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.
Key words:system of equations of longitudinal vibrations, viscoelastoplastic materials, method of two-scale homogenization, system of quasilinear operator-differential equations, initial-boundary value problem.