Free vibration behavior of a thermally post-buckled FG Timoshenko beam under large deflection using a tangent stiffness-based method

For thermally postbuckled configurations, the free vibration behavior of functionally graded (FG) Timoshenko beams are investigated. The postbuckling configurations are obtained through a geometrically nonlinear static problem. The free vibration problem around the postbuckled configuration is formulated using its tangent stiffness. The energy based governing equations are solved following the Ritz method. The elements of the tangent stiffness matrix are obtained using the Ritz coefficients. The results are shown to exhibit the effects of FG material, material profile parameter, and length-thickness ratio. The comparative results are presented for both the cases of the physical neutral surface and the geometrical neutral surface.