Open Access

ARTICLE

Transient Analysis of Elastic Wave Propagation in Multilayered Structures

Yi-Hsien Lin¹, Chien-Ching Ma^1,2

1 Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617,R.O.C.
2 Corresponding author. Tel.: +886-2-23659996; fax:+ 886-2-23631755. E-mail address: ccma@ntu.edu.tw (C. C. Ma)

Computers, Materials & Continua 2011, 24(1), 15-42. https://doi.org/10.3970/cmc.2011.024.015

Abstract

In this article, explicit transient solutions for one-dimensional wave propagation behavior in multi-layered structures are presented. One of the objectives of this study is to develop an effective analytical method for constructing solutions in multilayered media. Numerical calculations are performed by three methods: the generalized ray method, numerical Laplace inversion method (Durbin's formula), and finite element method (FEM). The analytical result of the generalized ray solution for multilayered structures is composed of a matrix-form Bromwich expansion in the transform domain. Every term represents a group of waves, which are transmitted or reflected through the interface. The matrix representation of the solution can be used to calculate the transient response, without tracing the ray path manually. Numerical inversion of the Laplace transform by Durbin's formula is also used to construct transient responses. This numerical Laplace inversion technique has the advantage of calculating long-time transient responses for complicated multilayered structures. FEM results agree well with calculations obtained by the generalized ray method and numerical Laplace inversion.

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Keywords

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