Torsional wave dispersion relations in a pre‐stressed bi‐material compounded cylinder

TLDR: In this article, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated under the assumption that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential.

Abstract: Within the framework of the piecewise homogeneous body model and through the application of the three-dimensional linearized theory of elastic waves in an initially stressed body, the torsional wave dispersion in pre-stretched bi-material compounded cylinders is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential. The numerical investigations are made for steel (St) (as a material for the solid cylinder) and bronze (Br) (as a material for a hollow covering cylinder). According to the numerical results obtained, the influence of the problem parameters such as the initial stresses in the components of the bi-material compounded cylinder, the values of the mechanical and physical constants of the components, and the geometrical parameters (such as the relation of the thickness of the covering cylinder with the radius of the inner solid cylinder on the dispersion curves) are analyzed.