JP2001350741A - Method and device for analyzing vibration and computer readable recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method, a device and a computer readable recording medium for the method of characteristics matrix identification by way of single site excitation experiment. SOLUTION: A program contains processing for finding coordinate data at the measuring point of an analysis target, processing for finding a frequency response function by exciting the analysis target on a single site, processing for finding a limit conditional expression between characteristics matrix components from the principle of mechanics that the mass matrix of an arbitrary elastic structure model can be transformed to a rigid mass matrix, the rigid mass matrix becomes a certain specified component and the analysis target does not generate distortion and stress in all areas in a rigid body moving state, processing for identifying mode characteristics by setting a resonance frequency inside an identification frequency band and processing for finding the mass matrix and the rigid matrix while using a nonattenuated peculiar vibration number and a peculiar mode, which are provided by identifying the mode characteristics, as a target value, and such a program is stored from an FD 101, which is a storage medium, to a storage device 129 and run by a central processing unit 128.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD The present invention relates to an experimental characteristic matrix identification method for directly obtaining a characteristic matrix from a vibration experiment result,
The present invention relates to a method and an apparatus for analyzing a vibration of a structure using a multipoint frequency response function obtained by applying a single excitation to the structure. Further, the present invention relates to a computer-readable recording medium on which a program for executing the method is recorded.

[0002]

2. Description of the Related Art When it is necessary to take some measure against vibrations of various machines and structures, first, vibration characteristics are grasped by some method, and a mathematical model expressing dynamic characteristics is determined. Determining the mathematical model is generally referred to as "identifying the system". The identification method includes a theoretical identification method and an experimental identification method.

In the theoretical identification method, a method of discriminating a structure using a finite element method (FEM) and determining a characteristic matrix is mainly used. On the other hand, in the experimental identification method, a modal characteristic identification method of performing a vibration experiment on a structure to be analyzed and obtaining a frequency response function (transfer function) to identify a modal characteristic is mainly used. Further, the modal characteristic identification method includes a one-degree-of-freedom method, a multipoint degree of freedom method, and a multipoint reference method. The one-degree-of-freedom method focuses on only one eigenmode included in one frequency response function and identifies it. The multi-degree-of-freedom method is a method for simultaneously identifying the mode characteristics of a plurality of eigenmodes while considering the influence of different eigenmodes. The multipoint reference method is a method of simultaneously referring to a plurality of frequency response functions to improve the accuracy of the entire term (eigenfrequency, mode damping ratio) and obtain a consistent mode characteristic.

[0004]

However, in the theoretical identification method, since discretization is performed, there is a problem that it is difficult to accurately model a complicated structure. There is also a problem that the attenuation matrix, which is one of the characteristic matrices, cannot be determined. On the other hand, the experimental identification method is an approximation method that takes out only the necessary modes from the low-order natural frequencies and reduces the degrees of freedom.Therefore, it is difficult to construct a characteristic matrix with all degrees of freedom. is there. Furthermore, in the experimental identification method, even though three of the six degrees of freedom can be made to depend on the other three degrees of freedom according to the laws of physics, since the three degrees of freedom are still independent, at least three different degrees of location are different.
There is a problem that it is necessary to perform a vibration experiment on a point.

Accordingly, an object of the present invention is to provide a vibration analysis method and apparatus capable of directly obtaining a characteristic matrix from a multipoint frequency response function obtained by applying a single excitation to a structure. I do. It is another object of the present invention to provide a computer-readable recording medium on which a program for executing this method is recorded.

[0006]

According to a first means of the present invention, in a vibration analyzing apparatus, a first processing means for obtaining coordinate data at a measurement point of an object to be analyzed and one location of the object to be analyzed are added. Second processing means for shaking to obtain a frequency response function at the measurement point, that the mass matrix of any elastic structure model can be converted to a rigid body mass matrix, that the rigid body mass matrix has a specific element configuration, and A third processing means for obtaining a constraint expression between characteristic matrix components from a dynamic principle that an object to be analyzed does not generate strain and stress in all regions in a rigid body motion state, and identification based on a frequency response function. Fourth processing means for setting a resonance frequency within a power frequency band and identifying a mode characteristic, and a constraint condition expression using a target value of an undampered natural frequency and an eigenmode obtained from the identification of the mode characteristic Constructed and a fifth processing means for determining the mass matrix and the stiffness matrix based.

According to a second means of the present invention, in the apparatus of the first means, a sixth processing means for obtaining an attenuation matrix from the measured frequency response function;
The apparatus further includes seventh processing means for optimizing a frequency response function determined from the stiffness matrix and the damping matrix so as to substantially match the measured frequency response function. Also,
According to the third means of the present invention, in the device of the first means or the second means, the mass matrix of any elastic structure model in the principle of dynamics can be converted into a rigid mass matrix by the following equation 1 And Expression 2.

Further, in the fourth means of the present invention, it will be described later that in the device of the first means or the second means, the rigid body mass matrix in the dynamic principle has a specific element configuration. It is expressed by Equation 3. According to a fifth aspect of the present invention, in the device of the fourth aspect, the correction coefficient α is 1.0
≤ correction coefficient α ≤ 1.3.

