Thompson Ian, Abrahams I David, Norris Andrew N
Department of Mathematics, University of Manchester, United Kingdom.
J Acoust Soc Am. 2002 Nov;112(5 Pt 1):1756-65. doi: 10.1121/1.1506686.
This paper is concerned with an investigation into the existence of waves propagating along a free edge of an orthotropic plate, where the edge is inclined at arbitrary angle to a principal direction of the material. After deriving the governing equation and edge conditions, an edge wave ansatz is substituted into this system to reduce it to a set of algebraic equations for the edge wave wave number and wave vector. These are solved numerically for several typical composite materials although analytic expressions can be obtained in the case of special values of the material parameters and inclination angle. It is found that a unique edge wave solution, which generally exhibits oscillation as well as decay away from the free edge, exists in all cases, and its wave speed is independent of its direction of propagation along the plate.
本文关注对沿正交各向异性板自由边传播的波的存在性的研究，其中该边与材料的主方向成任意角度倾斜。在推导控制方程和边界条件后，将一个边波假设代入该系统，以将其简化为一组关于边波波数和波矢量的代数方程。尽管在材料参数和倾斜角的特殊值情况下可以得到解析表达式，但对于几种典型复合材料，这些方程是通过数值求解的。结果发现，在所有情况下都存在唯一的边波解，该解通常在远离自由边时既表现出振荡又表现出衰减，并且其波速与其沿板的传播方向无关。
