An application of the contour integral method to a mixed problem of dynamic impact theory
type: Item
instance of: scholarly article
title: An application of the contour integral method to a mixed problem of dynamic impact theory
zbMATH Open document ID: 1029.35162
DOI: 10.1023/A:1014807710622
author: S. I. Gaĭduk
author: Nikolaĭ Iosifovich Yurchuk
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: We study the problem on transverse vibrations of a thick viscoelastic plate induced by a dynamic impact at a single point (an instantaneous application of a lumped force). In the mathematical statement, the problem is reduced to finding the function \(u(x,y,t)\) that describes the displacement of points of the midplane of the plate. This function must satisfy the equation \[ {\partial^2u \over\partial t^2}+ \alpha^2\Delta \Delta u+\beta^2 {\partial\over \partial t}(\Delta\Delta u)= {A\over\rho h}\delta (x-x_0,y-y_0) \] in the domain \(D_0=(0<x<a\), \(0<y<b\), \(0<t\leq T<\infty)\), with initial and boundary conditions.
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1916011
zbMATH Keywords: transverse vibrations of a thick viscoelastic plate
zbMATH Keywords: dynamic impact at a single point
MaRDI profile type: Publication
full work available at URL: a:1014807710622
OpenAlex ID: W203988086
description: scientific article; zbMATH DE number 1916011