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Abstract <p>The nonstationary dynamic viscoelasticity problem for a piecewise homogeneous body is considered. It is known that, under certain conditions, the construction of a solution to such a problem can be reduced to finding the eigenvalues of the free oscillation problem. The properties of a spectral set are considered, and a method for searching for its elements if proposed. The theoretical considerations are used to study the unsteady dynamics of a piecewise homogeneous viscoelastic plane-parallel layer. For some specific parameters of this layer, the elements of the spectrum are found, and, then, the transition wave process is studied.</p>

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Spectral Decompositions in Dynamic Linear Viscoelasticity Problems for Piecewise Homogeneous Bodies

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • S. G. Pshenichnov

摘要

Abstract

The nonstationary dynamic viscoelasticity problem for a piecewise homogeneous body is considered. It is known that, under certain conditions, the construction of a solution to such a problem can be reduced to finding the eigenvalues of the free oscillation problem. The properties of a spectral set are considered, and a method for searching for its elements if proposed. The theoretical considerations are used to study the unsteady dynamics of a piecewise homogeneous viscoelastic plane-parallel layer. For some specific parameters of this layer, the elements of the spectrum are found, and, then, the transition wave process is studied.