens _± is visualized by a contour display, the mode separation index Sens _± contour distribution becomes maximum. It is also possible to preferentially select existing vertices as response measurement points and determine the positions of the required number of response measurement points instead of the response measurement points where the values are negative.

Further, when the node i is not used as a response measurement point, the mode separation index Sens ₊ becomes large when there are many combinations whose MAC value approaches 1 in combination with other modes, and the MAC value becomes 1 in combination with other modes. The mode separation index Sens ₊ becomes small when there are few combinations approaching. Therefore, in the mode separation index Sens ₊ distribution, by selecting a place where the mode separation index Sens ₊ has a large value, the MAC value of the same natural vibration mode is always the same shape, and in combination with other modes. The position of the response measurement point that tends to be a value close to 0 can be selected. In other words, in order to avoid that the mode shapes between the target modes are apparently indistinguishable, it is better to set a place where the mode separation index Sens ₊ has a large value as a response measurement point. For example, although the number of response measurement points that are absolutely necessary differs depending on the frequency range to be measured and the number of modes, when the mode separation index Sens ₊ is visualized by a contour display or the like, the mode separation index Sens ₊ contour distribution becomes a maximum. The position of a required number of response measurement points may be determined by preferentially selecting a given vertex as a response measurement point.

Further, when the node i is not used as a response measurement point, the mode separation index Sens ₋ is small when there are many combinations whose MAC value approaches 0 in combination with other modes, and the MAC value becomes 0 in combination with other modes. The mode separation index Sens ₋ increases when there are few approaches to approach. Therefore, by selecting a mode separation index Sens ₋ distribution other than the one where the mode separation index Sens ₋ has a small value, the MAC values of the same natural vibration modes are always the same shape, so that the combination with other modes is always 1 Then, the position of the response measurement point that tends to be a value close to 0 can be selected. That is, in order to avoid that the mode shapes between target modes are apparently indistinguishable, it is better not to set the mode separation index Sens _{− to} have a small value as a response measurement point. For example, although the number of response measurement points that are absolutely necessary differs depending on the frequency range to be measured and the number of modes, when the mode separation index Sens ₋ is visualized by contour display or the like, the mode separation index Sens ₋ contour distribution becomes a minimum. The position of the required number of response measurement points may be determined by removing the vertices and selecting the response measurement points.

  Alternatively, the response measurement point may be determined by automatically executing the response measurement point determination step 230 by determining conditions such as the threshold of the mode separation index and the number of response measurement points.

[Example 1]
An embodiment of the present invention will be described using a flat plate model 700 shown in FIG.

FIG. 7 shows a model of a nylon flat plate having a width of 500 mm, a height of 300 mm, and a thickness of 11 mm to be analyzed as a shell element. The physical property data of the flat nylon is a Young's modulus of 3.13 GPa, a Poisson's ratio of 0.35, and a density of 1.13 × 10 ⁻⁶ kg / mm ³ .

  The natural frequency and mode shape of the flat plate model were obtained by performing eigenvalue analysis using general-purpose structural analysis software “Abacus (registered trademark)” manufactured by Dassault Systèmes.

  From the low-order modes, 14 modes excluding the rigid body mode are targeted, and mode shape vectors with only displacement in the Z direction are used. The MAC value was used for the autocorrelation coefficient.

Mode separation indices Sens _± and Sens ₊ are calculated for all elements, and are shown in FIGS. 8 and 9, respectively.

FIG. 8 shows that the mode separation index Sens _± is decreased from the center of the flat plate to the four corners. Therefore, when the vicinity of the four corners is included in the response measurement points, it can be determined that the MAC value due to the combination with other modes becomes high. Therefore, as shown in FIG. 10, response measurement points 1001 to 1021 are provided by dividing the four corners in a grid-like position divided into four equal parts in the horizontal direction and four equal parts in the height direction.

