一种求解瑞利波散射问题的修正边界元方法  

A Modified Boundary Element Method for Scattering Problem of Rayleigh Wave

作　　者：笪益辉 王彬[1] 钱征华[1] 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, Nanjing, 210016)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室/航空宇航学院,南京210016

出　　处：《固体力学学报》2017年第5期379-390,共12页Chinese Journal of Solid Mechanics

基　　金：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

摘　　要：边界元法的一大优势是用于求解半空间等无限域问题,但在求解弹性波的传播问题中,传统边界元法采用的全平面或全空间格林函数会在截断边界处产生虚假的反射回波,这会引起散射场求解的误差.为了避免这种误差,论文在传统边界元法基础上提出一种修正边界元法,该修正方法主要包括:以瑞利波形式的远端散射场代替原本因截断而舍去的部分,通过互易定理建立单位瑞利波和全平面格林函数的积分方程,求得修正系数,并代入修正边界元矩阵,计算出瑞利波的散射场.文中基于该方法计算了无缺陷平面的瑞利波(与解析解的误差为1.24×10-5),并运用该方法计算了不同缺陷的散射场.由文中对比结果表明,论文所提修正边界元法可准确求解瑞利波散射场,为基于表面波的缺陷反演问题研究提供了有效的正演途径.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.

关 键 词：修正边界元法 瑞利波 散射场 格林函数 

分 类 号：O347.41[理学—固体力学]