JPH05133861A - Measuring method of modulus of elasticity of test object - Google Patents
Measuring method of modulus of elasticity of test objectInfo
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- JPH05133861A JPH05133861A JP3295746A JP29574691A JPH05133861A JP H05133861 A JPH05133861 A JP H05133861A JP 3295746 A JP3295746 A JP 3295746A JP 29574691 A JP29574691 A JP 29574691A JP H05133861 A JPH05133861 A JP H05133861A
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- wave
- velocity
- sound velocity
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- longitudinal
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Abstract
Description
【０００１】[0001]
【産業上の利用分野】本発明は、各種の薄板（以下、被
検体と総称する）中を伝搬する超音波からヤング率やポ
アソン比などの弾性定数を求める被検体の弾性定数測定
法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring an elastic constant of a subject for obtaining elastic constants such as Young's modulus and Poisson's ratio from ultrasonic waves propagating in various thin plates (hereinafter collectively referred to as a subject).
【０００２】[0002]
【従来の技術】一般に、圧延鋼板製造ラインを移動する
圧延鋼板その他の種々の薄板などの被検体の弾性定数を
測定する方法としては、一般に弾性波動である超音波を
用いて測定する方法が代表的な方法であるとされてい
る。2. Description of the Related Art Generally, as a method for measuring the elastic constants of an object such as a rolled steel plate or various other thin plates moving on a rolled steel plate production line, a method of using ultrasonic waves which are generally elastic waves is representative. It is said that this is an effective method.
【０００３】以上のような被検体のうち、等方性を有す
る被検体の場合、そのヤング率Ｅおよびポアソン比σは
縦波音速CL、横波音速CSおよび密度ρなどを用いて次の
ような演算式で求めることができる。 Ｅ＝μ（３λ＋２μ）／（λ＋μ） ……（１） σ＝λ／｛２（λ＋μ）｝ ……（２） 但し、λ＝ρCL2 −２ρCS2 、μ＝ρCS2 である。In the case of an isotropic object among the above-mentioned objects, the Young's modulus E and Poisson's ratio σ are calculated as follows using longitudinal wave sound velocity CL, transverse wave sound velocity CS and density ρ. It can be calculated by an arithmetic expression. E = μ (3λ + 2μ) / (λ + μ) (1) σ = λ / {2 (λ + μ)} (2) where λ = ρCL 2 -2 ρ CS 2 , Μ = ρ CS 2 Is.
【０００４】なお、ここで，等方性を示す物体とは測定
された弾性的性質に何ら方向依存性をもたない物体をい
う。無秩序に配向された多くの微結晶の集合体は等方的
であると言える。Here, an object exhibiting isotropic property means an object having no direction dependence on the measured elastic property. It can be said that many randomly oriented aggregates of crystallites are isotropic.
【０００５】ところで、この方法で適用対象となる薄板
被検体内部を伝搬する超音波は板波と呼ばれている。こ
の板波音速には、超音波の入射角によって決まる位相速
度と実際に被検体内部を伝搬する実速度である群速度と
の２種類が上げられる。この板波（超音波）は被検体内
で速度分散性をもって伝搬する性質があり、伝搬速度，
群速度とともに周波数によって異なるものである。速度
分散性とは、ある板厚、ある位相速度およびある周波数
のとき、伝搬する性質をもっていることをいう。例えば
位相速度を例にとってみると、この位相速度と周波数と
板厚とは一定の関係を満たしている。すなわち、板波は
ある板厚である位相速度のとき、ある周波数でしか伝搬
しないという特徴をもっている。By the way, the ultrasonic wave propagating inside the thin plate subject to which this method is applied is called a plate wave. There are two types of the plate wave sound velocity: a phase velocity determined by the incident angle of ultrasonic waves and a group velocity that is an actual velocity that actually propagates inside the subject. This plate wave (ultrasonic wave) has the property of propagating with velocity dispersion in the subject,
It depends on the frequency as well as the group velocity. Velocity dispersion means that it has the property of propagating at a certain plate thickness, a certain phase velocity and a certain frequency. For example, taking the phase velocity as an example, the phase velocity, the frequency, and the plate thickness satisfy a certain relationship. That is, the plate wave is characterized in that it propagates only at a certain frequency when the phase velocity has a certain plate thickness.
【０００６】図４はかかる関係を表す位相速度曲線を示
す図であって、その横軸は板厚ｄと周波数ｆとの積（以
下、ｆｄ値と呼ぶ）、縦軸は位相速度を示している。こ
の図４は、位相速度曲線を示しているが、速度分散性を
有する板波はかかる曲線近傍で伝搬する。図中，S0,S1,
S2, …は超音波による被検体の変位が厚み方向に非対称
である非対称モードであってそれぞれ０次，１次，２
次，…モードであり、一方、A0,A1,A2, は超音波による
被検体の変位が対象である対称モードであってそれぞれ
０次，１次，２次，…モードとなっている。FIG. 4 is a diagram showing a phase velocity curve showing such a relationship. The horizontal axis shows the product of the plate thickness d and the frequency f (hereinafter referred to as fd value), and the vertical axis shows the phase velocity. There is. Although FIG. 4 shows a phase velocity curve, a plate wave having velocity dispersion property propagates in the vicinity of this curve. In the figure, S0, S1,
S2, ... Are asymmetric modes in which the displacement of the subject due to ultrasonic waves is asymmetric in the thickness direction,
On the other hand, A0, A1, A2, are symmetric modes which are intended for displacement of the subject by ultrasonic waves, and are 0th, 1st, 2nd, ... Modes, respectively.