Further, according to a sixth aspect of the present invention, in the apparatus according to any one of the first to fifth aspects, the eigenmode and the non-attenuation set as the target value are added to the obtained mass matrix. Using the natural frequency, modify the mass matrix and the stiffness matrix according to Equations 8 and 9 described below.
It further comprises processing means. According to a seventh aspect of the present invention, in the apparatus of any one of the first to fifth means, the obtained mass matrix and stiffness matrix and the eigenmode set as the target value are used. Ninth processing means for obtaining a constraint condition expression between characteristic matrix components of Expression 10 described later, and tenth processing means for moving all the residual natural frequencies to frequencies higher than the frequency band to be identified. Be composed.

Further, according to an eighth aspect of the present invention, in the apparatus according to any one of the first to seventh means, the resonance frequency is the first resonance frequency. The present invention treats an object to be analyzed as an elastic structure, and generates an inter-element constraint condition of a characteristic matrix to be identified from the following three dynamic principles and the coordinates of a measurement point. This dynamic principle is
That the mass matrix of any elastic structure model can be converted to a rigid body mass matrix, that the rigid body mass matrix has a specific element configuration, and that in the case of rigid body motion, the object to be analyzed has strain and stress in all its regions. And does not occur.

The characteristic matrix is identified by using the first-order resonance mode of the frequency response function measured experimentally or a plurality of resonance modes from the first-order resonance mode to an appropriate order. As a result, all rigid body characteristics can be identified.

[0012]

Embodiments of the present invention will be described below with reference to the drawings.

(Structure of the Embodiment) The present embodiment is an analyzer according to the present invention. FIG. 1 is a block diagram of an analyzer according to the present embodiment. In FIG. 1, the analysis device is roughly divided into a measurement unit and an analysis unit. The measuring unit includes a hammer 111, a force converter 112, an accelerometer 113, amplifiers 114 and 115, and an external interface unit 121. The analysis unit is a flexible disk device (hereinafter, “FD device”).
Abbreviated. ) 122, a flexible disk control unit (hereinafter abbreviated as “FD control unit”) 123, an input device 124, an input control unit 125, an output device 126, an output control unit 127, a bus 130, a central processing unit 128, and a storage device. 129.

The impact hammer 111 applies vibration to the object 140 to be analyzed, and the magnitude of the applied force is converted into an electric signal by a force converter 112 provided on the impact hammer 111. This electric signal is output to the external interface 121 after being amplified by the amplifier 114.

The accelerometer 113 is used as a converter, measures the magnitude of acceleration generated on the object 140 by a piezo element, and converts it into an electric signal.
This electric signal is output to the external interface 121 after being amplified by the amplifier 115. The analyst decides the measurement points with an appropriate distribution and number so that the eigenmodes up to the order of interest can be expressed geometrically well enough,
The accelerometer 113 is attached to the determined location.

The external interface 121 samples the input electric signal, converts it into a digital signal, adjusts the signal level to a level suitable for the analysis unit, and outputs the signal to the bus 130. The FD device 122 is controlled by the FD control unit 123, and installs the program according to the present invention, which is recorded on a flexible disk (hereinafter abbreviated as “FD”) 101, which is one of the recording media, into the analysis device 100. Alternatively, the analysis result is recorded in the FD 101 or another FD.

The input device 124 is an input device such as a keyboard, a mouse, and a digitizer.
5. The analyst operates the input device 125 to input various data such as a command and a shape to be analyzed. The output device 126 is an output device such as a display such as a CRT or a printer, and is controlled by the output control unit 127. The output device 126 is the input device 124
The output includes various data and commands input to the program, menus for executing programs, analysis results, and the like.

The storage device 129 is a semiconductor memory, a hard disk, or the like, and stores programs according to the present invention, temporary data during execution of each program, analysis results, and the like.

The central processing unit 128 has an external interface 121, an FD control unit 123, an input control unit 125, an output control unit 127, and a storage unit 12 via a bus 130.
9 to give instructions to them,
9 and performs processing such as Fourier transform and an experimental characteristic matrix identification method in accordance with each program. (Correspondence relationship between the present invention and the present embodiment) In the invention according to claims 9 to 16, the first processing means corresponds to the input device 124, the input control unit 125, the central processing device 128, and the storage device 129. The second processing means includes a hammer 111, a force transducer 112, an accelerometer 113, and an amplifier 1
14, 115, the external interface 121, the central processing unit 128, and the storage device 129, and the third to tenth processing units correspond to the central processing device 128 and the storage device 129.

In the invention according to claims 17 to 24, the recording medium corresponds to the FD101. (Operation and Effect of the Embodiment) Next, the operation and effect of the embodiment will be described. FIG. 2 to FIG. 5 are flowcharts of the analyzer according to the present embodiment.

An analyst prepares an object 140 to be analyzed. The object 140 to be analyzed is suspended by an elastic body such as a rubber cord or a tire tube, so that a free state around is realized approximately. In addition, an elastic support state may be sufficient. 2 to 5, the analyst starts the analysis device from the input device 124. The central processing unit 128 reads and executes an experimental characteristic matrix identification method program stored in the storage device 129 (S1).

Next, the central processing unit 128 requests the analyst via the output screen 126 to input initial data such as the shape and dimensions of the object 140 to be analyzed. The analyst
Measurement point coordinate data of the object to be analyzed is input from the input device 124 (S2).

