Equations of Transversal Vibration of a Two-Layer Viscoelastic Plate of Constant Thickness

Abstract

This article discusses the analysis of the general equations of the transverse oscillation of a piecewise-homogeneous viscoelastic plate obtained in the "Oscillations of two-layer plates of constant thickness" article [1].

In this paper, on the basis of a mathematical method, an approximate theory of oscillation of piecewise homogeneous plates is developed, based on considering the plate as a three-dimensional body, on the exact formulation of the three-dimensional mathematical boundary value problem of oscillation under external forces causing transverse oscillations.The theoretical results obtained for solving dynamic problems of transverse vibrations of piecewise homogeneous two-layer plates of constant thickness, taking into account the viscous properties of their material, make it possible to more accurately calculate the stress-strain state of the plates under non-stationary external loads.In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations.The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.