Study on the scattering of 2-D Rayleigh waves by a cavity based on BEM simulation

Weiwei Liu,조윤호,PHANHAI DANG,Jan D. Achenbach 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.3

A frequency domain boundary element method is introduced in this paper to simulate the scattering of two-dimensional Rayleigh waves by a cavity on the surface of an elastic half-space. This numerical method allows the Rayleigh wave to escape the truncated boundary without producing any spurious reflections. The numerical results of the displacements and stresses of a 2-D Rayleigh wave which travels along a flat surface of an elastic half-infinite medium are in good agreement when compared with theoretical ones. The problem of a Rayleigh wave scattering by a cavity on the surface of an elastic half-infinite medium is simulated by the proposed numerical method. The result is taken as the benchmark to introduce an approximate analytical method for such problems of scattering by a cavity on the surface. This numerical method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary scheme is discussed in detail.

Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe

Lee, Jaesun,Achenbach, Jan D.,Cho, Younho Elsevier 2018 Ultrasonics Vol.84 No.-

<P><B>Abstract</B></P> <P>Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The scattering of the lowest torsional mode is analyzed by the reciprocity theorem. </LI> <LI> The solution of wave scattering amplitude ratio is presented in simple form. </LI> <LI> The presented method is simple to obtain the scattered amplitude compared to FEM. </LI> <LI> This results can play a significant role in quantitative signal interpretation. </LI> </UL> </P>

Boundary Element Method for Scattering Problems of Surface Waves in a Half-space

Haidang Phan,Younho Cho,Jan D. Achenbach 대한기계학회 2013 대한기계학회 춘추학술대회 Vol.2013 No.5

A Treatment for Truncated Boundary in a Half-Space with 2-D Rayleigh Wave BEM

Taeho Ju,Younho Cho,Haidang Phan,Jan D. Achenbach 한국비파괴검사학회 2011 한국비파괴검사학회지 Vol.31 No.6

Analysis of two-dimensional Rayleigh wave scattering pattern by a surface defect is studied through modified boundary element method. BEM proposed in this paper has special treatment at each end of boundary which should have the Rayleigh wave go away without any generation of virtual reflections. It is shown that treatment for truncated boundary which is used to model two-dimensional Rayleigh waves" behavior in an elastic half-space is successfully implemented. To check numerical results" accuracy, time domain IFFT signal of the displacements is presented. Improvement on getting rid of unwanted influence of truncated boundary induced by 2-D Rayleigh waves on a flat surface of an elastic half-infinite medium is shown. As a final goal, the numerical results of Rayleigh wave scattering trend are plotted and they are compared with theoretical curves to prove its accuracy.

위상배열 유도초음파 검사의 이론적 고찰

이재선(Jaesun Lee),조윤호(Younho Cho),Jan D. Achenbach 한국비파괴검사학회 2011 한국비파괴검사학회지 Vol.31 No.4

유도초음파를 활용한 진단 기술은 기존의 체적파를 이용한 진단 기법과 달리 장거리 진단의 장점 때문에 널리 사용된다. 대부분의 산업현장에서는 배관이 코팅되어 있거나 땅속이 묻혀있다. 이러한 경우 감쇠의 영향으로 기존의 방식으로는 진단에 어려움이 있다. 본 연구에서는 배관에서 전파되는 유도초음파 전파 모드별 음장을 직교모드확장기법을 이용하여 계산하였다. 단일 탐촉자에 의해 전파되는 유도초음파의 음장과 다중 탐촉자 모델링을 바탕으로 배관에서 전파되는 음장 특성을 해석하기 위해 유도초음파 모드별 집속 기술이 사용되었다. 추가적으로 배관에서 전파되는 유도초음파를 가진하는 탐촉자의 개수에 따른 집속 민감도가 종형 모드와 휨형 모드를 이용하여 계산되었다. 본 연구를 통하여 단일 탐촉자에 의해 가진된 유도초음파와 집속 알고리즘을 적용한 다중 탐촉자에 의해 가진된 음장을 비교하여 높은 에너지가 집속 되는 것을 확인 하였다. Guided waves inspection techniques that are different with inspection technique by bulk waves are widely used in pipe line evaluation due to advantages of long distance inspection. However, most of pipe lines at industrial fields are buried and/or coated. In this case, due to the attenuation effect from soil and/or coating material, there are a lot of difficulty on inspection by conventional ultrasonic technique. In this paper, guided waves propagating patterns are calculated with respect to excitation mode by Normal Mode Expansion(NME). Guided waves patterns based on excited by single transducer and guided wave focusing technique have employed to analyze focusing pattern on a pipe. A longitudinal mode and high order flexural modes are used with various number of transducers to determine sensitivity. Guided waves energy excited by multi transducer with focusing algorithm was successfully focused at a desired point.

