JP2003207390A - Method and device for detecting resonance mode of solid, and method and device for measuring elastic constant of solid - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enable to derive resonance mode for resonance frequency. <P>SOLUTION: A solid sample 12 is applied an ultrasonic wave from a transmitter 34b and is vibrated at the resonance frequency. The sample 12 is scanned along its surface with a laser interferometer 48 and a vibration speed of the surface of the sample 12 is derived. At an amplitude distribution detecting part 50, vibration amplitude is derived by dividing the vibration speed derived with the laser interferometer 48 by the resonance frequency, and the distribution of the vibration amplitude on the sample surface is derived. At a resonance mode calculation part 56, the resonance frequency is derived by using an assumed elastic constant, and the distribution of the vibration amplitude on the sample surface for the resonance frequency is calculated. At a comparator part 58, the measured vibration amplitude distribution is compared with the calculated vibration amplitude distribution and the resonance mode for the resonance frequency vibrating the sample 12 is identified. At an elastic constant calculating part 20, the elastic constant with which the resonance frequency can be obtained is calculated based on the identified resonance mode. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for detecting a resonance mode of a solid, and more particularly to a resonance mode of a solid vibrating at a resonance frequency, and a solid elastic constant for obtaining a solid elastic constant based on the specified resonance mode. Resonant mode detection method and device, and elastic constant measurement method and device.

[0002]

2. Description of the Related Art For new materials, such as various metallic materials, amorphous materials, composite materials, piezoelectric materials, superconductors, etc., which are being rapidly developed, it is extremely important to grasp their mechanical properties for practical use. In particular, the elastic constant is a physical property value required as soon as a material is developed, and measurement for obtaining the elastic constant is essential.

The elastic constants have been measured by a resonance method in which a rod-shaped sample is resonated for a long time and the elastic constant is determined from its resonance frequency (natural frequency), or an ultrasonic wave is propagated in the sample and its reflected wave is reflected. There is a pulse echo method in which the acoustic velocity is determined from the time until the reflected wave returns and the elastic constant is determined based on the acoustic velocity. However, these methods cause a problem when the elastic symmetry (crystal shape symmetry) of the solid is low.

For example, in the case of an orthorhombic crystal, there are nine independent elastic constants. To determine all of these, the rod resonance method requires nine samples with different orientations, and the pulse echo method requires at least four samples. That is, the rod resonance method or the pulse echo method can be applied only to a material having a large original size (a sample of at least several centimeters square is required). Therefore, for thin films, wires, thin plates, single crystals that can be made only in a small size, it is difficult to cut out samples with different orientations, and even if it can be measured, it is only a specific elastic constant. In general, the elastic constant of a material having such a shape is more anisotropic, and the number of independent elastic constants increases.

In recent years, in order to solve this problem, an ultrasonic resonance method (Resonance Ultrasound S) is used.
has been devised. The principle is as follows. The resonance frequency (natural frequency) of free vibration of a solid having a regular shape such as a sphere, a cylinder, or a rectangular parallelepiped is determined by dimensions, density, and all independent elastic constants. In fact, they can be used to calculate the resonant frequency. Then, the size and density of the sample can be easily measured.

Therefore, in the ultrasonic resonance method, the resonance frequency is measured by continuously changing the frequency of the ultrasonic wave applied to the sample. Further, the resonance frequency is calculated using an elastic constant that is appropriately assumed, and this is compared with the measured resonance frequency. Then, the value of the elastic constant that is assumed to match each other is changed, and the elastic constant when the matching is achieved with sufficient accuracy is determined as the true value. That is, inverse calculation is performed. This allows, in principle, to determine all independent elastic constants from one small sample.

[0007]

However, the ultrasonic resonance method described above has serious drawbacks. In order to determine an accurate elastic constant by the above inverse calculation, when comparing the calculated resonance frequency with the measured resonance frequency, the same resonance mode (vibration mode and resonance order) must be performed. That is, for example, in the case of an orthorhombic (including isotropic, cubic, hexagonal, and tetragonal) rectangular parallelepiped,
Free vibration is divided into eight groups of vibration mode due to the symmetry of the displacement, A _g mode called respiratory vibration, torsional vibration in which A _u mode, x along the three sides of a rectangular parallelepiped orthogonal, y, z-axis It is classified into B _3g mode, B _2g mode and B _1g mode which are shear vibrations around it, and B _3u mode, B _2u mode and B _1u mode which are bending vibrations around x, y and z axes.

However, no information on the vibration mode can be obtained from the resonance frequency measured by the conventional ultrasonic resonance method. Therefore, in the ultrasonic resonance method, if the elastic constant close to the true value is not adopted as the initial value in advance, the calculated resonance frequency and the measured resonance frequency will be erroneously associated, and as a result, Elastic constants that have no physical meaning are obtained as true values. In particular, in a high frequency region, since higher-order resonance frequencies of each vibration mode appear close to each other, it is difficult to associate the vibration mode with the resonance frequency, and it is necessary to substantially obtain the true value of the elastic constant. I can't. Of course, for the analyst,
Since it is not known whether the vibration modes correspond to each other, the elastic constant obtained is believed to be the true value.

