Abstract：The nonlinear dynamics of composite laminated cantilever plates subjected to in-plane and transversal excitations is investigated in this paper. With the wing flutter of a flying aircraft as the background, based on the Reddy's high-order shear deformation theory and von Kármán type equations for the geometric nonlinearity, the nonlinear governing partial differential equations of motion are derived for the composite laminated cantilever plate subjected to in-plane and transverse excitations by using the Hamilton's principle with considerations of the effects of higher-order transverse shear deformation, nonlinear geometry deformation and transversal damping. The Galerkin approach is utilized to transform the nonlinear partial differential governing equations of motion for the composite laminated cantilever plate to a two-degree-of-freedom nonlinear system. The principal parametric resonance, the 1/2 subharmonic resonance and the 1:2 internal resonance are considered. The method of multiple scales is employed to obtain the four-dimensional averaged equations of the composite laminated cantilever plate subjected to in-plane and transverse excitations. The dynamical behaviors of the cantilever plate under combined in-plane and transversal excitations are investigated with numerical simulations of the averaged equations. The two-dimensional phase portrait, waveform and three-dimensional phase portrait are obtained as results of the nonlinear dynamic behaviors of the composite laminated cantilever plate. The results of numerical simulations demonstrate that there exist one-periodic, multi-periodic and chaotic motions of the composite laminated cantilever plate.
2010, Vol. 28 
