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Steady vibrations problem in the theory of viscoelasticity for Kelvin‐Voigt materials with voids
Author(s) -
Svanadze Maia M.
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210131
Subject(s) - viscoelasticity , uniqueness , boundary value problem , mathematical analysis , kelvin–voigt material , mathematics , vibration , singular integral , uniqueness theorem for poisson's equation , integral equation , physics , thermodynamics , quantum mechanics
In this paper the linear theory of viscoelasticity for Kelvin‐Voigt materials with voids is considered. The uniqueness and existence theorems for internal boundary value problem (BVP) of steady vibrations are proved by means of the potential method (boundary integral method) and the theory of singular integral equations. The application of this method to the 3D BVP of the considered theory reduces this problem to 2D singular integral equation. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)