Wave-propagation in an incompressible hollow elastic cylinder with residual stress

Abstract

A study is presented to observe the effect of residual stress on waves in an incompressible, hyper-elastic, thick and hollow cylinder of infinite length. The problem is based on the non-linear theory of infinitesimal deformations occurring after a finite deformation. A prototype model of strain energy function is used which adequately includes the effects of residual stress and deformation. The expressions for internal pressure and the axial load are calculated and graphical illustrations are presented. Analysis of infinitesimal wave propagation is carried for the axisymmetric case in the considered cylinder. Numerical solution is obtained in the undeformed configuration and analyzed for the two-point boundary-value problem. Dispersion curves are plotted for varying choice of parameters.