Alternative Spatial Growth and Decay Estimates for Constrained Motion in an Elastic Cylinder with Voids
Emilian Bulgariu · Annals of the Alexandru Ioan Cuza University - Mathematics · 2011
Alternative Spatial Growth and Decay Estimates for Constrained Motion in an Elastic Cylinder with Voids The aim of this paper is to study the alternative spatial growth and decay behavior for the motion of a finite or semi-infinite cylinder composed of a non-homogeneous anisotropic linear elastic material with voids, subject to null supply terms and null lateral boundary conditions. The motion induced by displacement and volume fraction field prescribed on the base is constrained to have the displacement, velocity, volume fraction and the derivative with respect to time of volume fraction at a given time proportional to their respective initial values. Neither initial data nor the asymptotic behavior at large axial distance are specified. The estimates that are either exponentially grow or decay are derived from a differential inequality depending on cross-sectional energy flux. An explicit bound, in terms of the problem data, is constructed for the amplitude in each decay estimate.