Transient Analysis of Rectangular Laminated Plates Subjected to Dynamic Transverse Loading Using a Layerwise Theory

摘要

An analytical solution of dynamic response of thick cross-ply laminated plates, based on the full layerwise theory, is presented in this paper. Analytical solutions are determined by a simple but efficient method which involves a transformation into the generalized coordinates and applying the orthogonality conditions of the principal modes in order to uncouple the equations. Since the generalized coordinates could be interpreted as contribution of any principal mode in the overall response, this approach also allows immediate deduction on how the laminated plates respond to external loads. The simply supported rectangular plates subjected to constant and time-varying transverse loads are examined as case studies. The analytical solution presented herein is validated by successfully comparing the results obtained from the layerwise theory with those obtained from the classical, first-order and third-order laminated plate theories. The response of the laminated plates to the external load is represented in terms of deflection as well as distributions of the in-plane and interlaminar stresses. The forced vibration analysis using a layerwise theory is reported for the first time in this paper. Results of the accurate layerwise theory represent substantial oversimplifications inherent in application of equivalent single-layer theories to forced vibration analysis of orthotropic laminates.