Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 972930, 19 pages
Research Article

Modal Decoupling Using the Method of Weighted Residuals for the Nonlinear Elastic Dynamics of a Clamped Laminated Composite

Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA

Received 21 July 2008; Revised 30 January 2009; Accepted 28 March 2009

Academic Editor: Giuseppe Rega

Copyright © 2009 Xiaoling He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop an approach to reduce the governing equation of motion for the nonlinear vibration of a clamped laminated composite to the Duffing equation in a decoupled modal form. The method of weighted residuals enables such a reduction for laminates with clamped boundary conditions. Both rigidly clamped and loosely clamped boundary conditions are analyzed using this method. The reduction method conserves the total energy of the system. The decoupled modal form Duffing equation has constant modal parameters in terms of the laminated composite material's properties and geometries. The numerical computations illustrate the individual modal response with an emphasis of the transitional phenomena to chaos caused by the large load.