Mechanics

Spectral decompositions in dynamic linear viscoelasticity problems for piecewise homogeneous bodies

S. G. Pshenichnov

Lomonosov Moscow State University, Institute of Mechanics

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 is 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.

Key words: wave processes, viscoelasticity, dynamics of piecewise homogeneous bodies, layer package, spectral decomposition, eigenvalues.

UDC: 539.551, 534.5, 534-16

Received: 20.03.2024

DOI: 10.55959/MSU0579-9368-1-66-2-8

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2025, 80:2, 63–72

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