A Hierarchical Finite Element for Geometrically Non-linear Vibration of Thick Plates

A p-version, hierarchical finite element for moderately thick isotropic plates is derived and free vibrations are studied. The effects of the rotatory inertia, transverse shear and geometrical non-linearity, due to moderately large displacements, are taken into account. The time domain free vibration equations of motion are obtained by applying the principle of virtual work, and are mapped into the frequency domain by the harmonic balance method. The ensuing frequency domain equations are solved by a predictor–corrector method. The convergence properties of the element, the influence of the plate's thickness and of the width to length ratio on the backbone curves and on the non-linear mode shapes are investigated. The first and higher order modes are analysed and results are compared with published results.