Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel

In this article, based on three-dimensional thermoelasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel is presented in the context of Lord-Shulman (LS), Green-Lindsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. Three displacement potential functions are introduced so that the equations of motion and heat conduction are uncoupled and simplified. It is noticed that the purely transverse mode is independent of temperature change and rest of the motion. The equations for free vibration problems are further reduced to four second-order ordinary differential equations after expanding the potential and temperature functions with an orthogonal series. A modified Bessel function solution with complex arguments is then directly used for complex eigenvalues. Numerical examples are presented to clarify the developed method and compare the results to the existing one.