In the study of wave propagation through plates and laminates, there are no complete three-dimensional solutions especially if the plate or plies are made of an anisotropic material. In such cases, laminate theories are approximate and often give poor results in comparison with exact solutions. When laminae or plate is highly anisotropic, the small parameter, which is appropriate is usually the modulus ratio, that is, the ratio of some elastic moduli. In the study of wave propagation, in some of the ranges of a wave number, a geometrical parameter, non-dimensional wave number, may be dominant in dispersion relations. The interaction between these two parameters, the modulus ratio and the geometric parameter, is a complicated one and it is not obvious which parameter will dominate in the given circumstances. The influence of these two parameters on dynamical behaviour of the plate, especially in the dispersion relation is examined in the present paper. To consider the singular perturbation problem, where at least one boundary layer arises, it is usual to apply the method of asymptotic expansions. In that case, a matched asymptotic expansion is suitable for the consideration. To satisfy well the corresponding equations, it was necessary to develop outer and inner expansions which are valid in the so-called outer and inner regions, respectively. Then, matching conditions have been derived, which lead to establishing an asymptotic expansion which is valid uniformly in the whole domain.

在研究通过板和层压板传播的波时，没有完整的三维解决方案，尤其是当板或层板由各向异性材料制成时。在这种情况下，层压理论是近似的，与精确解相比，通常会给出较差的结果。当薄层或板具有高度各向异性时，比较合适的小参数通常是模量比，即某些弹性模量的比值。在波传播的研究中，在波数的某些范围内，几何参数，无量纲波数，可能在色散关系中占主导地位。模量比和几何参数这两个参数之间的相互作用是一个复杂的相互作用，在给定的情况下哪个参数占主导地位并不明显。本文研究了这两个参数对板动力学行为的影响，特别是在色散关系中。为了考虑至少出现一个边界层的奇异扰动问题，通常应用渐近展开的方法。在这种情况下，匹配的渐近展开适合于考虑。为了很好地满足相应的方程，有必要分别开发在所谓的外部和内部区域中有效的外部和内部扩展。然后，推导出匹配条件，这导致建立在整个域中一致有效的渐近展开。在至少出现一个边界层的地方，通常采用渐近展开法。在这种情况下，匹配的渐近展开适合于考虑。为了很好地满足相应的方程，有必要分别开发在所谓的外部和内部区域中有效的外部和内部扩展。然后，推导出匹配条件，这导致建立在整个域中一致有效的渐近展开。在至少出现一个边界层的地方，通常采用渐近展开法。在这种情况下，匹配的渐近展开适合于考虑。为了很好地满足相应的方程，有必要分别开发在所谓的外部和内部区域中有效的外部和内部扩展。然后，推导出匹配条件，这导致建立在整个域中一致有效的渐近展开。