【０００７】しかして、以上のような位相速度曲線は、
下記の式を満足する条件を求めることによって決定でき
る。ここで、下記（３）式は非対称モード、（４）式は
対象モードである。 ｔａｎ（K1b ）／ｔａｎ（K2b ） ＝−（KP2 −K22 ）2 ／（４KP2 K1K2）…（３） ｔａｎ（K1b ）／ｔａｎ（K2b ） ＝−（４KP2 K1K2）／（KP2 −K22 ）2 …（４） 但し、K1＝｛（ω／CL）2 −（ω／CP）2 ｝1/2 K2＝｛（ω／CS）2 −（ω／CP）2 ｝1/2 ω＝２πｆ（ω：角周波数，ｆ：周波数） ｂ＝ｄ／２（ｄ：板厚） KP＝ω／CP CP：位相速度，CL：縦波音速，CS：横波音速である。However, the above phase velocity curve is
It can be determined by finding the condition that satisfies the following formula. Here, the following expression (3) is an asymmetric mode, and expression (4) is a target mode. tan (K1b) / tan (K2b ) = - (KP 2 −K2 2 ) 2 / (4KP 2 K1K2) ... (3) tan ( K1b) / tan (K2b) = - (4KP 2 K1K2) / (KP 2 −K2 2 ) 2 (4) However, K1 = {(ω / CL) 2 -(Ω / CP) 2 } 1/2 K2 = {(ω / CS) 2 -(Ω / CP) 2 } 1/2 ω = 2πf (ω: angular frequency, f: frequency) b = d / 2 (d: plate thickness) KP = ω / CP CP: phase velocity, CL: longitudinal wave sound velocity, CS: transverse wave sound velocity ..
【０００８】従って、板波の位相速度CP、板波の周波数
ｆ、板厚ｄが既知であれば、これら（３）式および
（４）式を満足するように前記縦波音速CL、横波音速CS
を求めた後、この縦波音速CL、横波音速CSを用いて前記
（１）式，（２）式より弾性定数を求めることができ
る。Therefore, if the phase velocity CP of the plate wave, the frequency f of the plate wave, and the plate thickness d are known, the longitudinal wave sound velocity CL and the transverse wave sound velocity satisfy the formulas (3) and (4). CS
After obtaining the above, the elastic constant can be obtained from the equations (1) and (2) using the longitudinal wave sound velocity CL and the transverse wave sound velocity CS.
【０００９】ところで、この種の板波の速度分散性超音
波を励起検出する場合、図３に示すような原理構成の装
置が採用されている。同図において、１ａは超音波励起
用探触子、１ｂは超音波検出用探触子、２ａ，２ｂはく
さび、３は被検体、４は発振器、５は電圧計、６は接触
媒質である。これら超音波励起用探触子１ａによる超音
波入射角と超音波検出用探触子１ｂの超音波受信角とは
同じθiに設定する。さらに、この図は２個の探触子を
使う透過法の原理を示しているが、１個の探触子を用い
る反射法でも原理的には同じである。ここで、接触式超
音波探触子を用いたものは、位相速度と超音波の入射角
とは一定の関係，つまり下記の（５）式で表すような関
係をもっている。 CP＝CW／ｓｉｎθi ……（５） 但し、CWはくさび２ａ，２ｂの音速を表す。従って、上
式から超音波の周波数と入射角との関係を求めることに
より、ｆｄ値と位相速度の関係を求めることができる。
なお、板厚ｄは予め求めておく。By the way, in the case of exciting and detecting velocity dispersive ultrasonic waves of this type of plate wave, an apparatus having a principle configuration as shown in FIG. 3 is adopted. In the figure, 1a is an ultrasonic wave excitation probe, 1b is an ultrasonic wave detection probe, 2a and 2b are wedges, 3 is a subject, 4 is an oscillator, 5 is a voltmeter, and 6 is a contact medium. .. The ultrasonic wave incident angle of the ultrasonic wave exciting probe 1a and the ultrasonic wave receiving angle of the ultrasonic wave detecting probe 1b are set to the same θi. Further, this figure shows the principle of the transmission method using two probes, but the principle is the same for the reflection method using one probe. Here, in the one using the contact type ultrasonic probe, the phase velocity and the incident angle of the ultrasonic wave have a constant relationship, that is, the relationship represented by the following expression (5). CP = CW / sin θi (5) where CW represents the speed of sound of the wedges 2a and 2b. Therefore, the relationship between the fd value and the phase velocity can be calculated by calculating the relationship between the ultrasonic wave frequency and the incident angle from the above equation.
The plate thickness d is obtained in advance.
【００１０】そこで、従来、かかる原理構成を用いてｆ
ｄ値と位相速度との関係を求める方法として、次の２つ
の方法を見い出した特許出願が提案されている（特公昭
６３−２９２２０号公報）。Therefore, conventionally, by using such a principle configuration, f
As a method for obtaining the relationship between the d value and the phase velocity, a patent application has been proposed which has found the following two methods (Japanese Patent Publication No. 63-29220).
【００１１】その第１の方法は、超音波の周波数を一定
にした状態で超音波の入射角を可変とする方法である。
具体的には、発振器４の周波数を一定とした状態で超音
波の入射角を可変しながら超音波を被検体３に入射し、
このとき被検体３内部を伝搬してくる板波速度分散性超
音波の強度を電圧計５で観察し、検出強度が最大となる
入射角から位相速度を計算し、周波数と位相速度との関
係を求める方法である。The first method is a method in which the incident angle of ultrasonic waves is variable while the frequency of ultrasonic waves is constant.
Specifically, while the frequency of the oscillator 4 is constant, the ultrasonic wave is incident on the subject 3 while changing the incident angle of the ultrasonic wave,
At this time, the intensity of the plate wave velocity dispersive ultrasonic wave propagating inside the subject 3 is observed by the voltmeter 5, the phase velocity is calculated from the incident angle at which the detected intensity is maximum, and the relationship between the frequency and the phase velocity is calculated. Is a method of asking for.
【００１２】次に、第２の方法は、第１の方法と全く逆
の方法であって、超音波の入射角を一定にした状態で周
波数を可変する方法である。この方法は、超音波の入射
角を一定とした状態で発振器４の周波数を可変しながら
超音波を被検体３に入射し、このとき被検体３内部を伝
搬してくる板波速度分散性超音波の強度を電圧計５で観
察し、検出強度が最大となる周波数を求める方法であ
る。Next, the second method is a method which is completely opposite to the first method, in which the frequency is varied while the incident angle of ultrasonic waves is kept constant. In this method, the ultrasonic wave is incident on the subject 3 while varying the frequency of the oscillator 4 with the incident angle of the ultrasonic wave being constant, and at this time, the plate wave velocity dispersive ultrasonic wave propagating inside the subject 3 is transmitted. This is a method of observing the intensity of a sound wave with a voltmeter 5 and obtaining the frequency at which the detected intensity is maximum.
