Nonlinear Dynamics Behaviors of a Composite Laminated Cantilevered Plate Under Transverse Excitation

The nonlinear dynamics analyses of a composite laminated cantilevered rectangular plate are studied, which is forced by the transverse excitation. We use the Hamilton's principle and establish the nonlinear partial differential governing equations of motion for the composite laminated cantilevered rectangular plate. Numerical simulations are presented to investigate the effects of the transverse excitation on the steady-state responses of the cantilevered plate. The bifurcation diagrams of the composite laminated cantilevered plate for w ₁ via the base excitation amplitude F is obtained. From the bifurcation diagram, it is found that the motions of the system are as follows: from periodic motion to multiple periodic motion, then to chaotic motion. Based on the above bifurcation diagrams and using the same parameters, the base excitation amplitude F are changed to obtain the waveforms, the two-dimensional phase portraits, the three-dimensional phase portraits and the Poincare maps of the system. The results of numerical simulation demonstrate that there exist the periodic and chaotic motions of the composite laminated cantilevered rectangular plate. (paper)