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《Chinese Journal of Solid Mechanics》 2017-05
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A Modified Boundary Element Method for Scattering Problem of Rayleigh Wave

Yihui Da;Bin Wang;Zhenghua Qian;State Key Laboratory of Mechanics and Control of Mechanical Structures/College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics;  
The boundary element method(BEM)has the advantage of solving infinite field problems such as those concerning half-spaces.However,for elastic wave propagation problems,spurious reflected waves will occur at the truncation points when using the conventional BEM,if the full-space Green's function is adopted.How to reduce this error produced by spurious reflected waves is studied in this paper.A modified BEM based on the conventional BEM is proposed to analyze scattered fields of the two-dimensional Rayleigh waves in 2-D half plane.It consists of three steps:(1)establishing a modified boundary integral equation and extracting correction factors;(2)calculating correction factors;(3)converting boundary integral equations into matrix equations and solving the matrix equations.In the first step,two infinite integrals in the boundary integral equation are defined as two correction factors,respectively.In the second step,the two correction factors are solved by the conventional BEM in the left half plane and the right half plane,respectively.In the third step,matrix assembly of the conventional BEM is adjusted in accordance with the correction factors,so that a least-squares solution is obtained.Within this modified method,Rayleigh waves are calculated in a half plane without defects,and a higher precision is obtained than using the conventional BEM.Meanwhile,spurious reflected waves cannot be observed in time domain by the modified BEM.In simulations of defects of different shapes,the scattered waves calculated by the modified BEM can satisfy the boundary integral equation,where the Rayleigh wave component of half-plane fundamental solution is adopted.Comparison of the results show that the modified BEM proposed in the paper can accurately solve the scattering problem of Rayleigh waves,which provides an effective forward simulation way to further investigate the inverse problem of flaw reconstruction based on surface waves.
【Fund】: 国家自然科学基金(51405225 11502108和11232007);; 江苏省自然科学基金(BK20140808和SBK20140037);; 教育部新世纪优秀人才支持计划(NCET-12-0625);; 南京航空航天大学基本科研业务费(NE2013101)资助
【CateGory Index】: O347.41
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