Vibrations and Stability of a Thermoelastic Cylindrical Shell Being in External Contact with a Thermoelastic Isotropic Medium

Abstract

Transient vibrations and dynamic stability of an infinitely long, shallow thermoelastic circular cylindrical shell compressed along its generator by forces uniformly distributed along its guide are considered. The shell is embedded into an unbounded thermoelastic medium with a cylindrical cavity and is being in an external smooth contact with the surrounding medium, whose thermal features are described by Green-Naghdy theory. At the initial instant of time the shell's internal side is suddenly subjected to normal displacement velocities and/or to the instantaneous change in the shell temperature, resulting in generation and propagation of three types of cylindrical shock waves in the contacting thermoelastic isotropic medium. The solution behind the wave fronts up to the contact boundary is constructed using a ray series. Coefficients of the ray series are found from recurrent differential equations of the ray method within the accuracy of arbitrary functions dependent on angular and axial coordinates. Arbitrary functions, in turn, are determined from the conditions of continuity for displacements and stresses on the contact boundary of the shell and the medium and the condition of heat exchange between the shell and the surrounding medium, as well as from the initial conditions. The solution constructed allows one to investigate stability of the cylindrical shell with respect to nonstationary excitations.