Vibrations of multilayer plates under the effect of impulse loads. Three-dimensional theory
type: Item
instance of: scholarly article
title: Vibrations of multilayer plates under the effect of impulse loads. Three-dimensional theory
zbMATH Open document ID: 0955.74032
DOI: 10.1016/S0020-7683(98)00156-5
author: A. N. Shupikov
author: S. V. Ugrimov
published in: International Journal of Solids and Structures
publication date: 2001-02-21T00:00:00Z
review text: In the case of relative thickness, two-dimensional theories of multilayer plates yield incorrect results by the investigation of wave processes. The behavior of multilayer plates can be described more accurately by using the three-dimensional theory of elasticity. In the reviewed paper, the authors propose an analytical numerical approach to the study of transient vibrations of a multilayer plate under impulsive loading by employing the three-dimensional theory of elasticity. The behavior of plate is described by Lamé's equations. The solution for displacement functions are expressed as double Fourier series in direction of plane coordinates, satisfying boundary conditions on the plate contour. The partial derivatives of these functions in the direction of the normal coordinate are replaced by their finite-difference approximations. As a result, the problem is reduced to the integration of a system of ordinary differential equations with constant coefficients. The procedure described in this paper allows to obtain the solution of the title problem without large computational difficulties.
reviewed by: Yuri N. Sankin
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 1341404
zbMATH Keywords: multilayer plate
zbMATH Keywords: impulsive loading
zbMATH Keywords: three-dimensional theory of elasticity
zbMATH Keywords: Lamé's equations
zbMATH Keywords: double Fourier series
zbMATH Keywords: finite-difference approximations
zbMATH Keywords: system of ordinary differential equations with constant coefficients
MaRDI profile type: Publication
full work available at URL: s0020-7683(98)00156-5
OpenAlex ID: W2016915959
description: scientific article; zbMATH DE number 1341404