Next, the analyst hits the analysis object 140 at any one position (single point) among the positions where the accelerometer 113 is attached by the hitting hammer 111. The analyst uses the impact hammer 111 to analyze the analysis object 14.
The impact added to zero is measured by the force transducer 112,
The signal is taken into the central processing unit 128 via the amplifier 115 and the external interface unit 121. The vibration generated on the object 140 due to the impact is also measured by the accelerometer 113 and is transmitted via the amplifier 115 and the external interface unit 121 to the central processing unit 128.
It is taken in. In this way, a single-point excitation test is performed (S3).

Next, the central processing unit 128 converts the data into a frequency spectrum by performing a Fourier transform (for example, a fast Fourier transform). The central processing unit 128 calculates a power spectrum and a cross spectrum from an input (output of the force transducer 112) and an output (output of the accelerometer 113), and calculates a frequency response function and a coherence function.

Here, the coherence function (association degree function)
Is the inner product of the input and the output, and indicates the correlation between the input and the output. When the value is 0, the input and output are uncorrelated, and the correlation increases as the value approaches 1. Since the value of the coherence function indicates the reliability of the measurement data, the weight function of the weighted least squares method described later uses the value of the coherence function.

From the viewpoint of obtaining more reliable data, this single-point excitation test is repeated a plurality of times, each power spectrum and cross spectrum are averaged, and the average value is used as a frequency response function and a coherence function. It is preferable to use the power spectrum and the cross spectrum used for the calculation. In addition, these data are stored in the storage device 129 or the FD 101 in advance, and the analysis device displays the stored content on the output device 126 according to the activation, and the analyst selects the coordinate data and the single-point excitation Test data may be input.

The processing of S2 to S4 is the vibration measurement processing. Next, the definition of the structural connection between the measurement points
Make settings. That is, the analyst inputs from the input device 124 which measurement points are structurally connected to which measurement points between the measurement points, thereby modeling the physical connection state between the measurement points (S5).

Next, the central processing unit 128 satisfies the equations (1) and (3).
Then, a constraint condition expression between the components of the characteristic matrix composed of Expression 4 is calculated (S6). Thereby, the physical constraint condition of the analysis target 140 is determined, and the first physical modeling process is performed.

[Equation 19]

(Equation 20)

(Equation 21)

(Equation 22) Equations (1) to (4) are the basic equations of the method for identifying an experimental characteristic matrix of single-point excitation according to the present invention. These basic equations will be described. For convenience of explanation, the coordinate system is
Although an xyz rectangular coordinate system is used, analysis can be similarly performed in any coordinate system.

The degrees of freedom of the mass matrix and the stiffness matrix of the characteristic matrix to be identified are (measurement points × 3). Here, the identified mass matrix is represented as [M]. [Ψ] is a matrix of n rows and 6 columns as shown in Equation 2, and is obtained from the coordinate values of the measurement points in terms of x-direction unit translation displacement, y-direction unit translation displacement, z-direction unit direction translation displacement, and x-axis unit rotation. It is a matrix in which rigid displacement vectors of displacement, unit rotational displacement around y-axis, and unit rotational displacement around z-axis are arranged in order. This is because the rigid body degree of freedom is 6 considering the configuration of [Ψ] in the most general case,
It is a matrix composed of three translational displacement modes in directions orthogonal to each other and three rotational displacement modes for them.

Note that △ x, △ y and △ z are exactly multiplied by the direction cosine, but the direction cosine is approximated to “1”. G is a gravitational acceleration, and the numbers attached to 添 x, △ y, and △ z correspond to the numbers of the measurement points. [Ψ] ^T is the transposed matrix of [Ψ]. The transposed matrix is the superscript 1/4
It is displayed with a “T” at the corner.

This [Ψ] is called a rigid displacement mode matrix. On the other hand, [Mrigid] in Equation 1 becomes Equation 3 based on the above-described principle of dynamics. Here, w is the analysis object 14
The weight of 0, Ixx, Iyy, and Izz are moments of inertia around respective axes passing through the coordinate origin, and Iyx, Izx, and Iyz are products of inertia. A, B, and C are values resulting from the deviation between the point of the rigid body representation and the center of gravity. If the mass of the object 140 is m and the coordinates of the center of gravity are (xg, yg, zg), A = mx
g, B = myg, C = mzg. Α is a correction coefficient for increasing the identification accuracy. [Mrigid]
It is a symmetric matrix as shown in Equation 3.

If the component represented by the gravitational acceleration of [Ψ] is “1”, w is the mass m of the object 140 to be analyzed. The relationship shown in Expression 3 holds for the component of [Mrigid] even when the mass and the position of the center of gravity are undetermined. Thus, from the relationship of Equation 1, a system of linear equations is constructed for the unknown matrix components of the mass matrix [M], and unknown components equal to the number of equations can be made dependent on other components. It can be used as a physical constraint expression for the matrix [M].

Here, the mass (weight) of the object 140 to be analyzed
If a rigid characteristic value is given as known, a constraint condition expression between matrix components may be generated by substituting this value into Expression 3. If a known rigid body characteristic value is obtained as described above, there is an advantage that the known rigid body characteristic value does not need to be represented by another component.

Further, the stiffness matrix [K] to be identified is expressed by Equation 4 based on the above-described principle of dynamics. Therefore, a physical constraint expression between the components of the stiffness matrix [K] is derived from Expression 4. That is, some of the components of the stiffness matrix [K] can be set as independent variables, and other components can be made dependent on the components set as the independent variables.