【００１３】[0013]
【発明が解決しようとする課題】しかしながら、以上の
ような２つの測定法は、測定に際してどの板波モードを
選択すればよいのか不明であこと、また、位相速度，周
波数，板厚から縦波音速および横波音速を求めることが
明確化されておらず、被検体の弾性定数を測定するに際
し未だ実用の域に達していないものである。However, in the above two measuring methods, it is unclear which plate wave mode should be selected for measurement, and the longitudinal wave is determined from the phase velocity, frequency and plate thickness. It is not clarified to obtain the sound velocity and the transverse wave sound velocity, and it has not reached the practical range when measuring the elastic constant of the subject.
【００１４】本発明は上記実情に鑑みてなされたもの
で、板波モードを適切に選択しつつその位相速度，周波
数などから縦波音速および横波音速を正確に求め、ひい
ては被検体の弾性定数を高精度に求め得る被検体の弾性
定数測定法を提供することを目的とする。The present invention has been made in view of the above-mentioned circumstances, and while appropriately selecting the plate wave mode, the longitudinal wave sound velocity and the transverse wave sound velocity are accurately obtained from the phase velocity, frequency, etc., and by extension, the elastic constant of the subject is determined. An object of the present invention is to provide a method for measuring an elastic constant of a subject that can be obtained with high accuracy.
【００１５】[0015]
【課題を解決するための手段】先ず、請求項１に対応す
る発明は上記課題を解決するために、被検体を伝搬する
板波超音波Ａ１モードと板波超音波Ｓ１モードの位相速
度と周波数とから横波音速と縦波音速を求めた後、これ
ら横波音速と縦波音速とから前記被検体の弾性定数を求
める被検体の弾性定数測定法である。First, in order to solve the above-mentioned problems, the invention corresponding to claim 1 has a phase velocity and frequency of a plate wave ultrasonic wave A1 mode and a plate wave ultrasonic wave S1 mode propagating through an object. This is a method for measuring the elastic constant of the subject after obtaining the acoustic velocity of the transverse wave and the acoustic velocity of the longitudinal wave from and then obtaining the elastic constant of the subject from the acoustic velocity of the transverse wave and the acoustic velocity of the longitudinal wave.
【００１６】次に、請求項２に対応する発明は、被検体
を伝搬する板波超音波Ａ１モードの位相速度および周波
数と適宜な縦波音速初期値とから１次近似横波音速を求
めた後、この１次近似横波音速と板波超音波Ｓ１モード
の位相速度および周波数とから１次近似縦波音速を求
め、さらに前記板波超音波Ａ１モードの位相速度および
周波数と前記１次近似縦波音速とから２次近似横波音速
を求め、この２次近似横波音速と前記板波超音波Ｓ１モ
ードの位相速度および周波数とから２次近似縦波音速を
求め、以降，順次次数を上げながら横波音速および縦波
音速が収束するまで同様の処理を繰り返し、この収束し
て得られた横波音速および縦波音速から被検体の弾性定
数を求める被検体の弾性定数測定法である。Next, in the invention corresponding to claim 2, after obtaining the first-order approximate transverse wave sound velocity from the phase velocity and frequency of the plate wave ultrasonic wave A1 mode propagating through the subject and an appropriate initial value of longitudinal wave velocity, The primary approximate longitudinal wave acoustic velocity is obtained from the primary approximate transverse wave acoustic velocity and the phase velocity and frequency of the plate ultrasonic wave S1 mode, and further the phase velocity and frequency of the plate ultrasonic wave A1 mode and the primary approximate longitudinal wave are obtained. The second-order approximate transverse wave sound velocity is obtained from the sound velocity, and the second-order approximate longitudinal wave sound velocity is obtained from the second-order approximate shear wave sound velocity and the phase velocity and frequency of the plate wave ultrasonic wave S1 mode. Thereafter, the transverse wave sound velocity is successively increased. And the same process is repeated until the longitudinal wave sound velocity converges, and the elastic constant of the subject is calculated from the transverse wave sound velocity and the longitudinal wave sound velocity obtained by the convergence.
【００１７】[0017]
【作用】従って、請求項１，２に対応する発明は以上の
ような手段を講じたことにより、測定に際して、被検体
を伝搬する板波超音波の位相速度曲線の特性変化に着目
してＡ１モードとＳ１モードを適切に選択することがで
き、Ａ１モードおよびＳ１モードの位相速度および周波
数を各々求めることにより、それらの値を用いて正確に
横波音速および縦波音速を算出することが可能となる。
よって、ここで正確に求められた横波音速および縦波音
速などを用いて前記（１）式および（２）式に基づいて
被検体の弾性定数を高精度に求めることができる。Therefore, according to the inventions corresponding to claims 1 and 2, by taking the above-mentioned means, attention is paid to the characteristic change of the phase velocity curve of the plate wave ultrasonic wave propagating through the object at the time of measurement. Mode and S1 mode can be selected appropriately, and by obtaining the phase velocity and frequency of the A1 mode and S1 mode respectively, it is possible to accurately calculate the transverse wave sound velocity and the longitudinal wave sound velocity using those values. Become.
Therefore, the elastic constant of the subject can be calculated with high accuracy based on the equations (1) and (2) using the transverse wave sound velocity and the longitudinal wave sound velocity that have been accurately obtained.
【００１８】[0018]
【実施例】以下、被検体の弾性定数測定法の実施例につ
いて説明する。EXAMPLE An example of the method for measuring the elastic constant of a subject will be described below.
【００１９】先ず、本発明者において前記（３）式およ
び（４）式によって求められる図４に示す位相速度曲線
について詳細に検討し、かつ、繰り返し実験を行った結
果、次のようなことを見い出すに至った。First, the inventors of the present invention have studied in detail the phase velocity curve shown in FIG. 4 which is obtained by the equations (3) and (4), and as a result of repeated experiments, the following is obtained. I came to find out.
【００２０】すなわち、薄板を伝搬する板波超音波Ａ１
モードの位相速度曲線に関し、横波音速を変化させたと
き、当該横波音速の変化に伴ってＡ１モードの位相速度
曲線が大きく変化するが、縦波音速を変化させた場合に
はその位相速度曲線は殆んど変化しない。このことは、
横波音速を測定するに際し、Ａ１モードを選択し、当該
Ａ１モードの位相速度と周波数を求めれば、横波音速を
精度よく求めることが可能である。That is, a plate wave ultrasonic wave A1 propagating through a thin plate.