배관에서 상반정리를 활용한 비틀림파의 산란 신호 진폭의 닫힘해 계산 연구

이재선(Jaesun Lee),조윤호(Younho Cho),Jan D.Achenbach 대한기계학회 2015 대한기계학회 춘추학술대회 Vol.2015 No.11

The use of guided wave is suitable for inspection of long range pipelines. Surface corrosion is often found as major defect type in pipelines. Guided wave interaction signal with the surface corrosion can provide useful feature for sizing and classification. Reciprocity relation is well established theorem to convert complicate mathematical expression to simpler manner. The approach has been already applied to the plate and half-space structures for the closed form solutions of scattered amplitude. However, the case for the cylindrical structure has not been reported yet. In this paper, the scattering of torsional wave, which is widely used in commercial units, is explored by the reciprocity theorem approach. The amplitudes of the propagating waves can easily be obtained with a much simpler calculation by reciprocity relation with closed form solution. The scattered amplitude ratio of circular and rectangular shape surface defect is presented in this paper as examples. The closed form solution can play a significant role in quantitative signal interpretation.

Frequency Window Method for the Vibration of Secondary Structural Systems

Kyung-Won Min(민경원),Takeru Igusa,Jan D. Achenbach 한국소음진동공학회 1991 한국소음진동공학회 학술대회논문집 Vol.1991 No.6

배관에서 상반 정리를 활용한 비틀림 파의 산란 신호 진폭의 닫힘 해 계산 연구

이재선(Jaesun Lee),조윤호(Younho Cho),Jan D. Achenbach 대한기계학회 2016 大韓機械學會論文集A Vol.40 No.7

유도초음파를 활용한 비파괴검사기법은 장거리 배관 검사에 많이 활용된다. 장시간 사용에 따라 배관에는 표면 부식과 같은 형태의 결함이 주로 발생한다. 표면 부식형 결함의 경우 장거리 유도 초음파 검사기법을 활용한 신호 해석에 어려움이 있다. 상반 정리는 복잡한 수학적 표현을 간단히 나타내주는 기법으로 잘 알려져 있다. 상반 정리는 평판, 반무한체의 산란 문제를 해결하는데 이미 적용된 바가 있지만 원통형 구조물에서는 적용된 사례가 없다. 이 논문에서는 배관 진단을 위해 상용 장비에서 많이 사용되는 비틀림파의 산란 신호를 상반 정리를 적용하여 해석하였다. 산란 신호는 상반 정리를 활용하여 산란 체의 형태와 위치에 따라 단순한 닫힘 해로 표현하였다. 타원형 결함과 사각 결함의 폭과 깊이 변화에 따라 주파수 별로 발생되는 산란 신호가 계산되었으며, 주파수 증가에 따른 주기적인 결과를 나타내는 것을 확인하였다. 산란 신호 해석을 위한 닫힘 해는 결함의 크기를 정량적으로 해석하는데 중요한 역할을 할 것으로 기대된다. Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation.

경계요소법을 활용한 Lamb 파의 산란 해석

주태호(Taeho Ju),조윤호(Younho Cho),Jan D. Achenbach,Jianmin Qu 대한기계학회 2013 대한기계학회 춘추학술대회 Vol.2013 No.5

A Treatment for Truncated Boundary in a Half-Space with 2-D Rayleigh Wave BEM

Ju, Tae-Ho,Cho, Youn-Ho,Phan, Haidang,Achenbach, Jan D. The Korean Society for Nondestructive Testing 2011 한국비파괴검사학회지 Vol.31 No.6

Analysis of two-dimensional Rayleigh wave scattering pattern by a surface defect is studied through modified boundary element method. BEM proposed in this paper has special treatment at each end of boundary which should have the Rayleigh wave go away without any generation of virtual reflections. It is shown that treatment for truncated boundary which is used to model two-dimensional Rayleigh waves' behavior in an elastic half-space is successfully implemented. To check numerical results' accuracy, time domain IFFT signal of the displacements is presented. Improvement on getting rid of unwanted influence of truncated boundary induced by 2-D Rayleigh waves on a flat surface of an elastic half-infinite medium is shown. As a final goal, the numerical results of Rayleigh wave scattering trend are plotted and they are compared with theoretical curves to prove its accuracy.