Free Vibration Analysis of Rigidly Fixed Axisymmetric Viscothermoelastic Cylinder

This paper represents the analysis of free vibrations of rigidly fixed, functionally graded generalized viscothermoelastic axisymmetric hollow cylinder which is considered undeformed at uniform temperature. The material of the cylinder is considered to be functionally graded according to the simple exponent law. The governing partial differential equations of motion and heat conduction have been transformed into ordinary differential equations due to time-harmonic analysis. The matrix Frobenius method of the series solution has been implemented to ordinary differential equations analytically to represent the solutions of displacement and temperature. The regular fixed boundary conditions are further solved by the use of numerical method of iteration technique with the help of MATLAB software tools. For numerical computations, we take polymethyl methacrylate material to represent natural frequencies, thermoelastic damping, frequency shift, temperature change and displacement. The behavior of frequencies, thermoelastic damping, temperature change and variation of displacement have been monitored (increase or decrease) with grading index (i.e. inhomogenous parameter).