Regarding the phase velocity curve of the mode, when the transverse wave sound velocity is changed, the phase velocity curve of the A1 mode greatly changes with the change of the transverse wave sound velocity. However, when the longitudinal wave sound velocity is changed, the phase velocity curve becomes It hardly changes. This is
When measuring the transverse wave sound velocity, if the A1 mode is selected and the phase velocity and frequency of the A1 mode are obtained, the transverse wave sound velocity can be obtained with high accuracy.
【００２１】一方、薄板を伝搬する板波超音波Ｓ１モー
ドの位相速度曲線に関し、縦波音速を変化させたとき、
当該縦波音速の変化に伴ってＳ１モードの位相速度曲線
が大きく変化するが、横波音速を変化させた場合にはそ
の位相速度曲線は殆んど変化しない。ゆえに、縦波音速
を測定するに際し、Ｓ１モードを選択し、当該Ｓ１モー
ドの位相速度と周波数を求めれば、縦波音速を精度よく
求めることができる。従って、以上のようにして求めた
横波音速と縦波音速とを用いれば、薄板の弾性定数を正
確に求めることができる。On the other hand, regarding the phase velocity curve of the plate wave ultrasonic wave S1 mode propagating through the thin plate, when the longitudinal wave sound velocity is changed,
Although the phase velocity curve of the S1 mode changes greatly with the change of the longitudinal wave sound velocity, the phase velocity curve hardly changes when the transverse wave sound velocity is changed. Therefore, when measuring the longitudinal wave sound velocity, if the S1 mode is selected and the phase velocity and frequency of the S1 mode are obtained, the longitudinal wave sound velocity can be obtained with high accuracy. Therefore, the elastic constant of the thin plate can be accurately obtained by using the transverse wave sound velocity and the longitudinal wave sound velocity obtained as described above.
【００２２】因みに、図１は縦波音速を５％ずつ変化さ
せながら計算により求めた位相速度曲線の図であり、図
２は横波音速を５％ずつ変化させながら計算により求め
た位相速度曲線の図である。Incidentally, FIG. 1 is a diagram of a phase velocity curve obtained by calculation while changing the longitudinal wave sound velocity by 5%, and FIG. 2 is a diagram of the phase velocity curve obtained by calculation while changing the transverse wave sound velocity by 5%. It is a figure.
【００２３】これらの図のうち、図１から明らかなよう
に、Ａ１モードは縦波音速を変化させてもあまり変化し
ないが、Ｓ１モードの位相速度が速い部分では縦波音速
が変化させるとその変化に応じて大きく変化しているこ
とが分かる。それに対し、図２では、Ａ１モードは横波
音速が変化すると大きく変化するが、Ｓ１モードは位相
速度が速い部分では横波音速が変化してもあまり変化し
ない。このことは、Ａ１モードの測定は横波音速の決定
に適しており、Ｓ１モードでは位相速度の速い部分の測
定が縦波音速の決定に適していることが理解できる。As is apparent from FIG. 1 among these figures, the A1 mode does not change so much even if the longitudinal wave sound velocity is changed, but when the longitudinal wave sound velocity is changed in the portion where the phase velocity is fast in the S1 mode, the change occurs. It can be seen that there is a great change in response to the change. On the other hand, in FIG. 2, the A1 mode changes greatly when the transverse wave sound velocity changes, but the S1 mode does not change much even when the transverse wave sound velocity changes in a portion where the phase velocity is fast. It can be understood that the measurement in the A1 mode is suitable for determining the transverse wave sound velocity, and that in the S1 mode, the measurement for a portion having a high phase velocity is suitable for determining the longitudinal wave sound velocity.
【００２４】このＳ１モードの位相速度の速い範囲は縦
波音速より速い範囲である。実際に、被検体の弾性定数
を測定する場合、おおよその縦波音速は容易に知り得る
ので、Ｓ１モードで測定する位相速度の範囲を知ること
ができる。The fast phase velocity range of the S1 mode is faster than the longitudinal sound velocity. Actually, when measuring the elastic constant of the object, the approximate longitudinal wave sound velocity can be easily known, so that the range of the phase velocity measured in the S1 mode can be known.
【００２５】次に、横波音速，縦波音速を演算によって
求める例について説明する。先ず、前記（３）式，
（４）式は位相速度CP、板波周波数ｆ、板厚ｄ、縦波音
速CL、横波音速CSの５つの変数から成り立っている。そ
のうち、位相速度CP、板波周波数ｆは板波の測定で求め
ることができ、また板厚ｄは厚さ計などで求めることが
できる。従って、変数は縦波音速CLと横波音速CSだけと
なる。Next, an example of obtaining the transverse wave sound velocity and the longitudinal wave sound velocity by calculation will be described. First, the equation (3),
Equation (4) consists of five variables: phase velocity CP, plate wave frequency f, plate thickness d, longitudinal wave sound velocity CL, and transverse wave sound velocity CS. Among them, the phase velocity CP and the plate wave frequency f can be obtained by measuring the plate wave, and the plate thickness d can be obtained by a thickness gauge or the like. Therefore, the variables are only the longitudinal sound velocity CL and the transverse sound velocity CS.
【００２６】そこで、初めに、Ａ１モードの位相速度CP
a と周波数faとを測定する。板厚ｄは予め厚さ計などを
用いて測定する。そして、得られたCPa ，fa，ｄは予め
メモリなどに保存しておく。このＡ１モードは、縦波音
速が変化しても殆んど変化しないことを利用すると、縦
波音速CLには適宜な縦波音速初期値を定め、同様にメモ
リなどに保存する。Therefore, first, the phase velocity CP of the A1 mode
Measure a and frequency fa. The plate thickness d is previously measured using a thickness gauge or the like. Then, the obtained CPa, fa, and d are stored in a memory or the like in advance. By utilizing the fact that the A1 mode hardly changes even if the longitudinal wave sound velocity changes, an appropriate longitudinal wave sound velocity initial value is set for the longitudinal wave sound velocity CL and is similarly stored in the memory or the like.
【００２７】しかる後、前記各測定値CPa ，fa，ｄ，縦
波音速初期値などを用いて前記（４）式が成り立つよう
に横波音速を数値計算により探すことにより、横波音速
を求めることができ、この横波音速を１次近似横波音速
とする。After that, the transverse wave sound velocity can be obtained by numerically searching the transverse wave sound velocity so that the above equation (4) is established using the measured values CPa, fa, d, the longitudinal wave sound velocity initial value, and the like. It is possible to make this shear wave velocity the first-order approximate shear wave velocity.