In order to overcome this problem, a method of controlling the generation position of the vibration source by electromagnetic force and limiting the vibration mode to be generated to a certain extent, or changing the shape of the sample little by little and specifying Methods such as finding a vibration mode that is sensitive to changes in the shape have been considered, but none of them have been fundamentally resolved.

The present invention has been made to solve the above-mentioned drawbacks of the prior art, and an object thereof is to be able to obtain the vibration mode which is the resonance mode of the obtained resonance frequency and the order of resonance. I am trying. Further, the present invention is
The purpose is to be able to accurately determine the elastic constant of a solid.

[0011]

[Means for Solving the Problems] Resonance frequency and resonance mode (the vibration mode and the order of resonance) for the above-mentioned vibration mode (in the case of the orthorhombic system, there are eight) for the above-mentioned rectangular parallelepiped, the surface on the surface of the rectangular parallelepiped The calculation method with the distribution of the vibration amplitude in the orthogonal direction (normal direction) has already been established. These are obtained by a method of approximating the displacement of a solid by a linear combination of Legendre functions to obtain the stationary point of Lagrangian. However, conventionally, it was considered that the distribution (vibration pattern) of the vibration amplitude on the surface of the solid due to the resonance frequency in a certain vibration mode depends on the elastic symmetry and elastic constant of the solid. Therefore, there has been no idea that the vibration pattern of the resonance frequency is obtained by detecting the vibration pattern of the solid surface and the elastic constant is calculated (back-calculated) using the obtained vibration mode and the resonance frequency. However, as a result of various analyzes and experiments, the inventors have found that there exists a vibration pattern that does not depend on the elastic symmetry and elastic constant of a solid. The present invention has been made based on such findings.

That is, the solid-state vibration mode detection method according to the present invention vibrates a solid having a predetermined shape at a resonance frequency, measures the distribution of vibration amplitude in the normal direction on the surface of the solid, and measures the size and density of the solid. Based on the assumed elastic constant, the resonance frequency for each vibration mode of the solid, and the distribution of the vibration amplitude in the normal direction on the surface of the solid at the resonance frequency are calculated, and the calculated vibration amplitude distribution And a distribution of the measured vibration amplitude are compared to obtain a resonance mode of a resonance frequency at which the solid is vibrated.

The solid-state resonance mode detecting apparatus according to the present invention for carrying out the solid-state resonance mode detecting method includes transmitting means for ultrasonically vibrating the solid while continuously changing the frequency, and Receiving means for detecting vibration, resonance detecting means for detecting the resonance frequency of the solid based on the detection signal of the receiving means, vibrating means for vibrating the solid at the detected resonance frequency, and the resonance frequency Surface vibration detecting means for detecting a displacement of the vibrated solid surface in the normal direction, and an amplitude distribution for detecting a distribution of vibration amplitude in the normal direction on the solid surface based on a detection signal of the surface vibration detecting means. A resonance frequency for each vibration mode of the solid, based on the given size, density, and elastic constant of the solid, and the resonance frequency. Of the vibration amplitude distribution in the normal direction on the surface of the solid by means of the resonance mode operation means, the distribution of the vibration amplitude obtained by the resonance mode operation means, and the vibration amplitude of the vibration solid obtained. And a resonance mode determining means for selecting a resonance mode from a resonance mode obtained by calculating a resonance mode of the resonance frequency in which the solid is vibrated.

Further, in the method for measuring the elastic constant of a solid according to the present invention, the vibration mode of the solid is obtained based on the resonance mode detected by the above-mentioned method for detecting the resonance mode of the solid. The elastic constant for obtaining the resonance frequency that vibrates the solid is calculated based on the dimension and the density.

Further, in the method for measuring the elastic constant of a solid according to the present invention, a step of ultrasonically vibrating a solid having a predetermined shape while continuously changing the frequency to obtain a plurality of resonance frequencies of the solid, and the obtained resonance A step of detecting the resonance mode of the solid by the method for detecting a resonance mode of the solid according to claim 1 by vibrating the solid according to any one of the frequencies; Based on the dimensions and the density, a step of calculating an elastic constant for obtaining a resonance frequency by vibrating the solid, the calculated elastic constant, and the vibration and vibration of the solid based on the size and the density of the solid. Calculating the distribution of the vibration frequency in the normal direction on the surface of the solid corresponding to the resonance frequency for the mode and the resonance frequency for which the resonance mode is not detected; Resonance calculated by measuring the distribution of the vibration amplitude in the normal direction on the solid surface at each resonance frequency by vibrating each resonance frequency and comparing the calculated vibration amplitude distribution with each resonance frequency. Identifying from the mode, the step of obtaining the vibration mode based on the identified resonance mode, the obtained vibration mode, the size of the solid, based on the density, the resonance frequency corresponding to each vibration mode, And a step of calculating the obtained elastic constant.

