Substantiation of two-scale homogenization of the equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material |
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| Authors: | A A Amosov I A Goshev |
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| Institution: | (1) Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), ul. Krasnokazarmennaya 14, Moscow, 111250, Russia |
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| Abstract: | Initial-boundary value problems for the system of quasilinear operator-differential equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material with nonsmooth rapidly oscillating coefficients and initial data are investigated. The system involves the hysteresis Prandtl-Ishlinskii operator. Passage to the limit to initial-boundary value problems for the corresponding system of two-scale homogenized operator integro-differential equations is strictly substantiated globally in time without assuming that the data are small. |
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| Keywords: | system of equations of longitudinal vibrations viscoelastoplastic materials method of two-scale homogenization system of quasilinear operator-differential equations initial-boundary value problem |
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