On the existence of surface‐wave solutions for anisotropic elastic half‐spaces with free surface
On the existence of surface‐wave solutions for anisotropic elastic half‐spaces with free surface
复制标题
自由表面各向异性弹性半空间面波解的存在性
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
D. Barnett
中科院分区：
文献类型：
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作者：
J. Lothe;D. Barnett
证明了对于半无限各向异性晶体自由表面上给定的传播方向，总是存在具有一定相速度 vR<vL 的表面波解，其中 vL 是极限速度，除非定义极限速度的体波满足自由表面条件的特殊情况。证明是根据表面阻抗，它将表面波表面的振幅与表面所需的外力联系起来。作为相速度函数的阻抗特性决定了对于特定相速度是否存在表面不需要外力的表面波。该证明对于进入分析的特征值问题的简并性也是有效的。
A proof is developed that for a given direction of propagation on the free surface of a half‐infinite anisotropic crystal, a surface‐wave solution with a certain phase velocity vR<vL, where vL is the limiting velocity, will always exist, except in the special case when the bulk wave defining the limiting velocity satisfies the condition of a free surface. The proof is in terms of the surface impedance, which relates the amplitude at the surface of a surface wave with the external forces needed at the surface. The properties of the impedance as a function of phase velocity determines whether a surface wave not requiring external forces at the surface exists for a certain phase velocity. The proof is valid also in the case of degeneracies in the eigenvalue problem entering the analysis.