A solid elastic constant measuring device according to the present invention for carrying out the above solid elastic constant measuring method is
The vibration mode of the solid is obtained based on the resonance mode of the solid detected by the resonance mode detection device of the solid described above, and the obtained vibration mode and the size and density of the solid are based on the vibration mode corresponding to the vibration mode. An elastic constant calculating means for calculating an elastic constant for obtaining a resonance frequency is provided.

[0017]

According to the present invention as described above, the resonance frequency of the solid in the vibration mode is obtained using the size and density of the solid and the assumed elastic constant, and the normal line on the surface of the solid by this resonance frequency is obtained. By calculating the distribution of the vibration amplitude in the direction and comparing the calculated distribution of the vibration amplitude with the distribution of the vibration amplitude measured by actually vibrating the solid at the resonance frequency, the resonance mode at the resonance frequency of the solid, that is, The vibration mode and the order of resonance can be specified. Therefore, it is possible to know which vibration mode the resonance frequency is due to, and it is possible to accurately calculate the elastic constant.

By calculating the resonance frequency and the distribution of vibration amplitude with the solid as an orthorhombic system, not only the independent elastic constants but also the elastic symmetry of the solid can be surely obtained. That is, the orthorhombic system has nine independent elastic constants, and by assuming these nine elastic constants, the elastic symmetry of a solid (symmetry of crystal shape) is unknown. Even in this case, the vibration mode about the resonance frequency can be specified with certainty, and the accurate elastic constant and elastic symmetry can be measured.

[0019]

BEST MODE FOR CARRYING OUT THE INVENTION Preferred embodiments of a solid resonance mode detecting method and apparatus, an elastic constant measuring method and an apparatus according to the present invention will be described in detail with reference to the accompanying drawings. FIG. 1 is a block diagram of a solid elastic constant measuring device according to an embodiment of the present invention. In FIG. 1, an elastic constant measuring device 10 includes an input unit 14, an elastic constant calculating unit (elastic constant calculating unit) 20, and a resonance mode detecting unit (resonance mode detecting device) 30. Input unit 14
Is composed of a keyboard, a mouse and the like (not shown), and the size and density of the sample 12, as well as the resonance frequency, vibration mode and elastic constant of the sample 12 can be input. Further, the elastic constant calculator 20 calculates the elastic constant of the solid sample 12 based on a formula given in advance, as described later.

The resonance mode detector 30 is a solid sample 12
Has a support portion 32 that supports the point. Further, the resonance mode detection unit 30 includes a transmission unit 34 that is a transmission unit and a vibration unit, and a receiver (reception unit) 36 that detects the vibration of the sample 12. The transmission unit 34 uses the sweep oscillator 3
4a and the transmitter 34b, the ultrasonic waves of the sample 12 can be applied to vibrate while continuously changing the frequency, and the sample 12 can be ultrasonicated at an arbitrary frequency. It can be vibrated. The frequency of oscillation of the sweep oscillator 34a is controlled by the control unit 40, and the oscillated frequency is given to the transmitter 34b as an electric signal. Also, the transmitter 34
In b, the signal output from the sweep oscillator 34a is converted into ultrasonic waves and applied to the sample 12, and the sample 12 is ultrasonically vibrated.

The receiver 36 includes a support 32 and an oscillator 3.
The sample 12 is supported together with 4b. Also, the receiver 3
Reference numeral 6 detects vibration of the sample 12 (ultrasonic waves propagating through the sample 12), converts it into an electric signal, and outputs it. And
On the output side of the receiver 36, a resonance frequency detecting section 42 which is a resonance detecting means is connected. This resonance frequency detector 4
2, the output signal of the sweep oscillator 34a of the transmitter 34 is input as a reference signal, and the resonance frequency of the sample 12 is detected from this reference signal and the output signal of the receiver 36.

The resonance mode detecting section 30 includes a laser interferometer 46 which is a surface vibration detecting means for detecting the vibration of the surface of the sample 12. The laser interferometer 46 is arranged above the sample 12, irradiates the surface (upper surface) of the sample 12 with the laser beam 52, and ultrasonically vibrates from the interference frequency between the emitted light and the reflected light. The fluctuation speed (vibration speed) of the sample surface is output. The laser interferometer 46 is attached to the driving device 48, and the driving device 48 drives the sample 1
2 is capable of scanning along the surface. The drive unit 48 is drive-controlled by the control unit 40.

On the output side of the laser interferometer 46, an amplitude distribution detecting section (amplitude distribution detecting means) 50 is provided. The amplitude distribution detection unit 50 calculates the vibration amplitude in the normal direction of the sample surface based on the vibration speed output from the laser interferometer 46, and uses the position signal input from the driving device 48, as will be described later. To obtain the distribution of vibration amplitude on the sample surface.