【００２８】次に、Ｓ１モードの位相速度CPs 、周波数
fsを測定し、既に求めた１次近似横波音速を用いて
（４）式が成立するように縦波音速を数値計算により探
すことにより、縦波音速を求めることができる。この縦
波音速を１次近似縦波音速とする。この１次近似縦波音
速は適当な値である初期値に比べてより真値に近い。Next, the phase velocity CPs and frequency of the S1 mode
The longitudinal wave sound velocity can be obtained by measuring fs and searching for the longitudinal wave sound velocity by numerical calculation so that the equation (4) is satisfied using the already obtained first-order approximate transverse wave sound velocity. This longitudinal wave sound velocity is referred to as a first-order approximate longitudinal wave sound velocity. This first-order approximate longitudinal wave sound velocity is closer to the true value than the initial value, which is an appropriate value.
【００２９】さらに、１次近似縦波音速とＡ１モードと
のCPa ，faから前記（４）式を用いて横波音速を求め、
これを２次近似横波音速とする。この２次近似横波音速
は、１次近似横波音速に比べると縦波音速により正確な
値を用いているので、より正確に値となる。さらに、２
次近似横波音速とＳ１モードとのCPs,fsから前記（３）
式を用いて縦波音速を求め、これを２次近似縦波音速と
する。このようにして順次高次の演算処理を繰り返して
いくと、横波音速，縦波音速は一定の値に収束し、正確
な値を求めることができる。Further, the transverse wave sound velocity is obtained from the first-order approximate longitudinal wave sound velocity and CPa and fa of the A1 mode by using the above equation (4),
This is defined as the second-order approximate shear wave sound velocity. This secondary approximated transverse wave sound velocity has a more accurate value than the first approximated transverse wave sound velocity because it uses a more accurate value for the longitudinal wave sound velocity. Furthermore, 2
(3) from the CPs, fs of the next approximate shear wave velocity and S1 mode
The longitudinal wave sound velocity is obtained using the formula, and this is used as the second-order approximate longitudinal wave sound velocity. When the higher-order arithmetic processing is sequentially repeated in this manner, the transverse wave sound velocity and the longitudinal wave sound velocity converge to constant values, and accurate values can be obtained.
【００３０】次に、本発明方法を用いて厚さ１mmのアル
ミニウム板の弾性定数を求める具体例について説明す
る。なお、かかる弾性定数の測定に関しては、図３の装
置を用いて板波の位相速度と周波数とを求めるものとす
る。この図において１ａは超音波励起用探触子、１ｂは
超音波検出用探触子、２ａ，２ｂはくさび、３は被検
体、４は発振器、５は電圧計、６は接触媒質である。Next, a specific example of obtaining the elastic constant of an aluminum plate having a thickness of 1 mm by using the method of the present invention will be described. Regarding the measurement of the elastic constant, the phase velocity and frequency of the plate wave are obtained by using the device shown in FIG. In this figure, 1a is an ultrasonic wave excitation probe, 1b is an ultrasonic wave detection probe, 2a and 2b are wedges, 3 is a subject, 4 is an oscillator, 5 is a voltmeter, and 6 is a contact medium.
【００３１】従って、以上のような構成であれば、発振
器４から連続的な正弦波を発生して超音波励起用探触子
１ａに供給する。この探触子１ａはその正弦波周波数の
超音波を発振するが、この超音波はくさび２ａおよび接
触媒質６を介して被検体３に伝達される。この被検体３
内部では超音波が板波として伝搬し、接触媒質６および
くさび２ｂを通って超音波検出用探触子１ｂに到達す
る。そして、当該探触子１ｂにおいて受波された超音波
が電気信号に変換され、その変換された超音波受信強度
が電圧計５に測定される。Therefore, with the above configuration, a continuous sine wave is generated from the oscillator 4 and supplied to the ultrasonic wave excitation probe 1a. The probe 1a oscillates an ultrasonic wave having the sinusoidal frequency, and the ultrasonic wave is transmitted to the subject 3 via the wedge 2a and the contact medium 6. This subject 3
Inside the ultrasonic wave, the ultrasonic wave propagates as a plate wave and reaches the ultrasonic wave detecting probe 1b through the contact medium 6 and the wedge 2b. Then, the ultrasonic wave received by the probe 1b is converted into an electric signal, and the converted ultrasonic wave reception intensity is measured by the voltmeter 5.
【００３２】ここで、各モードの位相速度および周波数
は次のようにして決定する。先ず、位相速度は前記
（５）式を用いてくさびの角度から求めることができ、
また周波数については、くさびの角度を一定とし、か
つ、発振器４の周波数を可変しながら被検体伝搬の板波
の強度を電圧計５で観察し、その最大強度時の周波数を
もって板波周波数として求めることが可能である。Here, the phase velocity and frequency of each mode are determined as follows. First, the phase velocity can be obtained from the wedge angle using the equation (5),
Regarding the frequency, the intensity of the plate wave propagating through the object is observed with a voltmeter 5 while the wedge angle is fixed and the frequency of the oscillator 4 is varied, and the frequency at the maximum intensity is determined as the plate wave frequency. It is possible.
【００３３】さて、第１の具体的な実施例として、例え
ばくさびの角度θi を２０°としたときのＡ１モードと
Ｓ１モードとの測定例について述べる。今、くさびの音
速CWを２４５３ｍ／ｓとすると、前記（５）式にくさび
の音速CWを適用すれば位相速度CPa,CPs は７１７２ｍ／
ｓとなる。一方、前述の方法から電圧計５の強度最大時
の板波周波数を求めており、このときのＡ１モードの周
波数faを２．４２ＭＨｚ、ＳＩモードの周波数fsは３．
１５ＭＨｚである。Now, as a first specific example, an example of measurement in the A1 mode and the S1 mode when the wedge angle θi is 20 ° will be described. Now, assuming that the sound speed CW of the wedge is 2453 m / s, applying the sound speed CW of the wedge to the equation (5), the phase velocities CPa and CPs are 7172 m / s.
s. On the other hand, the plate wave frequency at the maximum intensity of the voltmeter 5 is obtained from the above-mentioned method. At this time, the frequency fa of the A1 mode is 2.42 MHz and the frequency fs of the SI mode is 3.
It is 15 MHz.