As a result, the single-point excitation experimental characteristic matrix identification method converts the independent variables in the mass matrix [M] and the stiffness matrix [K] into the experimentally obtained eigenmodes and undamped natural frequencies. It is a kind of optimization problem that matches properly.
The eigenmode to be matched is called a target eigenmode, and the undamped eigenfrequency is called a target undamped eigenfrequency. Further, the mode damping ratio to be matched, which is used when optimizing the damping matrix, will be referred to as a target mode damping ratio.

Returning to FIGS. 2 to 5, this optimization will be described. First, the central processing unit 128 instructs input of a frequency band to be identified, and the
, The frequency band to be identified is input (S7). The identification frequency band ranges from a value lower than the primary resonance frequency to a certain required frequency. Next, the central processing unit 128 performs processing in accordance with a predetermined mode identification method, and uses the frequency response function of the identification frequency band including the first resonance frequency to use the inertial term parameter and the mode related to resonance within the identification frequency range. Identify properties and remainder parameter. The result obtained by the measurement is used as the frequency response function.

Thus, the central processing unit 128 sets the target eigenmode, the target undamped eigenfrequency and the target mode damping ratio (S8). Modal characteristic identification methods include:
Various generally known mode identification methods can be used. For example, a multipoint reference method (poly-reference method), a partial repetition method, a prory method (Prony's method), a circle fit method ( circle fit
method).

The processing in S7 and S8 is the processing for setting the target mode characteristics. Next, the central processing unit 128
For each of the mass matrix [M] and the stiffness matrix [K], a random number is applied to the independent unknown to create a matrix of initial values (S9). Next, the central processing unit 128 converts the mass matrix [M] into a positive definite value according to Expression 5 (S10). That is, regarding the mass matrix [M], the independent unknowns of the characteristic matrix are corrected so that all n eigenvalues become positive values. Further, the central processing unit 128 calculates the stiffness matrix [K] according to Equation 6.
(S11). That is, regarding the stiffness matrix [K], the eigenvalues of the number corresponding to the rigid body displacement degrees of freedom are already set to be necessarily zero from the physical constraint expression, but all other eigenvalues are positive. Modify the independent unknowns of the characteristic matrix to be the values.

(Equation 23)

(Equation 24) In S9, since the mass matrix [M] and the stiffness matrix [K] can simply be given initial values by random numbers, this S10
By S11 and S11, the condition that the mass matrix [M] must be physically a positive definite matrix and the condition that the stiffness matrix [K] must be a nonnegative definite matrix in which only the rigid body displacement degrees of freedom have eigenvalues zero exist.

The stiffness matrix [K] is a non-negative definite matrix under the peripheral free boundary condition, but is a positive definite matrix under the elastic constraint boundary condition. Next, the central processing unit 128 solves the general eigenvalue problem with respect to the unattenuated system represented by Expression 7, and obtains an unattenuated eigenfrequency and an eigenmode (S12, S12).
13, S14).

(Equation 25) Here, Ω is the undamped natural frequency, and {φ} is the vector of the natural mode. In this specification, a vector is indicated by ｛｝. More specifically, the central processing unit 1
First, the natural frequency Ω of the number existing within the identified frequency band from the lower order side shows a satisfactory match using Equation 7 so as to correspond to the target undamped natural frequency obtained in S8. The mass matrix [M] and the stiffness matrix [K] are corrected by the iterative sensitivity analysis up to (S12).

Next, the central processing unit 128 similarly performs a repetitive sensitivity analysis on the eigenmode {φ} using Equation 7 so as to correspond to the target eigenmode obtained in S8, and performs a mass matrix [ M] and the stiffness matrix [K] are corrected (S
13). Here, in the processing of S10 to S13,
Normalization processing is performed on the characteristic matrix to be processed. This is because solving the general eigenvalue problem requires some criterion. For example, a normalization process in which the maximum absolute value in the component of the characteristic matrix to be processed is “1” may be performed.

As the sensitivity analysis of this repetition, various generally known sensitivity analysis methods can be used. For example, the Newton method represented by the Newton method such as the steepest descent method and the conjugate gradient method can be used. A similar approach can be used. Next, the central processing unit 128 corrects the mass matrix [M] and the stiffness matrix [K] in S12 and S13, and determines whether or not these are positive definite matrices. In this case, the process of S15 is performed,
If the matrix is not a positive definite matrix, the process returns to S10 and the above-described S1
The processing from 0 to S13 is performed.

The processing from S9 to S14 is the first-stage identification processing. Although the mass matrix [M] and the stiffness matrix [K] are obtained by the first-stage identification process, the second matrix is further determined from the viewpoint of identifying them with higher accuracy.
It is preferable to perform a stage identification process. Next, the second-stage identification processing, S15 to S19, will be described.

The central processing unit 128 determines whether or not the mass matrix [M] and the stiffness matrix [K] obtained in the first-stage identification process match within an allowable range. , The processing of S20 is performed without performing the second-stage identification, and if they do not match, the processing of S16 is performed. In the determination in S15, a value indicating a correlation between the characteristic matrix obtained from the experimental result and the characteristic matrix obtained by calculation is calculated, and it is determined whether or not this value satisfies an allowable range. The tolerance determines the accuracy of the match. For example, the inner product is calculated, and it is determined whether the value is 0.9 or more.
For more accurate matching, a value closer to 1 than 0.9, for example, 0.95 may be set.

