Nonlinear vibration of plates by the hierarchical finite element and continuation methods

In this paper the hierarchical finite element (HFEM) and harmonic balance methods are applied to derive the equations of motion of thin, isotropic plates, in steady-state forced vibration with large amplitude displacements. Symbolic computation is used in the derivation of the model. The equations of motion are solved by the Newton and continuation methods. The stability of the obtained solutions is investigated by studying the evolution of perturbations of the solutions. The convergence properties of the HFEM, the influence of the number of degrees of freedom and of in-plane displacements are discussed. The HFEM results are compared with published experimental and numerical results and good agreement is found.