【００３４】従って、この値を用いて縦波音速CL、横波
音速CSを求めることができる。先ず、縦波音速の初期値
を６０００ｍ／ｓとする。この値の根拠は、一般にアル
ミニウムの縦波音速は６０００ｍ／ｓ近傍だからであ
る。そこで、この縦波音速初期値を利用し、ｄ＝１mm、
CP＝７１７２ｍ／ｓ、CL＝６０００ｍ／ｓ、ｆ＝２．４
２ＭＨｚの条件の下に、前記（４）式を満足させるよう
に横波音速を求めると、３１６９．６９１ｍ／ｓとな
る。この値が１次近似横波音速である。Therefore, the longitudinal wave sound velocity CL and the transverse wave sound velocity CS can be obtained by using these values. First, the initial value of the longitudinal sound velocity is set to 6000 m / s. The reason for this value is that the acoustic velocity of the longitudinal wave of aluminum is generally around 6000 m / s. Therefore, using this longitudinal wave velocity initial value, d = 1 mm,
CP = 7172 m / s, CL = 6000 m / s, f = 2.4
Under the condition of 2 MHz, the transverse wave sound velocity is calculated as 31699.691 m / s so as to satisfy the equation (4). This value is the first-order approximate shear wave acoustic velocity.
【００３５】次に、この値を利用し、ｄ＝１mm、CP＝７
１７２ｍ／ｓ、CS＝３１６９．６９１ｍ／ｓ、ｆ＝３．
１５ＭＨｚの条件の下に、前記（３）式を満足するよう
に縦波音速を求めると、６３９８．４６５ｍ／ｓとな
る。この値が１次近似縦波音速である。さらに、かかる
値を利用し、ｄ＝１mm、CP＝７１７２ｍ／ｓ、CL＝６３
９８．４６５ｍ／ｓ、ｆ＝２．４２ＭＨｚの条件の下
に、前記（４）式を満足するように横波音速を求める
と、３１４７．３４１ｍ／ｓとなる。以後、同様に得ら
れる縦波音速、横波音速を計算していくと、表１に示す
ように一定の値に収束する。Next, using this value, d = 1 mm, CP = 7
172 m / s, CS = 3169.691 m / s, f = 3.
Under the condition of 15 MHz, the longitudinal wave sound velocity is calculated to be 6398.465 m / s so as to satisfy the equation (3). This value is the first-order approximate longitudinal sound velocity. Furthermore, using such values, d = 1 mm, CP = 7172 m / s, CL = 63
Under the conditions of 98.465 m / s and f = 2.42 MHz, the transverse wave sound velocity is calculated to be 3147.341 m / s so as to satisfy the equation (4). After that, when the longitudinal wave acoustic velocity and the transverse wave acoustic velocity obtained in the same manner are calculated, they converge to constant values as shown in Table 1.
【００３６】[0036]
【表１】 [Table 1]
【００３７】そして、以上のようにして得られた値を基
づいて作成した位相速度曲線が図４に示すものである。
図中，点１はＡ１モードの測定点、点２はＳ１モードの
測定点である。実線は、縦波音速、横波音速の収束値か
ら求めた位相速度計算値である。測定点と計算値とは一
致しており、本発明方法によって被検体の縦波音速およ
び横波音速が求められることを確認できる。The phase velocity curve created based on the values obtained as described above is shown in FIG.
In the figure, point 1 is an A1 mode measurement point, and point 2 is an S1 mode measurement point. The solid line is the phase velocity calculation value obtained from the convergent values of the longitudinal wave sound velocity and the transverse wave sound velocity. Since the measurement points and the calculated values match, it can be confirmed that the longitudinal wave sound velocity and the transverse wave sound velocity of the subject are obtained by the method of the present invention.
【００３８】次に、第２の具体的な実施例として、例え
ばくさびの角度θi を２９°としたときのＡ１モードを
測定し、第１の具体的な実施例で測定したＳ１モードを
使用した場合について説明する。この場合、位相速度CP
a は５０６０ｍ／ｓ、cps は７１７２ｍ／ｓである。ま
た、Ａ１モード板波の周波数はfaは３．８９ＭＨｚであ
った、そこで、これらの値から縦波音速CL、横波音速CS
を求めるものとすると、縦波音速初期値を６０００ｍ／
ｓとし、ｄ＝１mm、CP＝５０６０ｍ／ｓ、CL＝６０００
ｍ／ｓ、ｆ＝３．８９ＭＨｚの条件の下に、前記（４）
式が成り立つ横波音速を求めると、３１５０．７０１ｍ
／ｓとなる。次に、この値を利用し、ｄ＝１mm、CP＝７
１７２ｍ／ｓ、CS＝３１５０．７０１ｍ／ｓ、ｆ＝３．
１５ＭＨｚの条件の下に、前記（３）式が成立する縦波
音速を求めると、６４１８．０１３ｍ／ｓとなる。以
後、第１の実施例と同様に計算を進めると、次の表２の
ように一定の値に収束した。Next, as a second specific example, the A1 mode was measured when the wedge angle θi was set to 29 °, and the S1 mode measured in the first specific example was used. The case will be described. In this case, the phase velocity CP
a is 5060 m / s and cps is 7172 m / s. Also, the frequency of the A1 mode plate wave was fa at 3.89 MHz, so from these values, the longitudinal sound velocity CL and the transverse wave sound velocity CS
To obtain the initial value of longitudinal sound velocity of 6000 m /
s, d = 1 mm, CP = 5060 m / s, CL = 6000
Under the condition of m / s, f = 3.89 MHz, the above (4)
When the speed of sound of the transverse wave that satisfies the formula is calculated, it is 3150.701 m.
/ S. Next, using this value, d = 1mm, CP = 7
172 m / s, CS = 3150.701 m / s, f = 3.
Under the condition of 15 MHz, the longitudinal wave sound velocity that satisfies the above equation (3) is 6418.013 m / s. After that, when the calculation was advanced in the same manner as in the first embodiment, it converged to a constant value as shown in Table 2 below.
【００３９】[0039]
【表２】 [Table 2]
【００４０】従って、ここで得られた横波音速，縦波音
速は第１の実施例で求めた値とほぼ等しく、第２の実施
例のようにＡ１モードとＳ１モードの位相速度が異なっ
ていても、被検体の縦波音速および横波音速が求められ
ることを確認できる。Therefore, the transverse wave sound velocity and the longitudinal wave sound velocity obtained here are almost equal to the values obtained in the first embodiment, and the phase velocities of the A1 mode and the S1 mode are different as in the second embodiment. Also, it can be confirmed that the longitudinal wave sound velocity and the transverse wave sound velocity of the subject are required.
