Axisymmetric longitudinal wave dispersion in a bi-layered circular cylinder with inhomogeneous initial stresses

Abstract

The paper studies the axisymmetric longitudinal wave propagation in a bi-layered hollow cylinder with inhomogeneous initial stresses by utilizing the 3D linearized theory of elastic waves in initially stressed bodies. It is assumed that the initial stresses in the cylinder are caused by the internal and external hydrostatic pressures. Assuming that the materials of the layers of the cylinder are sufficiently stiff, these initial stresses are determined within the scope of the classical linear theory of elasticity. The discrete analytical method is employed for the solution to the corresponding 3D linearized equations of motion. The dispersion equation is obtained which is solved numerically for various values of the problem parameters. As a result of this solution, the dispersion curves are constructed and, according to these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves obtained for the lowest first and second modes is established. Analysis of the results shows that the inhomogeneous initial stresses not only quantitatively but also qualitatively act on the character of the dispersion curves.