Abstract
The aim of this article is to study the exact solution for a free vibration in a thermoelastic hollow cylinder, which is initially undeformed and at uniform temperature. The formulation is applied in the context of two-temperature Green and Naghdi (2TGNIII) theory. Both the inner and outer curved surfaces of the cylinder are considered stress free and isothermal surfaces. The exact analytic solutions are obtained with the use of eigenvalue approach. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow cylinder are derived in a compact form. The validation of the roots for the dispersion relation are presented. The numerical results of natural frequency, thermoelastic damping and frequency shift of vibrations have been presented graphically.