Next, the central processing unit 128 requests the analyst via the output screen 126 to input whether or not the primary physical modeling condition is observed. Central processing unit 128
Determines whether it is necessary to comply with the primary physical modeling conditions based on the input instruction, and performs the processing of S17 if not necessary, and performs the processing of S18 if necessary. Perform (S16).

Even if the allowable value in S15 is set to a value smaller than 0.9, it is possible to make the same with high accuracy by forcibly performing the processing in S16 and subsequent steps. In the processing of S17, the central processing unit 128 calculates, for each eigenmode in the eigenmode {φ}, the correlation between the eigenmode obtained from the experimental result and the eigenmode obtained by calculation. Then, the eigenmode outside the predetermined allowable range is replaced with the target eigenmode. Let the replaced eigenmode vector be {Φ},
The mass matrix [M] and the stiffness matrix [K] are corrected using Equations 8 and 9 (S17).

(Equation 26)

[Equation 27] Here, [E] is an identity matrix, and [Φ] ⁻¹ is [Φ]
Is the inverse of. The inverse matrix is as follows:
It is displayed with the corner "-1". On the other hand, in the processing of S18, the central processing unit 128 obtains a constraint condition expression between the characteristic matrix components based on the calculated rigidity mode and target eigenmode based on Expression 10 (S18).

[Equation 28] Here, the subsquare “s” attached to φ and Ω
Indicates the order of the mode. Next, the central processing unit 128
All the residual natural frequencies are moved to a frequency band higher than the identification frequency band (S19). This will be described more specifically below.

The approximate predicted value of the amount of change in the s-th natural frequency when a certain independent variable kij (i-th row and jth column component) in the stiffness matrix is slightly increased by △ kij is given by equation (11).

(Equation 29) Here, the coefficient of △ kij in Expression 11 is a sensitivity (first-order differentiation) obtained by differentiating the equation of motion shown in Expression 12 with respect to kij, and Expression 13.

[Equation 30]

(Equation 31) Similarly, the approximate predicted value of the amount of change in the s-th natural frequency when a certain independent variable mij in the mass matrix [M] is slightly changed is Expression 14.

(Equation 32) Here, the sensitivity of the natural frequency that is actually present in the identified frequency band (the natural frequency observed by the experimental characteristic matrix identification method) becomes zero because the constraint condition has already been created. Therefore, if the natural frequency whose sensitivity is not zero is
If it is obtained within the identified frequency band from the calculation using the mass matrix [M] and the stiffness matrix [K] obtained in the stage identification, the sensitivity is used to raise the frequency to a frequency higher than the identified frequency band by Newton's method. What is necessary is just to move those natural frequencies. This calculation operation can be performed in the same manner as the calculation operation for the target correspondence of the undamped natural frequency in the first-stage identification processing.

Next, the central processing unit 128 sets an initial value of the attenuation matrix [C] (S20). The initial value may be given as a random number or the like, but from the viewpoint of shortening the convergence time,
A constant multiple of the rigidity matrix may be used as the initial value of the damping matrix. Next, the central processing unit 128 solves the general eigenvalue problem with respect to the attenuation matrix [C] by the same processing as S12 and S13, and adjusts the sensitivity of the repetition so as to correspond to the target mode attenuation ratio obtained in S8. The target correspondence of the mode damping ratio is performed by analysis (S21).

Next, the central processing unit 128 determines whether or not the attenuation matrix [C] obtained in the processing in S21 matches within an allowable range. If they match, the processing in S24 is performed. If they do not match, the process of S23 is performed (S22). The determination in S22 is performed by calculating a value indicating the correlation between the attenuation matrix [C] obtained from the experimental result and that obtained by calculation, similarly to the processing in S15.

In the processing of S23, the central processing unit 12
8 modifies the attenuation matrix [C] by using the equation (15) (S2
3).

[Equation 33] Here, ζ is a mode attenuation ratio. This S20 to S
The process of 23 is the process of identifying the attenuation matrix.

As described above, the natural frequency and the natural mode corresponding to the physically existing resonance mode (resonance mode as an experimental result) set as the target value in the identification frequency band are expressed, and the mass matrix [M] and A set of a stiffness matrix [K] and a damping matrix [C] is derived. Next, the central processing unit 128 multiplies the characteristic matrix by a constant ε so that the amplitude of the frequency response function h (ω) best matches the experimental result H (ω) according to Expression 16 (S24).

(Equation 34) Here, j is an imaginary unit. Next, the central processing unit 12
In Equation 8, optimization is performed using the degree of coincidence of the frequency response function h (ω) as an objective function in order to further increase the degree of coincidence of the frequency response function h (ω) according to Equation 17 (S25). This optimization is based on the theory of the maximum likelihood estimation method in statistics. In an identified frequency band, a frequency obtained from a set of an experimental frequency response function H (ω), which is a single-point excitation test result, and a determined characteristic matrix is obtained. The weighted least square method is used with the goal of maximizing the likelihood calculated by the response function h (ω).

(Equation 35) Here, [B] is a weight function of the weighted least squares method. * Represents conjugate transposition. S24 and S2
The process of No. 5 is a third stage identification process. Next, the central processing unit 128 displays the mass matrix [M], the stiffness matrix [K], the damping matrix [C], the frequency response function h (ω), and the like on the output device 126, and further stores these results in the storage device 129.
Or in an external recording medium such as FD101 (2
6) End the vibration analysis program based on the experimental characteristic matrix identification method (S27).