FIG. 9 shows that the mode separation index Sens ₊ around the flat plate is increased. Therefore, if the response measurement point does not include the periphery of the flat plate, it can be determined that the MAC value due to the combination with another mode is increased. Therefore, as shown in FIG. 11, response measurement points 1101 to 1120 are provided in seven equal parts in the lateral direction around the flat plate and in four equal parts in the height direction.
[Comparative Example 1]
An example in which the response measurement points are determined by the conventional method for the flat model 700 of the first embodiment will be described. It should be noted that, from the low-order mode, 14 modes excluding the rigid body mode were targeted, and the mode shape vector of only the Z-direction displacement was used. The MAC value was used for the autocorrelation coefficient. The MAC value for distinguishing the mode shape between the modes is set to 0.75 or less.

  First, as shown in FIG. 26, response measurement points 2601 to 2605 are set at typical locations on the flat plate, and then a MAC matrix as shown in FIG. 28 is created. From FIG. 28, there are many MAC values of 0.75 or more in combination with other modes such as the first mode and the fifth mode, the second mode and the seventh mode, and in the arrangement of the response measurement points as shown in FIG. It can be determined that there is no distinction between mode shapes.

  Next, the number of response measurement points is increased, response measurement points 2701 to 2709 are set as shown in FIG. 27, and a MAC matrix as shown in FIG. 29 is created. 29, there are many combinations in which the MAC value approaches 0 in combination with other modes than in FIG. 28, but there are many MAC values of 0.75 or more.

  Thus, when the MAC value between different modes takes a value that is equal to or higher than the criterion determined based on past knowledge, the position and number of response measurement points with reference to the natural vibration mode obtained by numerical analysis, etc. The MAC value was analyzed again and the above steps were repeated to determine an appropriate response measurement point.

It is a general result that the above steps are repeated and the response measurement points 1201 to 1225 are evenly arranged in a grid pattern on the entire flat plate as shown in FIG. FIG. 15 shows a MAC matrix in the case where response measurement points are arranged in a grid pattern as shown in FIG. In FIG. 15, it can be seen that there is no MAC value of 0.75 or more in combination with other modes, and this is a response measurement point that can distinguish the mode shape between the modes.
[Summary]
The MAC matrices in the arrangement of the response measurement points set in Example 1 and Comparative Example 1 are compared.

FIG. 13 shows the MAC matrix at the response measurement point selected from the distribution of the mode separation index Sens _± . FIG. 14 shows the MAC matrix at the response measurement point selected from the distribution of the mode separation index Sens ₊ . FIG. 15 shows a MAC matrix in the case where response measurement points are arranged in a grid pattern as shown in FIG.

The combination of modes in which the MAC value is 0.25 or more in the MAC matrix when the response measurement points are arranged in a grid pattern is the first mode and the ninth mode, the second mode and the thirteenth mode, There are three sets of the fourth mode and the fourteenth mode, and the combination of modes in which the MAC value is 0.60 or more is one set of the fourth mode and the fourteenth mode. (Here, since a response measurement point that does not have a MAC value of 0.75 or more in Comparative Example 1 is selected, in order to clearly show the effectiveness of the present invention, the reference value of the MAC value of Comparative Example 0. Comparison is made with a stricter standard value of 0.60 than 75.)
The combination of modes in which the MAC value is 0.25 or more in the MAC matrix at the response measurement point selected from the distribution of the mode separation index Sens _± is the first mode and the ninth mode, the fourth mode and the fourteenth mode. There are two sets of next modes, and a combination of modes in which the MAC value is 0.60 or more is one set of the fourth mode and the fourteenth mode. Therefore, the number of response measurement points can be reduced by four as compared to the case where response measurement points are simply arranged in a grid pattern, and response measurement points having a distribution equal to or higher than the MAC matrix distribution can be determined.

The combination of modes in which the MAC value is 0.25 or more in the MAC matrix at the response measurement point selected from the distribution of the mode separation index Sens ₊ is the first mode and the ninth mode, the second mode and the thirteenth mode. There are three combinations of the next mode, the fourth mode, and the fourteenth mode, and there is no mode combination in which the MAC value is 0.60 or more. Therefore, the number of response measurement points can be reduced by nine as compared with the case where response measurement points are simply arranged in a grid pattern, and response measurement points having a distribution equal to or higher than the MAC matrix distribution can be determined.