The resonance mode detecting section 30 has a resonance mode calculating section 56 and a comparison determining section 58. The resonance mode calculation unit 56 is configured to input the size and density of the sample 12, the vibration mode, the elastic constant, and the like from the input unit 14.
Then, the resonance mode calculation unit 56 uses the resonance frequency of the sample 12 and the resonance frequency of the sample 12 based on the equation given in advance and the dimensions, density, elastic constants, vibration modes, etc. of the sample 12 input from the input unit 54. Calculate the distribution (vibration pattern) of the vibration amplitude in the normal direction on the sample surface,
It outputs to the comparison determination unit 58 which is the resonance mode determination unit.

The input unit 14 is further connected to the elastic constant calculation unit 20, the control unit 40 of the resonance mode detection unit 30, and the amplitude distribution detection unit 50. In addition, the elastic constant calculator 20
The output side is connected to the resonance mode calculation unit 56 of the resonance mode detection unit 30, and the calculated elastic constant can be output to the resonance mode calculation unit 56.

The comparison / determination unit 58 is a resonance mode calculation unit 56.
Are connected, and the amplitude distribution calculation unit 60 is also connected. Then, the comparison / determination unit 58 calculates the vibration pattern on the surface of the sample 12 calculated by the resonance mode calculation unit 56 (calculation vibration pattern) and the vibration pattern detected from the sample 12 vibrated at the resonance frequency (measurement vibration pattern). ) And select a calculated vibration pattern that matches or is very similar to the measured vibration pattern.

The detection of the resonance mode and the measurement of the elastic constant by the elastic constant measuring device 10 of the embodiment having the above-mentioned configuration are performed as follows. The elasticity constant in this embodiment is measured by a method of approximating the displacement of the sample 12 by linear combination of Legendre functions to obtain the Lagrangian stationary point, as in the conventional case.

To obtain the resonance mode and elastic constant of a solid material, first, a rectangular parallelepiped sample 12 made of the material is prepared. Then, as shown in step 100 of FIG.
Measure the dimensions and density of sample 12. Next, assuming the elastic constant of the sample 12, the resonance frequency and the resonance mode (the vibration mode and the order of resonance) of the sample 12 and the vibration amplitude in the normal line direction on the surface of the sample 12 are assumed using the assumed elastic constant. Of the distribution (vibration pattern) is calculated (step 10
2). That is, the dimensions, the density, the vibration mode, and the assumed elastic constant of the sample 12 are input to the input unit 54 of the elastic constant measuring device 10 and given to the resonance mode operation unit 56 that constitutes the resonance mode detection unit 30.

In the case of an orthorhombic rectangular parallelepiped, the vibration mode is
A called respiratory oscillation_gMode, torsional vibration A_u
Mode, the x, y, and z axes along three orthogonal sides of a rectangular parallelepiped
Another shear vibration B_{3 g}Mode, B_{2 g}Mode, B_{1 g}
Modes and bending vibrations around the x, y and z axes
B_3uMode, B_2uMode, B_1uClassified into 8 modes
It FIG. 3 shows a part thereof. The figure (1) is A_gIn mode
Yes, (2) in the figure is A _uMode, B in the figure (3)_{3 g}Mo
Do, B in the figure (4)_3uIt is a mode.

The resonance mode calculator 56 first calculates the resonance frequency of the sample 12 in a given vibration mode by determining the stationary point of the Lagrangian function L defined by Equation 1.

[Equation 1] Where ρ is the density of the sample 12, ω is the resonance frequency of the sample 12, u _i and u _j are the displacements of the sample 12, C _IJ is the elastic constant (element of elastic modulus tensor), S _I and S _J are the sample Is the engineering strain within 12, and V is the volume of sample 12.

Further, the resonance mode calculation unit 56 calculates
The vibration pattern of the sample 12 (the distribution of the vibration amplitude in the normal direction on the surface of the sample 12) at the resonance frequency of the sample 12 obtained by is calculated. This vibration pattern is
Let x, y, z be the directions along the three orthogonal sides of the sample 12 (see FIG. 3), and let x → x ₁ , y → x ₂ , and z → x ₃ , then the x _i direction (i = 1, 2 3) the displacement u _i along
It is approximated by a linear combination of basis functions Ψ as in the following Expression 2.

[Equation 2] Here, k is the number of the basis function and a _k ⁽ⁱ⁾ is the displacement u _i
Is a coefficient relating to the k-th basis function for expressing

By using the product of the normalized Legendre function P _λ (λ = 1, m, n) of Equation 3 as the basis function Ψ, the sample 12 having a relatively small number of terms and high accuracy can be obtained.
An approximation of the vibration pattern on the surface of can be performed.

[Equation 3] However, in Equation 3, P _λ is a Legendre function of the λth order, and L _i is the length of the side of the rectangular parallelepiped sample 12 parallel to the x _i direction. The details of the calculation of this vibration amplitude distribution are
I. Ohno, J .; Phys. Earth, 1976,
24,335-379.