In the present embodiment, the non-stationary wave is applied by the impact hammer 111, but the present invention is not limited to this. A hydraulic or piezoelectric vibrator, a non-contact vibrator using sound pressure or a magnetic field, or the like can be used. In addition, not only non-stationary waves but also various excitation waveforms such as standing waves and periodic waves can be used. These are determined by the weight, size, magnitude of attenuation, density of eigenmodes, and the like in the analysis target 140.

In this embodiment, the case where the transducer is an accelerometer has been described, but the present invention is not limited to this. A non-contact displacement meter using an eddy current or a laser beam, a laser Doppler velocimeter, a strain gauge, or the like can be used. Further, in the present embodiment, the case where the FD is used as the recording medium has been described, but the present invention is not limited to this. Memory chips (for example, ROM chips), compact disk memories (for example, CD-Rs)
OM, CD-R, CD-RW), magneto-optical disk (M
O), optical disk (PD), digital video disk memory (for example, DVD-ROM, DVD-RA
Various recording media such as M) can be used.

Next, specific experimental / calculated results will be described. FIG. 6 is a diagram showing the structure of the analysis object used in the experiment. FIG. 6A is a perspective view of an object to be analyzed, FIG. 6B is a cross-sectional view of a member, and FIG.
Are the coordinate values of the measurement points 1 to 10. The analysis object used in the experiment is composed of steel tubular members 1 to 5 having a square cross section of 2 mm and a side length of 30 mm as shown in FIG. 6B. As shown in the figure, a kanji radical is a "keigae" -shaped structure. The members 2, 3 having a length of 0.80 m have one end having a length of 1.
The other end of each of the members 1 is joined to the members 4 and 5 having a length of 0.40 m at the center thereof.

The accelerometer is provided in close contact with the object at the coordinate position shown in FIG. In the single-point excitation test, the object to be analyzed is suspended approximately
Measurement point 1 was vibrated in the x direction with a hammer. FIG. 7 is a diagram illustrating rigid body characteristics.

FIG. 8 is a diagram showing the natural frequency and the mode damping ratio. FIG. 9 is a diagram illustrating a frequency response function. FIG. 9A shows the phase of the frequency response function.
(B) shows accelerance. The dashed line indicates the experimental result, and the solid line indicates the identification result.

FIG. 10 is a diagram showing mode forms of the first to fifth modes. FIG. 11 is a diagram showing mode forms of the sixth to tenth modes. In this single-point excitation experimental characteristic matrix identification, identification was performed with α = 1 in [Mrigid] shown in Expression 3. The reference value is an approximate value obtained by manual calculation from the material constant of the steel member and the shape data of the object to be analyzed.

As can be seen from FIG. 9, the calculation results obtained by the single-point excitation experimental characteristic matrix identification method according to the present invention and the experimental results agree well. As a result of performing such a case experiment a plurality of times, it was found that the moment of inertia was sometimes identified as a value larger than the reference value. Therefore, optimization of the correction coefficient α in [Mrigid] shown in Expression 3 was examined.

FIG. 12 is a diagram showing the results of identification of the main moment of inertia. As can be seen from FIG. 12, a correction coefficient α for correcting the moment of inertia to increase the identification accuracy.
Preferably satisfies 1.0 ≦ α ≦ 1.3. Further, when statistical processing is performed on the case result, the correction coefficient α is preferably about 1.17. On the other hand, the resonance frequency used in setting the target mode characteristics was studied.

FIG. 13 shows an identification frequency band of 6 Hz to 5 Hz.
FIG. 9 is a diagram illustrating a mass matrix and rigid body characteristics when the first to third resonance frequencies of 0 Hz are to be identified. FIG. 14 is a diagram illustrating a mass matrix and rigid body characteristics when the first to third resonance frequencies in the identification frequency band of 6 Hz to 26 Hz are to be identified. FIG. 15 is a diagram illustrating a mass matrix and rigid body characteristics when a first-order resonance frequency in an identification frequency band of 6 Hz to 20 Hz is set as an identification target.

In this single-point excitation experimental characteristic matrix identification, the object to be analyzed shown in FIG. 6 was identified with α = 1 in [Mrigid] shown in Equation 3. 13 to 15
As can be seen from the above, a practically satisfactory result can be obtained for only the first order or the first to third order resonance frequencies to be identified. Since it is advantageous to use more resonance frequencies for identification, after all, the resonance frequency to be identified can be set to only the first order, or from the first order to an arbitrary order, and a practically satisfactory accuracy. Can be obtained.

[0061]

According to the present invention, by applying a single excitation to a structure, a characteristic matrix can be directly obtained from multiple frequency response functions. According to the present invention, since the characteristic matrix can be experimentally identified, a physical coordinate model of a structure to be directly subjected to vibration analysis can be expressed. Therefore, the present invention can easily analyze any dynamic behavior of the structure. And the present invention
A substructure synthesis method that divides a structure into a plurality of substructures, finds the dynamic characteristics of each, synthesizes them, and analyzes the entire structure
The present invention can be directly applied to an optimal design for changing a dynamic characteristic to a value desired by a designer, integration with a finite element method, and various simulations.

Of course, according to the present invention, a target analysis process can be performed using data obtained by multi-point excitation.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a block diagram of an analysis device according to an embodiment.

FIG. 2 is a flowchart illustrating a first example of the analysis apparatus according to the embodiment.

