研究了在平面应变假设条件下，弹性体内一类表面波的求解以及一般解的结构。文献[6]只给出了表面波的一个右行波解，且无求解过程。基于表面波的解可表示为膨胀波和畸变波的叠加，利用分离变量法求出了表面波的一般解，一般解包含无穷多个行波解，这些行波解可能为左行波、右行波或左右行波的叠加。另外，还讨论了表面波一般解的结构以及不同行波解波速之间的关系，发现不同行波的波速大小相同。
Abstract
Under the assumption of plane strain, the solution and the solution structure of a class of surface waves in an elastic body have been studied in the previous literature. In reference [6], only one right traveling wave solution of a surface wave has been given, without a detailed solution process. Based on the fact that the solution of a surface wave can be expressed as the superposition of an expansion wave and a distorted wave, the general solution of surface wave is obtained by using the method of separating variables. The solution contains an infinite number of traveling wave solutions, which may be left traveling waves, right traveling waves or a superposition of left and right traveling waves with the same wave velocity. In addition, the solution space of surface waves and the velocity relationship between different solutions are discussed.
关键词
平面应变假设 /
膨胀波 /
畸变波 /
表面波
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Key words
plane strain hypothesis /
expansion wave /
distortion wave /
surface wave
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参考文献
[1] THOMSON W T. Transmission of elastic waves through a stratified solid medium[J]. Journal of Applied Physics, 1950, 21(2):89-93.
[2] HASKELL N A. The dispersion of surface waves on multilayered media[J]. Bulletin of the Seismological Society of America, 1953, 43(1):17-34.
[3] 杨天春, 王齐仁, 廖建平. 瑞利面波单点谱比曲线的理论计算与分析[J]. 应用力学学报, 2015, 32(4):630-635, 707. YANG T C, WANG Q R, LIAO J P. Study on spectral ratio of horizontal to vertical spectral ratio for Rayleigh waves[J]. Chinese Journal of Applied Mechanics, 2015, 32(4):630-635, 707. (in Chinese)
[4] 柴华友, 柯文汇, 黄祥国, 等. 表面源激发的瑞利波传播特性分析[J]. 岩土力学, 2017, 38(2):325-332, 340. CHAI H Y, KE W H, HUANG X G, et al. Analysis of propagation behavior of Rayleigh waves activated by surface sources[J]. Rock and Soil Mechanics, 2017, 38(2):325-332, 340. (in Chinese)
[5] 阎守国, 谢馥励, 张碧星. 含孔隙介质的分层半空间表面瑞利波的衰减特性[J]. 地球物理学报, 2018, 61(2):781-791. YAN S G, XIE F L, ZHANG B X. Attenuation of Rayleigh waves in a layered half-space surface with a porous layer[J]. Chinese Journal of Geophysics, 2018, 61(2):781-791. (in Chinese)
[6] 谷超豪, 李大潜, 沈玮熙. 应用偏微分方程[M]. 北京:高等教育出版社, 2014:54-62. GU C H, LI D Q, SHEN W X. Partial differential equation[M]. Beijing:Higher Education Press, 2014:54-62. (in Chinese)
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