100: computer 101: keyboard 102: mouse 103: display 104: auxiliary storage device 105: program 106: shape data 107: material data 108: boundary condition data 110: data reading means 111: output means 112: eigenvalue analysis means 113: mode Separation index analysis means 114: Response measurement point determination means 210: Eigenvalue analysis step 211: Numerical analysis model capture means 212: Eigenvalue analysis means 220: Mode separation index analysis step 221: All-node autocorrelation matrix calculation means 222: Each node self Correlation matrix calculation means 223: Sensitivity matrix calculation means 224: Mode separation index calculation means 230: Response measurement point determination process 301: Prototype process 302: Response measurement point / excitation point determination process 303: Correlation analysis process 304: MAC threshold value determination process 305: Transmission The number measuring step 306: Modal Parameter Identification Step 307: Vibration Characteristics 400: MAC Matrix 500: autocorrelation matrices 600: Sensitivity Matrix 700: flat Model 1000: slab model 1001: response measurement points 1
1002: Response measurement point 2
1003: Response measurement point 3
1004: Response measurement point 4
1005: Response measurement point 5
1006: Response measurement point 6
1007: Response measurement point 7
1008: Response measurement point 8
1009: Response measurement point 9
1010: Response measurement point 10
1011: Response measurement point 11
1012: Response measurement point 12
1013: Response measurement point 13
1014: Response measurement point 14
1015: Response measurement point 15
1016: Response measurement point 16
1017: Response measurement point 17
1018: Response measurement point 18
1019: Response measurement point 19
1020: Response measurement point 20
1021: Response measurement point 21
1100: Flat plate model 1101: Response measurement point 1
1102: Response measurement point 2
1103: Response measurement point 3
1104: Response measurement point 4
1105: Response measurement point 5
1106: Response measurement point 6
1107: Response measurement point 7
1108: Response measurement point 8
1109: Response measurement point 9
1110: Response measurement point 10
1111: Response measurement point 11
1112: Response measurement point 12
1113: Response measurement point 13
1114: Response measurement point 14
1115: Response measurement point 15
1116: Response measurement point 16
1117: Response measurement point 17
1118: Response measurement point 18
1119: Response measurement point 19
1120: Response measurement point 20
1200: Flat plate model 1201: Response measurement point 1
1202: Response measurement point 2
1203: Response measurement point 3
1204: Response measurement point 4
1205: Response measurement point 5
1206: Response measurement point 6
1207: Response measurement point 7
1208: Response measurement point 8
1209: Response measurement point 9
1210: Response measurement point 10
1211: Response measurement point 11
1212: Response measurement point 12
1213: Response measurement point 13
1214: Response measurement point 14
1215: Response measurement point 15
1216: Response measurement point 16
1217: Response measurement point 17
1218: Response measurement point 18
1219: Response measurement point 19
1220: Response measurement point 20
1221: Response measurement point 21
1222: Response measurement point 22
1223: Response measurement point 23
1224: Response measurement point 24
1225: Response measurement point 25
1300: MAC matrix 1400: MAC matrix 1500: MAC matrix 1601: Beam structure 1602: Response measurement point 1
1603: Response measurement point 2
1604: Response measurement point 3
1605: Response measurement point 4
1606: Response measurement point 5
1701: Mode shape 1702 of first-order mode of beam structure 1601: Response measurement point 1
1703: Response measurement point 2
1704: Response measurement point 3
1705: Response measurement point 4
1706: Response measurement point 5
1801: Mode shape 1802 of the third mode of the beam structure 1601: Response measurement point 1
1803: Response measurement point 2
1804: Response measurement point 3
1805: Response measurement point 4
1806: Response measurement point 5
1900: Numerical analysis model 1911 of a beam structure: Node 1
1912: Node 2
1913: Node 3
1914: Node 4
1915: Node 5
1921: Element 1
1922: Element 2
1923: Element 3
1924: Element 4
2000: Mode shape 2011 of the first-order mode of the numerical analysis model 1900: Node 1
2012: Node 2
2013: Node 3
2014: Node 4
2015: Node 5
2021: Element 1
2022: Element 2
2023: Element 3
2024: Element 4
2100: Mode shape 2112 of the second-order mode of the numerical analysis model 1900: Node 1
2112: Node 2
2113: Node 3
2114: Node 4
2115: Node 5
2121: Element 1
2122: Element 2
2123: Element 3
2124: Element 4
2200: Mode shape 2211 of the third mode of the numerical analysis model 1900: Node 1
2212: Node 2
2213: Node 3
2214: Node 4
2215: Node 5
2221: Element 1
2222: Element 2
2223: Element 3
2224: Element 4
2300: Autocorrelation matrix [MAC _ALL ]
2400: Autocorrelation matrix [MAC _not ⁽⁴⁾ ]
2500: Sensitivity matrix [Sens ⁽⁴⁾ ]
2600: Flat plate model 2601: Response measurement point 1
2602: Response measurement point 2
2603: Response measurement point 3
2604: Response measurement point 4
2605: Response measurement point 5
2700: Flat plate model 2701: Response measurement point 1
2702: Response measurement point 2
2703: Response measurement point 3
2704: Response measurement point 4
2705: Response measurement point 5
2706: Response measurement point 6
2707: Response measurement point 7
2708: Response measurement point 8
2709: Response measurement point 92800: MAC matrix 2900: MAC matrix