[0033] According to the study of the inventors, if a solid (sample) is a rectangular parallelepiped, A _g mode, A _u mode, B _{3 g} mode,
B _2g mode, B _1g mode, B _3u mode, B _2u mode, B
Among the resonances of 8 vibration modes of _1u mode, the vibration pattern in the direction (normal direction) orthogonal to the surface of the rectangular parallelepiped surface in the specific resonance mode depends on elastic symmetry (symmetry of crystal shape) and elastic constants. I found out not. That is, the specific vibration pattern (distribution of vibration amplitude) shows almost the same vibration pattern even when the elastic symmetry and the elastic constant are different. The vibration modes exhibiting a vibration pattern that does not depend on this elastic symmetry and elastic constant are _Ag- 1, _Ag- 3, _Au- 1, _Au- 3, _B3g-.
1, _B3g- 2, _B3g- 3, _B2g- 1, _B2g- 2, _B2g-
There are 13 ways of _B3u- 1, _B2u- 1, _B2u- 2, and _B1u- 1.
The numbers indicated by a dash (-) after the symbols indicating these vibration modes indicate the order of resonance.

Therefore, in the case of this embodiment, the resonance mode calculation unit 56 calculates and calculates the resonance frequencies of about 20 to 50 from the lower frequency side, and the normal line on the surface of the sample 12 for the above 13 resonance modes. The vibration pattern, which is the distribution of the vibration amplitude in the direction, is calculated.

On the other hand, the sample 12 has a resonance mode detecting section 30.
The resonance frequency is measured by (step 104).
That is, the control unit 40 of the resonance mode detection unit 30 continuously changes the oscillation frequency of the sweep oscillator 34a of the transmission unit 34. Then, in the transmitter 34, the transmitter 34b converts the oscillation frequency of the sweep oscillator 34a into ultrasonic waves, and applies the ultrasonic waves to the sample 12 to vibrate the ultrasonic waves. Then, the receiver 36 receives the ultrasonic wave propagated through the sample 12, converts it into an electric signal, and inputs it to the resonance frequency detection unit 42 as a vibration detection signal. The resonance frequency detector 42 detects the resonance frequency of the sample 12 with reference to the oscillation frequency output from the sweep oscillator 34a.

After the resonance frequency of the sample 12 is detected in this way, the sample 12 is vibrated at the resonance frequency in step 106, and the surface of the sample 12 is perpendicular to the plane (normal line). Direction) vibration amplitude is detected. That is, first, the control unit 40 via the input unit 14
A resonance frequency to the sweep oscillator 3 by the control unit 40.
The oscillation frequency of 4a is controlled to the detected resonance frequency of the sample 12, and the sample 12 is vibrated by the resonance frequency via the transmitter 34b. Further, the laser interferometer 46 is driven to irradiate the surface of the sample 12 with the laser beam 52,
The vibration velocity in the surface normal direction of is detected. Further, the control unit 40 controls the drive device 48 to scan the laser interferometer 46 along the surface of the sample 12. The vibration velocity of the sample surface detected by the laser interferometer 46 is sent to the amplitude distribution detector 50 connected to the output side of the laser interferometer 46. The amplitude distribution detection unit 50 divides the vibration velocity detected by the laser interferometer 46 by the resonance frequency of the sample 12 that is being vibrated to obtain the vibration amplitude, and the vibration amplitude is also applied to the driving device. It is stored in association with the position signal output by 48, and the distribution of vibration amplitude (vibration pattern) on the surface of the sample 12 is detected.

The measured vibration pattern is input to the comparison / determination unit 58 together with the vibration pattern calculated by the resonance mode calculation unit 56 and compared (step 108). The comparison determination unit 58 uses a plurality of vibration patterns (calculation vibration patterns) calculated by the resonance mode calculation unit 56.
And the measured vibration pattern (measurement vibration pattern) are compared to determine whether or not there is a pattern that matches or is very similar to the measured vibration pattern among the calculated vibration patterns. If there is an operational vibration pattern that exists, select it. As a result, the resonance mode (the vibration mode and the order of resonance) of the sample 12 vibrating at the resonance frequency is specified (step 108). The comparison between the measured vibration pattern and the calculated vibration pattern is performed until a measured vibration pattern matches or extremely resembles any calculated vibration pattern.

Thereafter, the vibration mode and the resonance frequency obtained as described above are input to the input section 14 and given to the elastic constant calculation section 20 together with the size and density of the sample 12. The elastic constant calculation unit 20 uses the given data to calculate an elastic constant such that the input resonance frequency is obtained (step 110). Further, the elastic constant calculated by the elastic constant calculating unit 20 is given to the resonance mode calculating unit 56, and the sample 1
The resonance frequency of No. 2 is calculated, and the vibration pattern on the surface of the sample 12 is calculated for each resonance frequency whose resonance mode is not specified (step 112).

