Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods

摘要

The shooting, Newton and p-version, hierarchical finite element methods are applied to study geometrically nonlinear periodic vibrations of elastic and isotropic, beams and plates. Thin and thick or first-order shear deformation theories are followed. One of the main goals of the work presented is to demonstrate that the methods suggested are highly adequate to analyse the periodic, forced non-linear dynamics of beam and plate structures. An additional purpose is to investigate the differences in the predictions of non-linear motions when thin and thick, either beam or plate theories are followed. To this ends response curves are derived, defining both stable and unstable solutions and the characteristics of the motions are investigated using time plots, phase planes and Fourier spectra.