The exact analytic solutions are obtained with the use of the eigenvalue approach for a free vibration problem of a thermoelastic hollow cylinder in the context of Green and Naghdi theory (GNIII). 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 and the validation ... Read more

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 ... Read more

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 ... Read more

For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible ... Read more