The dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder with the initial inhomogeneous thermal stresses

Abstract

The paper studies the influence of the initial inhomogeneous thermal stresses on the dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder within the scope of the 3D linearized theory of elastic waves in initially stressed bodies. The initial static thermal stresses are determined within the scope of the uncoupled classical linear theory of thermo-elasticity and it is assumed that the temperature change in the cylinder is caused by the heating or cooling of the inner and outer surfaces of the cylinder. The discrete analytical solution method is employed for the solution to the corresponding equations of the wave propagation. Concrete numerical results are obtained for the cylinder, the materials of the layers of which are steel and aluminum, as well for the cylinder made of steel only. Numerical results on the influence of the initial inhomogeneous thermal stresses on the dispersion curves related to the first, second and third modes are presented and discussed. In particular, it is established that the cooling or the heating of the outer and inner surfaces of the bi-layered hollow cylinder influences the dispersion curves not only in the quantitative sense, but also in the qualitative sense.