Next, the sample 12 is vibrated in the same manner as above at the resonance frequency for which the resonance mode cannot be specified, and the vibration pattern of the surface is measured (step 114). And
The measured vibration pattern (measured vibration pattern) is compared with each vibration pattern (calculated vibration pattern) calculated by the resonance mode calculator 56, and a calculated vibration pattern that is identical or very similar to the measured vibration pattern is selected to select each resonance frequency. The resonance mode of is specified (step 116). Further, using the vibration mode of the newly identified resonance mode, the elastic constant is calculated so as to obtain the resonance frequency with which this vibration mode can be identified (step 118).

After that, a plurality of resonance frequencies calculated by the resonance mode calculator 56 (for example, 2
It is determined whether or not the resonance mode can be specified for all (0 to 50) (step 120). When there is a resonance frequency for which the resonance mode has not been specified yet, steps 114 to 120 are repeated to specify the resonance mode for all the resonance frequencies. Step 120
When it is determined that the resonance mode can be specified for all the resonance frequencies, the measurement of the elastic constant is ended.

[0041]

Examples << Example 1: Measurement of elastic constants >> Length 11.9
A rectangular parallelepiped duralumin having a width of 2 mm, a width of 10.93 mm and a thickness of 9.86 mm was prepared, and the elastic constant was measured.
The density of this duralumin was 2788 kg / m ³ . Since duralumin is a polycrystal, an isotropic body is assumed and two elastic constants C ₁₁ and C ₄₄ are measured. In the duralumin sample, the thickness direction (direction parallel to the 9.86 mm side) is the z direction.

First, when the resonance frequency was measured, a resonance spectrum as shown in FIG. 4 was obtained. As shown in FIG. 4, many resonance peaks are observed, and the resonance mode cannot be specified only from this measurement. In particular, some peaks are overlapped, and it is not possible to judge whether these are two independent resonance peaks or one peak is broken for some reason. For example, if the frequency is 250-2
FIG. 5 is an enlarged view of the 53 kHz portion, and it can be seen that there are a plurality of peaks.

Then, in this state, the initial values of the elastic constants were measured as C ₁₁ = 100 GPa and C ₄₄ = 22 GPa (these values are values deviated from the true values described later by about 10% and about 20%, respectively). The conventional inverse calculation of the elastic constant was performed so that the resonance frequency was obtained. That is,
Correspondence between calculated values and measured values was made by comparing only the numerical values of the resonance frequency. As a result, a convergent solution could not be obtained. As described above, in the conventional method, a correct result cannot be obtained unless the initial value of the elastic constant is close to the true value.

Next, a vibration pattern was calculated using the same initial value and compared with the measured vibration pattern. FIG. 6 is a comparison of distributions of displacement amplitudes (vibration amplitudes) in the z direction on a plane orthogonal to the z direction of the duralumin sample. In FIG. 6, the left column shows the distribution of vibration amplitudes of the duralumin sample actually measured, and the middle column shows C ₁₁ = 100 GP.
a is a distribution of vibration amplitudes obtained by calculation with C ₄₄ = 22 GPa. The right column of the figure, C ₁₁ = 20
It is a distribution of the vibration amplitude calculated as 0 GPa and C ₄₄ = 50 GPa. Further, the distribution of vibration amplitude string on 1st is in the vibration mode of A _g -4, 2-th row A _u-3,3-th column B _1g -5,4 th column B _{2 g} -5 , The bottom row shows the distribution of the vibration amplitude in the vibration mode of B _1u −7.

As shown in FIG. 6, the distribution of the actually measured vibration amplitude and the distribution of the vibration amplitude obtained by the calculation assuming the elastic constant are in very good agreement. In particular, A
_The two vibration modes of _g -4 and _Au -3 have a difference in resonance frequency of only 0.1% as shown in FIG. 5, and the peaks overlap in the resonance spectrum of FIG. Nevertheless, both vibration patterns (vibration amplitude distribution)
Is completely different. In this way, by comparing the vibration patterns, it is possible to easily find an accurate correspondence between the resonance mode and the resonance frequency.

Therefore, after the resonance pattern is specified by performing the correspondence of the vibration pattern as described above, the elastic constant is set so that the resonance frequency corresponding to the specified resonance mode is obtained using the vibration mode of this resonance mode. Inverse calculation was performed, and the vibration pattern at each resonance frequency was compared with the measured vibration pattern based on the calculated elastic constants to identify the resonance mode. The resonance pattern is measured for all the resonance modes measured in this way, the accurate resonance mode is specified for the resonance frequency, the elastic constant is inversely calculated, and the resonance frequency is calculated. The result of comparison with the frequency is shown in FIG. The convergent solutions of the elastic constants are C ₁₁ = 109.26 GPa, C ₄₄ = 26.
It was 72 GPa. This is the true value of the elastic constant. The average deviation between the value obtained by actually measuring the resonance frequency and the resonance frequency calculated based on the elastic constant measured as described above is shown in FIG. As such, it is about 0.2%, and an accurate elastic constant can be obtained.

