Nonlinear Vibration of Plates and Higher Order Theory for Different Boundary Conditions

There are numerous applications of plate structures found in structural, aerospace and marine engineering. The present study extends the previous work by Amabili and Sirwan [1] investigating the performance of isotropic and laminate composite rectangular plates with different boundary conditions subjected to an external point force with an excitation frequency that lies in the neighbourhood of the fundamental mode of the plate. The analysis is performed using three different nonlinear plate theories, namely: i) the classical Von Ka´rman theory, ii) first-order shear deformation theory, and iii) third-order shear deformation theory. Three different boundary conditions are considered in the investigation: a) classical clamped boundary conditions, b) simply-supported ends with immovable edges, and c) simply-supported ends with movable boundaries. In addition, the effect of thickness was also considered in the analysis and different values for the plate thickness were assumed. The results investigate the accuracy of lower order theories versus higher order shear deformation theories, the effect of boundary conditions and highlight the differences in the responses obtained from isotropic and laminate composite rectangular plates.