Exact solutions for elastic surface waves with general lateral dependencies in layered structure

在这个建议中，我们计划发展一个表面波理论，具有一般的横向依赖性。为了更深入地了解这个问题，这将首先在由线性各向同性弹性层组成的结构中进行。在这些结果确定之后，将采用类似的方法来研究各向异性和/或预应力的影响。对于各向同性的情况，我们期望找到广泛的精确解，这取决于深度和两个横向变量。这些解在两个横向变量中明显表现出不同的行为。在一些特殊情况下，我们期望用平面波前和多项式横向依赖来描述波。对于在导论中提到的与弹性连续体相关的适当类型的偏微分方程，将采用各种分析方法。为了比较解析解和作为辅助分析的初步指导，我们将大量依赖于用于波传播的先进的各种渐近过程，特别是在非均匀介质中。这将包括，例如，射线方法。射线法是一种建议的访问教授具有重要国际专业知识的方法。层状结构很可能需要在各向异性和/或预应力理论框架内使用传播子和传递矩阵方法以及Stroh公式。

Within this proposal we are planning to develop a theory for surface waves, with general lateral dependency. To gain some insight into the problem, this will initially be carried out in respect of structures composed of linear isotropic elastic layers. After these results have been established, a similar approach will be applied to investigate the influence of anisotropy and/or pre-stress. In respect of the isotropic case we expect to find a wide class of exact solutions, depending on depth and on the both lateral variables. These solutions will clearly show distinctly different behavior in both lateral variables. Among particular cases of interest, we expect to describe waves with plane wave fronts and polynomial transverse dependency. Various analytical methods will be employed for the appropriate type of partial differential equations associated with elastic continua which were mentioned in the Introduction. Both for comparison of analytical solutions and as an initial guide to aid analysis, we will rely heavily on advanced various asymptotic procedures used for wave propagation, especially in inhomogeneous media. This will include, for example, the ray method. The ray method is a method in which the proposed visiting Professor has significant international expertise. The layered structures may well require use of propagator and transfer matrix methods and the Stroh formulism, within both an anisotropic and/or pre-stressed theoretical framework.