Claims (7)

An eigenvalue analysis step for obtaining a mode shape in a predetermined frequency range by eigenvalue analysis for a numerical analysis model of a structure, and a response measurement point determination step for obtaining an autocorrelation coefficient between modes and determining a response measurement point A response measurement point determination method for experimental modal analysis having
A mode separation index analysis step of analyzing a mode separation index indicating the magnitude of the influence on the autocorrelation coefficient for each node;
A response measurement point determination method in experimental modal analysis, wherein in the response measurement point determination step, a response measurement point is determined from a mode separation index calculated in the mode separation index analysis step. In the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (1),

(D) Subsequently, the mode separation index Sens _± ⁽ⁱ⁾ of the node i is calculated by the equation (2),

(E) Find the mode separation index Sens _± for all n nodes.
The method of determining a response measurement point in an experimental modal analysis according to claim 1, further comprising a mode separation index analysis step. In the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (3),

(D) Subsequently, the mode separation index Sens ₊ ⁽ⁱ⁾ of the node i is calculated by the equation (4),

(E) Find the mode separation index Sens ₊ for all n nodes.
The method of determining a response measurement point in an experimental modal analysis according to claim 1, further comprising a mode separation index analysis step. In the mode separation index analysis step,
(A) An autocorrelation coefficient between modes is obtained for a mode shape of a mode calculated in the eigenvalue analysis step for a numerical analysis model of a structure composed of n nodes, and an autocorrelation matrix [MAC _all ]
(B) The autocorrelation coefficient between the modes calculated in the eigenvalue analysis step is calculated for the nodes excluding the node i (1 ≦ i ≦ n) from all nodes targeted in (a). _not ⁽ⁱ⁾ ],
(C) Next, the sensitivity matrix [Sens ⁽ⁱ⁾ ] of the node i is calculated by the equation (5),

(D) Subsequently, the mode separation index Sens node i _- calculates ⁽ⁱ⁾ in equation (6),

(E) Find the mode separation index Sens ₋ for all n nodes.
The method of determining a response measurement point in an experimental modal analysis according to claim 1, further comprising a mode separation index analysis step. An eigenvalue analysis step for obtaining a mode shape in a predetermined frequency range by eigenvalue analysis for a numerical analysis model of a structure, and a response measurement point determination step for obtaining an autocorrelation coefficient between modes and determining a response measurement point A numerical analysis device for determining a response measurement point of an experimental modal analysis having
A mode separation index analysis step of analyzing a mode separation index indicating the magnitude of the influence on the autocorrelation coefficient for each node;
A numerical analysis apparatus for determining a response measurement point in an experimental modal analysis, wherein the response measurement point is determined from the mode separation index calculated in the mode separation index analysis step in the response measurement point determination step. The program for making a computer perform the response measuring point determination method in the experimental modal analysis in any one of Claims 1-4. A computer-readable recording medium on which the program according to claim 6 is recorded.

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