Exact Solution for a Free Vibration of Thermoelastic Hollow Cylinder Under GNIII Model

Abstract

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 of the roots for the dispersion relation is presented. To illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the frequency, thermoelastic damping and frequency shift of vibrations in a hollow cylinder of copper material with MATHEMATICA and MATLAB software.

Vibration analysis of transversely isotropic hollow cylinder considering three different theories using the matrix Frobenius method

“…Abbas (2015) proposed an eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source. Abbas (2016) reported the exact solution for the free vibration of a thermoelastic hollow cylinder under the GN III model. Zenkour and Abbas (2014) considered magneto-thermoelastic response in an infinite functionally graded cylinder using the finite element method.…”