Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method .1. The fundamental mode of isotropic plates

After successful applications of the hierarchical finite element method (HFEM) to geometrically nonlinear static analysis of laminated plates, and linear free and forced vibration analysis of laminated plates, the geometrically nonlinear free vibration of isotropic rectangular plates with fully clamped edges is analysed using the HFEM in this paper. The von Karman type of geometrically nonlinear strain-displacement relationships, and harmonic balance method were used in deriving the equation of motion. The influences of large vibration amplitude on the mode frequency, mode shape and mode stresses of the fundamental mode are discussed. A modified form of Berger's hypothesis was employed to study the in-plane membrane forces averaging effect on the geometrically nonlinear behaviour. A cancellation effect was discovered. The nonlinear frequencies predicted by the present method were compared with both numerical and experimental results from the published literature. An excellent agreement was found. (C) 1997 Elsevier Science Ltd.