【００４１】因みに、以上のようにして得られた音速CL
＝６４２３ｍ／ｓ、CS＝３１４６ｍ／ｓと密度ρ＝２６
９０kg／ｍ3 とから、ヤング率Ｅは７１．４６ＧＰａ、
ポアソン比σは０．３４２２となり、一般に知られる
値，つまりＥ＝７０．３ＧＰａ、σ＝０．３４５（国立
天文台編 理科年表 １９８９年）に近い値であり、本
発明方法によって被検体の弾性定数を測定できることが
容易に確かめられた。By the way, the sound velocity CL obtained as described above
= 6423 m / s, CS = 3146 m / s and density ρ = 26
90 kg / m 3 Therefore, Young's modulus E is 71.46 GPa,
The Poisson's ratio σ is 0.3422, which is a value close to a generally known value, that is, E = 70.3 GPa, σ = 0.345 (Nippon Observatory ed. Science chronology 1989), and the elasticity of the subject is measured by the method of the present invention. It was easily confirmed that the constant could be measured.
【００４２】従って、以上のような実施例の方法によれ
ば、薄板を伝搬する板波超音波Ａ１モードの位相速度曲
線に関し、横波音速を変化させたとき、当該横波音速の
変化に伴ってＡ１モードの位相速度曲線が大きく変化す
るが、縦波音速を変化させた場合にはその位相速度曲線
は殆んど変化しないこと、また板波超音波Ｓ１モードの
位相速度曲線に関し、縦波音速を変化させたとき、当該
縦波音速の変化に伴ってＳ１モードの位相速度曲線が大
きく変化するが、横波音速を変化させた場合にはその位
相速度曲線は殆んど変化しないこという特性を考慮しつ
つ、横波音速の測定時にＡ１モードを選択し、縦波音速
の測定時にＳ１モードを選択し、それぞれのＡ１モード
およびＳ１モードの位相速度と周波数とを求めれば、前
記（３）式および（４）式から正確に横波音速および縦
波音速を正確に測定でき、さらにこれら横波音速および
縦波音速から前記（１）式および（２）式を用いて高精
度に被検体の弾性定数を求めることができ、ひいては被
検体の異方性を評価するために役立つものである。Therefore, according to the method of the above embodiment, regarding the phase velocity curve of the plate wave ultrasonic wave A1 mode propagating in the thin plate, when the transverse wave sound velocity is changed, A1 is accompanied with the change of the transverse wave sound velocity. The phase velocity curve of the mode changes greatly, but when the longitudinal wave sound velocity is changed, the phase velocity curve hardly changes. Also, regarding the phase velocity curve of the plate wave ultrasonic wave S1 mode, the longitudinal wave sound velocity is changed. When changing, the phase velocity curve of the S1 mode changes greatly with the change of the longitudinal wave sound velocity, but when the transverse wave sound velocity is changed, the phase velocity curve hardly changes. On the other hand, if the A1 mode is selected when measuring the transverse wave sound velocity, the S1 mode is selected when measuring the longitudinal wave sound velocity, and the phase velocities and frequencies of the respective A1 mode and S1 mode are obtained, the above equation (3) and The acoustic velocity of the transverse wave and the acoustic velocity of the longitudinal wave can be accurately measured from the equation 4), and the elastic constants of the object can be obtained from the acoustic velocity of the transverse wave and the acoustic velocity of the longitudinal wave with high accuracy by using the equations (1) and (2). It is therefore possible to evaluate the anisotropy of the object.
【００４３】なお、上記実施例では、超音波の励起検出
に接触型の超音波探触子を用いたが、渦電流を利用して
電磁誘導的に超音波を励起検出する電磁超音波法やレー
ザーの熱により被検体に超音波を励起する一方、その励
起超音波を干渉計を用いて検出するレーザー超音波法な
どの非接触超音波計測法を用いても容易に実施できる。
その他、本発明はその要旨を逸脱しない範囲で種々変形
して実施できる。In the above embodiment, the contact type ultrasonic probe is used for detecting the excitation of the ultrasonic wave. However, the electromagnetic ultrasonic method for exciting and detecting the ultrasonic wave by electromagnetic induction utilizing the eddy current, This can be easily performed by using a non-contact ultrasonic measurement method such as a laser ultrasonic method in which an ultrasonic wave is excited in the subject by the heat of the laser and the excited ultrasonic wave is detected using an interferometer.
Besides, the present invention can be variously modified and implemented without departing from the scope of the invention.
【００４４】[0044]
【発明の効果】以上説明したように本発明によれば、板
波モードを適切に選択しつつそれらモードの位相速度，
周波数などから被検体の縦波音速および横波音速を正確
に求めることができ、さらにこれら被検体の縦波音速お
よび横波音速から高精度に被検体の弾性定数を決定で
き、かつ、被検体の異方性をも評価することができる。As described above, according to the present invention, the plate wave modes are appropriately selected and the phase velocities of the modes are
The longitudinal and transverse wave sonic velocities of the subject can be accurately obtained from the frequency, and the elastic constants of the subject can be accurately determined from the longitudinal and transverse wave sonic velocities of the subject, and the difference of the subject It can also be evaluated for tortuosity.
【図１】 本発明に係わる弾性定数測定法を説明するた
めに縦波音速を変化させた場合の位相速度曲線図。FIG. 1 is a phase velocity curve diagram when a longitudinal wave sound velocity is changed in order to explain an elastic constant measuring method according to the present invention.
【図２】 本発明に係わる弾性定数測定法を説明するた
めに横波音速を変化させた場合の位相速度曲線図。FIG. 2 is a phase velocity curve diagram when the acoustic velocity of a transverse wave is changed in order to explain the elastic constant measuring method according to the present invention.
【図３】 被検体の弾性定数を測定する装置の構成図。FIG. 3 is a configuration diagram of an apparatus for measuring an elastic constant of a subject.
【図４】 板波の測定結果と検算結果との関係を説明す
る図。FIG. 4 is a diagram illustrating a relationship between a plate wave measurement result and a verification result.
