Dispersion Relations of Axisymmetric Wave Propagation in Finite Pre-Stretched Compound Circular Cylinders Made from Highly Elastic Incompressible Materials

Abstract

Dispersion relations of axisymmetric longitudinal wave propagation in a finite pre-strained compound (bi-material) cylinder made from high elastic incompressible materials are investigated within the scope of a piecewise homogeneous body model utilizing three-dimensional linearized theory wave propagation in the initially stressed body. The materials of the inner and outer cylinders are assumed to be neo-Hookean. The numerical results regarding the influence of the initial strains in the inner and outer cylinders on the wave dispersion are presented and discussed. These results are obtained for the case where the material of the inner solid cylinder is stiffer than that of the outer hollow cylinder. At the same time, the following results have been obtained for the following two cases (distinguished from each other by the thickness of the external hollow cylinder): Case 1: The thickness is infinite; Case 2: The thickness is finite.