FIG. 3 is a flowchart illustrating an example of an analysis apparatus according to the embodiment;

FIG. 4 is a diagram illustrating a flowchart of the analysis device according to the present embodiment, that is, FIG.

FIG. 5 is a flowchart of the analysis device according to the embodiment, which illustrates a fourth example of the flowchart.

FIG. 6 is a diagram showing a structure of an analysis object used in an experiment.

FIG. 7 is a diagram showing rigid body characteristics.

FIG. 8 is a diagram showing a natural frequency and a mode damping ratio.

FIG. 9 is a diagram showing a frequency response function.

FIG. 10 is a diagram showing mode shapes of a first-order mode to a fifth-order mode.

FIG. 11 is a diagram showing mode forms of a first-order mode to a fifth-order mode.

FIG. 12 is a diagram showing a result of identification of a main moment of inertia.

FIG. 13 shows a first example of an identification frequency band of 6 Hz to 50 Hz.
FIG. 9 is a diagram illustrating a mass matrix and rigid body characteristics when the second to third resonance frequencies are to be identified.

FIG. 14 shows a first identification frequency band of 6 Hz to 26 Hz.
FIG. 9 is a diagram illustrating a mass matrix and rigid body characteristics when the second to third resonance frequencies are to be identified.

FIG. 15 shows a first example of an identification frequency band of 6 Hz to 20 Hz.
It is a figure which shows the mass matrix and rigid body characteristics when the next resonance frequency is made into an identification object.

[Explanation of symbols]

 111 Impact hammer 112 Force transducer 113 Accelerometer 121 External interface 101 Flexible disk 122 FD device 128 Central processing unit 129 Storage device

Claims (24)

