Abstract
The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically.