Torsional Wave Dispersion in a Pre-Strained Hollow Sandwich Cylinder With Soft Core

Abstract

In this work a torsional wave dispersion in a pre-strained three-layered (sandwich) hollow circular cylinder made from hyper-elastic materials is studied. It is assumed that the material of the core layer is soft than the materials of skin layers and the investigations are carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The mechanical relations of the materials of the cylinders are described through their harmonic potential. The analytical expression is obtained for the low wave number limit values of the torsional wave propagation velocity. Moreover, numerical results on the influence of the problem parameters, such as initial strains arising as a result of the stretching or compression of the cylinders along the torsional wave propagation direction, thickness of the layers, mechanical constants of the layers’ materials and etc, are presented and discussed.