Development of a three dimensional perfectly matched layer for transient elasto-dynamic analyses

by Johnson, Anthony N.

A time dependent, three dimensional finite element approach to the development of a perfectly matched layer for numerical calculations of surface wave radiation in a half space is presented. The development of this new element required the coupling of a system of linear, second-order, partial differential equations which describe elastic wave propagation, together with their related boundary conditions, into a single weak-form (Galerkin) wave equation, from which the characteristics of a composite finite element matching layer were derived. An important problem of interest, and the motivation for this work, is the optimization of a source for use in a seismo-acoustic sonar for the detection of buried mines. Validation of the perfectly matched layer occurs by employing it in a finite element analysis to compute the radiation from a particular transient seismo-acoustic source array and showing that the results agreed with the results of previous field experiments using the same source performed by Naval Postgraduate School students. Various source excitations are presented which maximize the energy of the unidirectional Rayleigh wave while suppressing the energy of associated body waves. Radiation characteristics are analyzed in a linear, isotropic, homogeneous half space with a discrete number of transient seismic sources. The hp-adaptive finite element code SAFE-T (Solid Adaptive Finite Element - Transient), a Finite Element Method (FEM) implementation developed by the author utilizing Altair Engineering’s Prophlex kernel, is used to perform the numerical computations. Results for radial and vertical wave strengths are given in terms of their total displacement magnitudes. This work represents an important step forward in the development of tools needed to pursue seismo-acoustic sonar technology for buried mine detection, as well as for the analysis of all three-dimensional, time-dependent elasto-dynamic problems. v