[Claims] 1. A process for obtaining coordinate data at a measurement point of an object to be analyzed, a process for exciting a location of the object to be analyzed to obtain a frequency response function at the measurement point, and an arbitrary elastic structure model That the mass matrix can be converted into a rigid body mass matrix, that the rigid body mass matrix has a specific element configuration, and that the object to be analyzed does not generate strain and stress in all regions thereof in a rigid body motion state, A process of obtaining a constraint condition expression between characteristic matrix components based on the dynamic principle, a process of setting a resonance frequency within a frequency band to be identified based on the frequency response function, and a process of identifying a mode characteristic, and a process of identifying the mode characteristic. And obtaining a mass matrix and a stiffness matrix based on the constraint equation using the undamped natural frequency and eigenmode obtained from the target values as target values. The method of vibration analysis. 2. A process for obtaining a damping matrix from the measured frequency response function, and converting the obtained frequency response function determined from the mass matrix, the stiffness matrix and the damping matrix into the measured frequency response function. The method for vibration analysis according to claim 1, further comprising a process of optimizing the vibration analysis so as to substantially match. 3. The fact that the mass matrix of any elastic structure model in the dynamic principle can be converted to a rigid body mass matrix is as follows: (Equation 2) Where [M] is the mass matrix and [Mrigid]
Is a rigid mass matrix, [Ψ] is a matrix composed of translational displacement modes in directions orthogonal to each other and rotational displacement modes for them, △ x, △ y, and △ z are translational displacements in the x direction and units in the y direction, respectively. The translational displacement, the translational displacement in the z-direction unit direction, and g is a gravitational acceleration.
Alternatively, the vibration analysis method according to claim 2. 4. The fact that the rigid body mass matrix in the dynamic principle has a specific element configuration is given by Where w is the weight of the object to be analyzed, Ixx, I
yy and Izz are the moments of inertia around each axis passing through the coordinate origin, Iyx, Izx and Iyz are the products of inertia, A, B and C are the mass of the object to be analyzed as m and the barycentric coordinates are (xg, yg and zg). 3. The method according to claim 1, wherein A = mxg, B = myg, C = mzg, and α are correction coefficients for increasing identification accuracy. 5. The method according to claim 4, wherein the correction coefficient α satisfies 1.0 ≦ correction coefficient α ≦ 1.3. 6. Using the obtained eigenmode and undampered eigenfrequency as the target value in the obtained mass matrix, (Equation 5) The method according to any one of claims 1 to 5, further comprising a step of correcting the mass matrix and the stiffness matrix by: 7. Using the obtained mass matrix and stiffness matrix and the eigenmode set as the target value, 6. The method according to claim 1, further comprising: a process of obtaining a constraint condition expression between the characteristic matrix components of (1) and (2); and a process of moving all residual natural frequencies to a frequency higher than the frequency band to be identified. The method for vibration analysis according to any one of the preceding claims. 8. The method according to claim 1, wherein the resonance frequency is a first resonance frequency. 9. A first processing means for obtaining coordinate data at a measurement point of the object to be analyzed; a second processing means for exciting a location of the object to be analyzed to obtain a frequency response function at the measurement point; That the mass matrix of any elastic structure model can be converted to a rigid body mass matrix, that the rigid body mass matrix has a specific element configuration, and that in the case of rigid body motion, the object to be analyzed has strain and stress in all its regions. And a third processing means for obtaining a constraint condition expression between characteristic matrix components based on the dynamic principle of not generating a resonance frequency within a frequency band to be identified based on the frequency response function, and identifying a mode characteristic. And a mass matrix and a stiffness matrix are determined based on the constraint equation using the undamped natural frequency and eigenmode obtained from the identification of the mode characteristics as target values. That apparatus for the vibration analysis, characterized in that it comprises a fifth processing means. 10. A sixth processing means for obtaining a damping matrix from the measured frequency response function, and a frequency for which a frequency response function determined from the obtained mass matrix, the stiffness matrix and the damping matrix is measured. The vibration analysis apparatus according to claim 9, further comprising: a seventh processing unit that optimizes the response analysis so as to substantially match the response function. 11. The fact that the mass matrix of any elastic structure model in the dynamic principle can be converted into a rigid mass matrix is as follows: (Equation 8) Where [M] is the mass matrix and [Mrigid]
Is a rigid mass matrix, [Ψ] is a matrix composed of translational displacement modes in directions orthogonal to each other and rotational displacement modes for them, △ x, △ y, and △ z are translational displacements in the x direction and units in the y direction, respectively. 10. The translational displacement, the translational displacement in the z-direction unit direction, and g is a gravitational acceleration.
Alternatively, the vibration analysis apparatus according to claim 10. 12. The fact that the rigid body mass matrix in the dynamic principle has a specific element configuration is expressed by the following equation. Where w is the weight of the object to be analyzed, Ixx, I
yy and Izz are the moments of inertia around each axis passing through the coordinate origin, Iyx, Izx and Iyz are the products of inertia, A, B and C are the mass of the object to be analyzed as m and the barycentric coordinates are (xg, yg and zg). 11. The vibration analysis apparatus according to claim 9, wherein A = mxg, B = myg, C = mzg, and α are correction coefficients for increasing identification accuracy. 13. The apparatus according to claim 12, wherein the correction coefficient α satisfies 1.0 ≦ correction coefficient α ≦ 1.3. 14. Using the obtained eigenmode and undampered eigenfrequency as the target value in the obtained mass matrix, [Equation 11] The vibration analysis apparatus according to any one of claims 9 to 13, further comprising an eighth processing unit that corrects the mass matrix and the stiffness matrix according to: 15. Using the obtained mass matrix and the stiffness matrix and the eigenmode set as the target value, 9. A ninth processing means for obtaining a constraint expression between the characteristic matrix components of the following, and a tenth processing means for moving all the residual natural frequencies to a frequency higher than the frequency band to be identified. An apparatus for vibration analysis according to any one of claims 9 to 13. 16. The vibration analysis apparatus according to claim 9, wherein the resonance frequency is a first resonance frequency. 17. A process for obtaining coordinate data at a measurement point on an object to be analyzed, a process for exciting a location of the object to be analyzed to obtain a frequency response function at the measurement point, and an arbitrary elastic structure model. That the mass matrix can be converted into a rigid body mass matrix, that the rigid body mass matrix has a specific element configuration, and that the object to be analyzed does not generate strain and stress in all regions thereof in a rigid body motion state, A process of obtaining a constraint condition expression between characteristic matrix components based on the dynamic principle, a process of setting a resonance frequency within a frequency band to be identified based on the frequency response function, and a process of identifying a mode characteristic, and a process of identifying the mode characteristic. A process of obtaining a mass matrix and a stiffness matrix based on the constraint equation using the undamped natural frequency and eigenmode obtained as the target values. A computer-readable recording medium in order to execute that program on a computer. 18. A process for obtaining a damping matrix from the measured frequency response function, and converting the obtained frequency response function determined from the mass matrix, the stiffness matrix and the damping matrix into the measured frequency response function. 18. The computer-readable recording medium according to claim 17, further comprising a process of optimizing the recording medium so as to be substantially suitable. 19. The mass matrix of any elastic structure model in the dynamic principle can be converted into a rigid mass matrix by: [Equation 14] Where [M] is the mass matrix and [Mrigid]
Is a rigid mass matrix, [Ψ] is a matrix composed of translational displacement modes in directions orthogonal to each other and rotational displacement modes for them, △ x, △ y, and △ z are translational displacements in the x direction and units in the y direction, respectively. The translational displacement, the translational displacement in the z-direction unit direction, and g is a gravitational acceleration.
A computer-readable recording medium according to claim 7 or claim 18. 20. The fact that the rigid body mass matrix in the dynamic principle has a specific element configuration is expressed by the following equation. Where w is the weight of the object to be analyzed, Ixx, I
yy and Izz are the moments of inertia around each axis passing through the coordinate origin, Iyx, Izx and Iyz are the products of inertia, A, B and C are the mass of the object to be analyzed as m and the barycentric coordinates are (xg, yg and zg). 19. The computer-readable recording medium according to claim 17, wherein A = mxg, B = myg, C = mzg, and .alpha. Are correction coefficients for increasing identification accuracy. 21. The computer-readable recording medium according to claim 20, wherein the correction coefficient α satisfies 1.0 ≦ correction coefficient α ≦ 1.3. 22. By using the eigenmode and the undampered eigenfrequency set as the target value in the obtained mass matrix, [Equation 17] 17. The method according to claim 17, further comprising the step of correcting the mass matrix and the stiffness matrix by using
2. The computer-readable recording medium according to claim 1. 23. Using the obtained mass matrix and the stiffness matrix and the eigenmode set as the target value, 22. The method according to claim 17, further comprising: a process of obtaining a constraint condition expression between the characteristic matrix components of: and a process of moving all residual natural frequencies to a frequency higher than the frequency band to be identified. The computer-readable recording medium according to claim 1. 24. The computer-readable recording medium according to claim 17, wherein the resonance frequency is a first resonance frequency.