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ADDITIONAL TECHNICAL PAPERS

General Three-Dimensional Analysis of Transient Elastic Waves in a Multilayered Medium

[+] Author and Article Information
Chien-Ching Ma1

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of Chinaccma@ntu.edu.tw

Genn-Sheng Lee

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China

1

Corresponding author.

J. Appl. Mech 73(3), 490-504 (Jul 28, 2005) (15 pages) doi:10.1115/1.2125989 History: Received November 29, 2004; Revised July 28, 2005

The propagation of transient elastic waves in a three-dimensional multilayered medium subjected to general dynamic loadings is analyzed in this study. One of the objectives of this study is to develop an effective analytical method for determining transient full-field solutions in the multilayered medium subjected to nonaxisymmetric dynamic loadings. The wave field is decomposed into two parts; one is the P-SV system of waves and the other is the SH system, each of which propagates independently in a horizontally layered medium. A simple relationship between solutions of two- and three-dimensional problems in the Fourier transform domain is also presented. A matrix solution in the triple transform domain is obtained by Brownwich expansion and the inverse transform is inverted by Cagniard’s method. The matrix representation of the solution can be easily used to calculate the transient response of the multilayered medium without tracing the ray path manually. The formulas presented in this study enable us to calculate the long-time transient responses of the multilayered medium for three-dimensional configuration. The theoretical transient solution for a layer overlaying a half-space subjected to an arbitrarily oriented point force is presented in detail. The numerical calculations are compared with experimental measurements for the surface displacement response on a plate and a layer overlaying a half-space subjected to an axisymmetric point force. The numerical investigation is also carried out for nonaxisymmetric loading problem of a layer overlaying a half-space.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometrical configuration and coordinate system of a three-dimensional n-layered medium

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Figure 2

One layer of elastic solid overlaying a half-space subjected to axisymmetric and nonaxisymmetric loadings

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Figure 3

The transient response of vertical displacement at x=2h on the free surface subjected to an axisymmetric loading

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Figure 4

The transient response of radial displacement at x=2h on the free surface subjected to an axisymmetric loading

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Figure 5

The transient responses of vertical displacements at r=2h, 4h, 6h, 8h, 10h, 12h, and 14h on the free surface subjected to an axisymmetric loading

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Figure 6

The transient responses of vertical displacements at r=2h, 4h, 6h, 8h, 10h, 12h, and 14h on z=−h∕2 subjected to an axisymmetric loading

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Figure 7

The transient responses of vertical displacements at r=2h, 4h, 6h, 8h, 10h, 12h, and 14h on the interface subjected to an axisymmetric loading

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Figure 8

The transient responses of vertical displacements at x=2h on the free surface subjected to an axisymmetric loading for various values of μ(2)∕μ(1)

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Figure 9

The transient responses of displacements along x and z directions at x=2h on the free surface subjected to a non-axisymmetric loading along the x direction

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Figure 10

Comparison of measured and calculated transient vertical displacements on the free surface of a half-space made of aluminum

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Figure 11

Comparison of measured and calculated transient vertical displacements on the free surface of a aluminum plate (3cm)

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Figure 12

Comparison of measured and calculated transient vertical displacements on the free surface of a aluminum plate (6cm)

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Figure 13

The calibration experiment for pencil lead breaking source and NBS conical transducer

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Figure 14

Comparison of measured and calculated transient vertical displacements on the free surface of an acrylic plate

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Figure 15

Comparison of measured and calculated transient vertical displacements on the free surface of an acrylic-steel plate

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