The vibration pattern is hardly affected by the elastic constant, as shown in FIG. That is, as shown in the right column of the figure, C ₁₁ = 200 GPa, C ₄₄
= 50 GPa (These are about 83% from the true value,
Even when the vibration pattern is calculated using a value that is significantly different from the true value, which is a value that is shifted by about 85%), there is almost no change from the measured vibration pattern. In fact, C ₁₁ = 5
Even if an abnormal value of 00 GPa and C ₄₄ = 10 GPa was used, the calculation result of the vibration pattern did not change. That is, even if an elastic constant having an initial value that is completely different from the true value is used, the true value of the elastic constant can be obtained as a result by specifying the vibration mode and performing the inverse calculation of the elastic constant. In fact, the true value of the elastic constant could be obtained by performing the inverse calculation by specifying the vibration mode using the initial values of C ₁₁ = 200 GPa and C ₄₄ = 50 GPa. And
As long as it was an isotropic body, the distribution of the vibration amplitude did not change regardless of the elastic constant.

Example 2: Independence of vibration pattern on elastic symmetry The inventors have found that the resonance mode in which the distribution of the vibration amplitude in the normal direction on the surface of a rectangular parallelepiped sample does not change significantly even if the elastic symmetry is different. Found that there is. FIG. 8 shows a vibration pattern of z-direction displacement in the z-plane (plane orthogonal to the z-axis) of a rectangular parallelepiped having the same shape as having different elastic symmetries (isotropic and orthorhombic) and different elastic constants. is there. The sample used is duralumin, which has the same dimensions and density as in Example 1.

The upper stage in FIG. 8 assumes an isotropic body,
This is a vibration pattern obtained by calculation with C ₁₁ = 109.26 GPa and C ₄₄ = 26.72 GPa. In the lower stage, assuming an orthorhombic system, C ₁₁ = 100 GPa, C ₂₂ =
150 GPa, C ₃₃ = 200 GPa, C ₁₂ = 70 GP
a, C ₁₃ = 60 GPa, C ₂₃ = 50 GPa, C ₄₄ = 20
It is a vibration pattern obtained by calculation with GPa, C ₅₅ = 30 GPa, C ₆₆ = 40 GPa.

As is clear from the figure, the upper isotropic body and the lower orthorhombic crystal have different resonance frequencies, but have the same vibration pattern. That is, in these resonance modes, a vibration pattern that does not depend on elastic symmetry is exhibited. Then, even when the such an elastic symmetry and elastic constants are different, for substantially the same vibration pattern, the case of a rectangular _{parallelepiped, A g -1, A g -3} , A u -1, A u -3, B _3g
-1, B _3g -2, B _3g -3, B _2g -1, B _2g -2, B _2g
-13, _B2u- 1, _B2u- 2, _B1u- 1.

Therefore, for a solid whose elastic constant as well as elastic symmetry is unknown, first, assuming an orthorhombic system, an elastic constant of 9 is appropriately set as an initial value, and the above-mentioned resonance is obtained. The vibration pattern is calculated using only the mode, and the resonance mode of the resonance frequency is specified by comparing with the measured vibration pattern of the sample. After that, the elastic constant is inversely calculated so as to obtain the corresponding resonance frequency by using the specified resonance mode, and the approximate elastic constant is determined. Further, thereafter, the true values of the elastic constants can be obtained by completely specifying the resonant modes for all the resonant frequencies again using the elastic constants and further performing the inverse calculation of the elastic constants.

In the above embodiment, the case where the sample 12 is a rectangular parallelepiped has been described, but it can be applied to a round bar sample, a spherical sample, an arbitrary polyhedron sample, etc. by using the finite element method or the like. You can Further, the above embodiment is an explanation of one aspect of the present invention, and is not limited to this. For example, although a case has been described with the above embodiment where the resonance frequency is applied from the input unit 14 to the amplitude distribution detection unit 50, the oscillation frequency of the sweep oscillator 34a may be applied to the amplitude distribution detection unit 50. Further, the output signals of the resonance frequency detection unit 42 and the comparison determination unit 58 may be given to the elastic constant calculation unit 20 to calculate the elastic constant.

[0053]

As described above, according to the present invention, the resonance frequency of a solid in a vibration mode is determined using the size and density of the solid and the assumed elastic constant, and the solid with this resonance frequency is used. By calculating the distribution of the vibration amplitude in the normal direction on the surface and comparing the calculated distribution of the vibration amplitude with the distribution of the vibration amplitude measured by actually vibrating the solid at the resonance frequency, The resonance mode, that is, the vibration mode and the order of resonance can be specified. Therefore, it is possible to know which vibration mode the resonance frequency is due to, and it is possible to accurately calculate the elastic constant. Then, by calculating the resonance frequency and the distribution of the vibration amplitude using the solid as an orthorhombic system, many independent elastic constants are assumed, so that the elastic constant of the solid can be reliably obtained.

[Brief description of drawings]

FIG. 1 is a block diagram of an elastic constant measuring device according to an embodiment of the present invention.

