This paper presents an analytical solution to the mixed boundary value problem for a dynamic rigid rectangular plate on the surface of a layered transversely isotropic half-space. For the contact problem, the mixed boundary conditions at the surface are converted into linear equations by means of Bessel series expansions. Solving these linear equations can get the expression of the contact stress, which can be further utilized to obtain the stresses and displacements of this model by the analytical layer element method of layered media. Additionally, the contact stresses can be used to evaluate the vertical and rocking compliances of a rectangular plate. A good agreement with existing solutions verifies the accuracy of the proposed method, and numerical examples are carried out to investigate the effect of angular frequency, length-to-width ratios, transverse isotropy and the stratification of media.

本文提出了分层横向各向同性半空间表面上动态刚性矩形板混合边值问题的解析解。对于接触问题，通过贝塞尔级数展开将表面的混合边界条件转化为线性方程。求解这些线性方程可以得到接触应力的表达式，进一步利用该表达式可以通过层状介质的解析层元法得到该模型的应力和位移。此外，接触应力可用于评估矩形板的垂直和摇摆柔量。与现有解决方案的良好一致性验证了所提出方法的准确性，并通过数值例子研究了角频率、长宽比、