Theoretical Analysis and Numerical Simulation of Transient Wave in Homogeneous and Nonhomogeneous Multilayered Media
Date Issued
2011
Date
2011
Author(s)
Lin, Yi-Hsien
Abstract
In this study, one-dimensional transient wave-propagation in homogeneously and inhomogeneously multilayered media are analyzed by Laplace transform technique. The numerical calculations for homogeneously multilayered media are performed by three methods: generalized ray method, numerical Laplace inversion method (Durbin’s formula), and finite element method (FEM). The analytical result of generalized ray solution for multilayered structures is composed of matrix-form Bromwich expansion in the transform domain. Every term represents a group of waves which is transmitted or reflected through the interface. The numerical inversion of Laplace transform by Durbin’s formula is also used to calculate the transient responses. This numerical Laplace inversion technique has the advantage of calculating the long-time transient responses for complicated multilayered structures. FEM result also agrees well with the calculations by generalized ray method and numerical Laplace inversion.
For the transient-wave problem of inhomogeneously multilayered media, we use Laplace transform technique and the numerical Laplace inversion (Durbin’s formula) to calculate the dynamic behavior of the polynomial FGM (functionally graded material) slab. In addition, the FGM slab is approximated as a multilayered medium with homogeneous material in each layer. The transient responses of FGM formulation and multilayered solution are discussed in detail. Furthermore, transient-wave in inhomogeneously multilayered media is analyzed. In the numerical calculation, three-layered functionally graded media is used for analysis and the degenerative problem of an FGM bounded to two elastic homogeneous materials is discussed.
Finally, the numerical calculations of the transient responses for randomly distributed, periodically distributed, and continuously distributed multilayered media are performed to investigate if the effective material concept is suitable for dynamic analysis.
Subjects
FGM
generalized ray
transient response
multilayered
Type
thesis
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