Stability and bifurcation analysis of a composite laminated cantilever rectangular plate by using the normal form theory. (December 2015)

• Record Type: Journal Article
• Authors: Chen, S. P.; Zhang, W.; Zhao, M. H.
• Is Part Of: Materials research innovations. Volume 19(2015)Supplement 10
• Page Start: S10-10
• Page End: S10-20
• Publication Date: 2015-12
• Subjects: Composite laminated cantilever rectangular plate -- Non-linear oscillations -- Normal form -- Bifurcation; Materials -- Research -- Periodicals; Matériaux -- Recherche -- Périodiques; 620.1105
• DOI: 10.1179/1432891715Z.0000000002077
• Languages: English
• ISSNs: 1432-8917

Abstract

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.