Three-dimensional Free Vibration Analysis of a Transversely Isotropic Thermoelastic Diffusive Cylindrical Panel

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mode is independent of thermal and concentration fields and gets decoupled from the rest of motion. The equations for free  vibration problem are reduced to four equations of second-order and one fourth-order ordinary differential equation after expanding the displacement potential, temperature change and concentration functions with an orthogonal series. The formal solution of this system of equations can be expressed by using modified Bessel function with complex arguments.  The numerical results for lowest frequency have been obtained and presented graphically. The effect of diffusion on lowest frequency has also been presented graphically. Some special cases of secular equation are also discussed.