Modeling of thermoelastic damping and frequency shift of vibrations in a transversely isotropic solid cylinder

Purpose - The purpose of this paper is to analyze the free vibrations in a stress free and thermally insulated (or isothermal), homogeneous, transversely isotropic, solid cylinder based on three-dimensional coupled thermoelasticity, which is initially undeformed and kept at uniform temperature. Design/methodology/approach - The displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple the purely shear and longitudinal motions. The system of governing partial differential equations is reduced to four second-order coupled ordinary differential equations in radial coordinate by using the method of separation of variables. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. The convergence analysis of matrix Frobenius method has been successfully carried out. Findings - The purely transverse mode is found to be independent of the rest of the motion and temperature change. The natural frequency, dissipation factor, inverse quality factor and frequency shift of vibrations in a stress free solid cylinder get significantly affected due to thermal variations and thermo-mechanical coupling. Originality/value - A new procedure is used and compared to other methods available in the literature.