Stability and bifurcation analysis of a composite laminated cantilever rectangular plate by using the normal form theory. (December 2015) - Chen, S. P.; Zhang, W.; Zhao, M. H.
Abstract : Stability and bifurcation analysis of a composite laminated cantilever rectangular plate subject to the supersonic gas flows and the in-plane excitations is presented in this paper. The non-linear governing equations of motion for the composite laminated cantilever rectangular plate are derived based on von Kármán-type plate equation, Reddy's third-order shear deformation plate theory and Hamilton's principle. Galerkin's method is utilised to convert the governing partial differential equations to a two-degree-of-freedom non-linear system under combined parametric and external excitations. The present study focuses on resonance case with 1:2 internal resonance and primary parametric resonance. The method of multiple scales is employed to obtain four non-linear averaged equations which are then solved by using the normal form theory to find the non-linear dynamic responses of the plate. It is found that double Hopf bifurcation of the plate occurs under certain conditions.