１ａ…超音波励起用探触子、１ｂ…超音波検出用探触
子、２ａ，２ｂ…くさび、３…被検体、４…発振器、５
…電圧計、６…接触媒質。1a ... Probe for ultrasonic wave excitation, 1b ... Probe for ultrasonic wave detection, 2a, 2b ... Wedge, 3 ... Subject, 4 ... Oscillator, 5
... Voltmeter, 6 ... Contact medium.
Claims (2)
と板波超音波Ｓ１モードの位相速度と周波数とから横波
音速と縦波音速を求めた後、これら横波音速と縦波音速
とから前記被検体の弾性定数を求めることを特徴とする
被検体の弾性定数測定法。1. A transverse wave sound velocity and a longitudinal wave sound velocity are obtained from the phase velocities and frequencies of the plate wave ultrasonic wave A1 mode and the plate wave ultrasonic wave S1 mode propagating through an object, and then the transverse wave sound velocity and the longitudinal wave sound velocity are calculated. A method for measuring an elastic constant of a subject, characterized by obtaining an elastic constant of the subject.
の位相速度および周波数と適宜な縦波音速初期値とから
１次近似横波音速を求めた後、この１次近似横波音速と
板波超音波Ｓ１モードの位相速度および周波数とから１
次近似縦波音速を求め、さらに前記板波超音波Ａ１モー
ドの位相速度および周波数と前記１次近似縦波音速とか
ら２次近似横波音速を求め、この２次近似横波音速と前
記板波超音波Ｓ１モードの位相速度および周波数とから
２次近似縦波音速を求め、以降，順次次数を上げながら
横波音速および縦波音速が収束するまで同様の処理を繰
り返し、この収束して得られた横波音速および縦波音速
から被検体の弾性定数を求めることを特徴とする被検体
の弾性定数測定法。2. A first-order approximate shear wave sound velocity and a plate wave are obtained after obtaining a first-order approximate shear wave sound velocity from the phase velocity and frequency of a plate wave ultrasonic wave A1 mode propagating through an object and an appropriate initial value of the longitudinal wave sound velocity. 1 from the phase velocity and frequency of ultrasonic S1 mode
A second-order approximate longitudinal wave sound velocity is obtained, and a second-order approximating transverse wave sound velocity is calculated from the phase velocity and frequency of the plate wave ultrasonic wave A1 mode and the first-order approximating longitudinal wave sound velocity. The second-order approximate longitudinal wave sound velocity is obtained from the phase velocity and frequency of the sound wave S1 mode, and thereafter, the same process is repeated while sequentially increasing the order until the transverse wave sound velocity and the longitudinal wave sound velocity converge, and the transverse wave obtained by this convergence is obtained. A method for measuring an elastic constant of a subject, which comprises obtaining the elastic constant of the subject from the speed of sound and the acoustic velocity of longitudinal waves.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP3295746A JP2792286B2 (en) | 1991-11-12 | 1991-11-12 | Method for measuring elastic constant of specimen |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP3295746A JP2792286B2 (en) | 1991-11-12 | 1991-11-12 | Method for measuring elastic constant of specimen |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH05133861A true JPH05133861A (en) | 1993-05-28 |
| JP2792286B2 JP2792286B2 (en) | 1998-09-03 |
Family
ID=17824630
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP3295746A Expired - Lifetime JP2792286B2 (en) | 1991-11-12 | 1991-11-12 | Method for measuring elastic constant of specimen |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2792286B2 (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010071888A (en) * | 2008-09-19 | 2010-04-02 | Nippon Steel Corp | Method and device for measuring acoustic velocity of longitudinal wave and transverse wave in material by laser ultrasonic method |
| JP2010071884A (en) * | 2008-09-19 | 2010-04-02 | Nippon Steel Corp | Method and device for measuring acoustic velocity of longitudinal wave and transverse wave in material by laser ultrasonic method |
| JP2011133338A (en) * | 2009-12-24 | 2011-07-07 | Nippon Steel Corp | Method and device for measuring poisson's ratio |
| KR101452441B1 (en) * | 2013-10-23 | 2014-10-24 | 한양대학교 산학협력단 | Measurement method for mechanical behavior of material using laser Ultrasonics and measurement apparatus of the same |
| CN114428119A (en) * | 2022-01-20 | 2022-05-03 | 重庆大学 | Method for inverting elastic constant of composite material with anisotropic characteristics |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101650172B1 (en) * | 2015-05-13 | 2016-08-23 | 한양대학교 산학협력단 | Apparatus and method for measuring the velocity of longitudinal wave and transverse wave |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5766355A (en) * | 1980-10-09 | 1982-04-22 | Kawasaki Steel Corp | Method for deciding aggregation organization of steel plate and material property depending upon aggregation organization by means of on-line system |
| JPS61274256A (en) * | 1985-05-30 | 1986-12-04 | Hitachi Constr Mach Co Ltd | Ultrasonic measurement for elastic constant of solid |
-
1991
- 1991-11-12 JP JP3295746A patent/JP2792286B2/en not_active Expired - Lifetime
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5766355A (en) * | 1980-10-09 | 1982-04-22 | Kawasaki Steel Corp | Method for deciding aggregation organization of steel plate and material property depending upon aggregation organization by means of on-line system |
| JPS61274256A (en) * | 1985-05-30 | 1986-12-04 | Hitachi Constr Mach Co Ltd | Ultrasonic measurement for elastic constant of solid |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010071888A (en) * | 2008-09-19 | 2010-04-02 | Nippon Steel Corp | Method and device for measuring acoustic velocity of longitudinal wave and transverse wave in material by laser ultrasonic method |
| JP2010071884A (en) * | 2008-09-19 | 2010-04-02 | Nippon Steel Corp | Method and device for measuring acoustic velocity of longitudinal wave and transverse wave in material by laser ultrasonic method |
| JP2011133338A (en) * | 2009-12-24 | 2011-07-07 | Nippon Steel Corp | Method and device for measuring poisson's ratio |
| KR101452441B1 (en) * | 2013-10-23 | 2014-10-24 | 한양대학교 산학협력단 | Measurement method for mechanical behavior of material using laser Ultrasonics and measurement apparatus of the same |
| CN114428119A (en) * | 2022-01-20 | 2022-05-03 | 重庆大学 | Method for inverting elastic constant of composite material with anisotropic characteristics |
| CN114428119B (en) * | 2022-01-20 | 2023-11-21 | 重庆大学 | Method for inverting elastic constant of composite material with anisotropic characteristic |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2792286B2 (en) | 1998-09-03 |
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