Analysis of three–dimensional free vibrations of isotropic visco-thermoelastic solid cylinder with two relaxation time parameters

Abstract

We explore the analysis of exact three-dimensional free vibrations of visco-thermoelastic solid cylinder, which has been considered at a uniform temperature and undeformed initially in the framework of generalized thermoelasticity. The formulation has been implemented with two relaxation time parameters, i.e., mechanical and thermal relaxation parameters. The series solution has been implemented to solve the differential equations along with the evaluation of stresses, displacements, and temperature by applying stress-free, rigidly fixed, thermally insulated and isothermal boundary conditions. The relations of frequency equations for the existence of different modes of visco-thermoelastic solid cylinder have been developed in compact form using assumed boundary conditions. Thermoelastic damping and frequency shift are presented graphically from the data generated by computations and simulations of numerical results. Also, the natural frequencies are represented in the form of tables which show that with an increase in the ratio of length to the radius and axial wave-number, the variation of vibrations keeps increasing.

Keywords:

• Cylindrical structures
• frobenius method
• Green–Lindsay model
• Lord–Shulman model
• thermoelastic damping
• vibrations