Effect of three-phase-lag model on the analysis of three-dimensional free vibrations of viscothermoelastic solid cylinder

Abstract

Herein we explore the effects of three-phase-lag (TPL) model of generalized thermoelasticity on the exact analysis of three-dimensional free vibrations of viscothermoelastic solid cylinder, which is assumed undeformed initially and at uniform temperature. The formulation has been put into practice with three different phase-lag parameters i.e., Phase-lag of the heat flux, Phase-lag of the temperature gradient, and Phase-lag of the thermal displacement gradient. The solution of matrix Frobenius method of continued series solution has been implemented to solve the differential equations for the evaluation of field functions i.e. stresses, displacements, and temperature by applying stress-free/rigidly-fixed thermal boundary conditions (i.e. thermally insulated and isothermal). The obtained frequency equations for the existence of different modes of TPL viscothermoelastic solid cylinder have been developed using considered stress free/rigidly fixed boundary conditions. The free vibration field functions i.e. frequency shift and thermoelastic damping have been presented graphically from the data generated by simulations and computations of numerical results. Also, the natural frequencies are presented in the form of tables which shows that with an increase in the axial wave-number and length to radius ratio, the behavior of vibrations goes on increasing. The behavior of vibrations of field functions in case of TPL model has larger in contrast to other models of generalized thermoelasticity.