Stability and bifurcation analysis of a composite laminated cantilever rectangular plate by using the normal form theory

• Published in: Materials research innovations Vol. 19; no. sup10; pp. S10-10 - S10-20
• Main Authors: Chen, S. P., Zhang, W., Zhao, M. H.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 31.12.2015
• Subjects: Bifurcation; Cantilever plates; Composite laminated cantilever rectangular plate; Dynamical systems; Excitation; Galerkin methods; Mathematical analysis; Non-linear oscillations; Nonlinear dynamics; Nonlinearity; Normal form; Rectangular plates
• ISSN: 1432-8917; 1433-075X
• DOI: 10.1179/1432891715Z.0000000002077

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.