Nonlinear vibrations of simply-supported plates by the p-version finite element method

The p-version, hierarchical finite element method is applied to study geometrically nonlinear periodic vibrations of isotropic simply supported plates, in the elastic regime. Free vibrations are studied by the harmonic balance and continuation methods. The nonlinear mode shapes and backbones curves are defined for the first three vibration modes. Resonance curves due to external excitations are also derived, employing the shooting method. The characteristics of the nonlinear motions under harmonic forces are investigated and new results presented.