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摘要:
An analysis on the nonlinear vibrations of a simply-supported composite laminated rectangular plate with both parametrical and forcing excitations was presented. Based on the Reddy's high-order shear deformation theory and the model of the von Karman type geometric nonlinearity, nonlinear governing partial differential equations of motion were derived by using the Hamilton principle. The linear external damping was supposde to existion the plate. Then, useing the second-order Galerkin discretization approach, the partial differential governing equations of motion were transformed to nonlinear ordinary differential equations under parametrical and forcing excitations, which leads to the periodic and chaotic oscillations. The method of multiple scales was used to get four averaged equations. From the averaged equations obtained here, the theory of normal form was used to give the explicit expressions of normal form, based on which, high-dimensional Melnikov method was utilized to analyze the global bifurcations and chaotic motions of composite laminated rectangular thin plates. The results obtained above illustrate the existence of chaos in the Smale horseshoe sense in parametrically excited and forcing excited composite laminated plates. The chaotic motions of composite laminated plates were also found by using numerical simulation. The simulation results indicate that there exist different shapes of chaotic responses in the nonlinear oscillations of composite laminated plate under certain force excitations, parametric excitations and initial conditions.
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来源 :
Journal of Vibration and Shock
ISSN: 1000-3835
年份: 2009
期: 6
卷: 28
页码: 139-144