期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 49, 期 3-4, 页码 567-575出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2011.10.025
关键词
Stratified layer; Viscoelastic solid; Matricant; Reflection-transmission; Low- and high-frequency approximations
类别
The paper investigates time-harmonic wave propagation in continuously stratified solids and provides the results of a reflection-transmission process generated by a layer sandwiched between homogeneous half-spaces. The layer is continuously stratified and allows for jump discontinuities at a finite number of planes. The dissipative effects are accounted for through the classical Boltzmann law of viscoelasticity. By using displacement and traction as convenient vector variables, the governing equations are considered in a vector Volterra integral equation and the solution is determined by means of a matricant. Next the matricant is applied to determine the reflection and transmission coefficients of a layer, with a generic piecewise continuous profile of the material properties. The reflection-transmission process produced by an obliquely incident wave, is considered for horizontally-polarized waves. The low-frequency approximation is derived for the reflection and transmission coefficients. Next, the high-frequency approximation is investigated by a WKB-like procedure which involves a complex valued frequency-dependent shear modulus. The displacement solution is obtained for the forward- and the backward-propagating waves in the layer along with the reflection and transmission coefficients. (C) 2011 Elsevier Ltd. All rights reserved.
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