FIG. 2 is a flowchart of a method for measuring an elastic constant of a solid according to an embodiment of the present invention.

FIG. 3 is a perspective view showing an example of a vibration mode of a rectangular solid.

FIG. 4 is a resonance spectrum of a rectangular duralumin.

FIG. 5 is a partially enlarged view of a resonance spectrum of a rectangular duralumin.

FIG. 6 is a diagram comparing a measured vibration pattern of a rectangular parallelepiped duralumin with a vibration pattern obtained by calculation assuming an elastic constant.

FIG. 7 is a diagram comparing a measured resonance frequency of a rectangular duralumin and a resonance frequency calculated by using an elastic constant obtained by the measurement.

FIG. 8 is a diagram showing an example of a vibration pattern that does not depend on elastic symmetry.

[Explanation of symbols]

10 ... Elastic constant measuring device, 12 ... Sample (solid), 14 ... Input unit, 20 ... Elastic constant calculating means (elastic constant calculating unit), 30 ... Resonance mode detecting unit, 3
4 ......... Transmission means, vibration means (transmission section), 34b ...
Transmitter, 36 ... Receiving means (receiver), 40 ... Control section, 42 ... Resonance detecting means (resonance frequency detecting section),
46 ... Surface vibration detection means (laser interferometer), 50 ...
...... Amplitude distribution detecting means (amplitude distribution detecting unit), 56 ......
Resonance mode calculation means (resonance mode calculation unit), 58 ...
Resonance mode determination means (comparison determination unit).

Claims (5)

[Claims] 1. A solid having a predetermined shape is vibrated at a resonance frequency to measure the distribution of vibration amplitude in the normal direction on the surface of the solid, and based on the size and density of the solid and an assumed elastic constant, The resonance frequency for each vibration mode of the solid,
The distribution of the vibration amplitude in the normal direction on the surface of the solid by this resonance frequency is calculated, and the distribution of the calculated vibration amplitude and the measured distribution of the vibration amplitude are compared to determine the resonance frequency of the vibration of the solid. A solid-state resonance mode detection method, characterized in that a resonance mode is obtained. 2. A transmitting means for ultrasonically vibrating a solid while continuously changing the frequency, a receiving means for detecting the vibration of the solid, and a resonance frequency of the solid based on a detection signal of the receiving means. Resonance detecting means for detecting, vibrating means for vibrating the solid by the detected resonance frequency, surface vibration detecting means for detecting displacement in the normal direction on the surface of the solid vibrated by the resonance frequency, and surface vibration Based on the detection signal of the detection means, amplitude distribution detection means for detecting the distribution of the vibration amplitude in the normal direction on the surface of the solid, based on the given size and density of the solid, and the elastic constant, the solid A resonance mode for each vibration mode, and resonance mode calculation means for calculating the distribution of the vibration amplitude in the normal direction on the solid surface due to the resonance frequency, The resonance mode is calculated by comparing the distribution of the vibration amplitude obtained by the resonance mode calculating means with the distribution of the vibration amplitude obtained for the vibrated solid, and calculating the resonance mode of the resonance frequency at which the solid is vibrated. A solid-state resonance mode detecting device, comprising: 3. A solid vibration mode is obtained based on the resonance mode detected by the solid resonance mode detection method according to claim 1, and then based on the obtained vibration mode and the size and density of the solid. A method for measuring an elastic constant of a solid, comprising: calculating an elastic constant for obtaining the resonance frequency by vibrating the solid. 4. A step of ultrasonically vibrating a solid having a predetermined shape while continuously changing the frequency, and obtaining a plurality of resonance frequencies of the solid; and vibrating the solid according to any of the obtained resonance frequencies. The step of detecting the resonance mode of the solid by the method for detecting the resonance mode of the solid according to Item 1 to obtain the vibration mode of the solid, and the vibration mode thus obtained, and the size and density of the solid. A step of calculating an elastic constant for obtaining a vibrated resonance frequency; a resonance frequency for the vibration mode of the solid and the resonance mode are detected based on the calculated elastic constant and the size and density of the solid. Not calculating the distribution of the vibration amplitude in the normal direction on the surface of the solid corresponding to the resonance frequency, and The distribution of the vibration amplitude in the normal direction on the solid surface by the number is measured, the resonance mode of each resonance frequency is compared with the calculated distribution of the vibration amplitude, and the resonance mode is specified from the calculated resonance mode. A step of obtaining the vibration mode based on, a step of calculating an elastic constant by which the resonance frequency corresponding to each vibration mode is obtained, based on the obtained vibration modes, the size of the solid, and the density, A method for measuring an elastic constant of a solid, comprising: 5. The vibration mode of the solid is obtained based on the resonance mode of the solid detected by the resonance mode detecting device of the solid according to claim 2, and based on the obtained vibration mode and the size and density of the solid. And an elastic constant calculating means for calculating an elastic constant for obtaining the resonance frequency corresponding to the vibration mode.