Vibrations of a nonlocal thermoelastic cylinder with void

The present work is devoted to the investigation of the free vibrations of a homogeneous isotropic nonlocal thermoelastic cylinder with void. Time-harmonic variations are used to reduce the governing partial differential equations to a system of ordinary differential equations. The frequency equation for the continuation of vibrations for the mode numbers in the considered cylinder is deduced in closed form for traction-free and isothermal/thermally insulated boundary conditions. To observe the free vibration, the frequency equation is further studied by using the numerical iteration method with the help of MATLAB software. The numerically simulated results from the analytical solutions are shown graphically for the natural frequency, thermoelastic damping and the frequency shift against mode numbers for the nonlocal as well as the local thermoelastic cylinders in the presence and absence of the void.