Non-linear vibration of heated orthotropic annular plates with immovably hinged edges

A computational analysis of the non-linear vibration and thermal buckling of a heated orthotropic annular plate with immovably hinged edges were presented. First, based on the von Karman's plate theory and Hamilton's principles, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assummg that harmonic responses of the system exist, the non-linear dynamic equations in von Kaman's version were converted into the corresponding non-linear ordinary differential equations through elimination of the time variable by using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the linear as well as non-linear vibration and thermal post-buckling of the heated, plate were numerically obtained.