Abstract
The hierarchical finite element (HFEM) and the harmonic balance methods are applied to analyse the geometrically nonlinear vibration of thin, isotropic plates. The von Kármán type of nonlinear strain–displacement relationships are used. Symbolic computation is employed in the derivation of the model. The equations of motion are solved by the Newton and continuation methods. Free and steady-state forced vibration are analysed. The excitations considered are harmonic plane waves at both normal and grazing incidence. The stability of the obtained solutions is investigated by studying the evolution of perturbations to the solutions. The convergence properties of the HFEM and the influence of the middle plane in-plane displacements are discussed and results compared with published experimental and numerical results.
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