Nonlinear vibrations and chaotic dynamics of graphene-reinforced titanium-based composite rectangular cantilever plate subjected to transverse excitations

In this paper, we investigate the linear vibration behaviors, nonlinear and chaotic dynamics of the functionally graded graphene reinforced titanium-based (FG-GRTB) composite laminated cantilever rectangular plate under the transverse excitation. Based on Halpin-Tsai model, the mechanical properties are calculated for the graphene reinforced titanium-based (GR-TB) composite laminated cantilever rectangular plate. Considering the classical laminated theory, von Karman large deformation theory and Hamilton principle, the partial differential governing equations of motion are derived for the GR-TB composite laminated cantilever rectangular plate subjected to the transverse excitation. The natural vibration behaviors of the system are investigated by Rayleigh-Ritz method. The results are compared with the finite element simulation using COMSOL MUTIPHYSIC software. The ordinary differential equations of the GR-TB composite laminated cantilever rectangular plate are obtained by Galerkin method. The internal and primary resonances of the system are studied by the multi-scale method. The amplitude-frequency and force-amplitude response curves are depicted by the average equations. The chaotic vibrations of the system are studied by using the bifurcation diagram, max Lyapunov exponent, time histories, phase portrait and Poincare map. The results indicate that the graphene volume fraction and graphene distributed type have a significant influence on the natural vibration characteristics of the GR-TB composite laminated cantilever rectangular plate. In addition, the system exhibits the soft spring nonlinear properties in the case of the combination of the internal and primary resonances. Moreover, the system under larger external amplitude or smaller damping triggers the chaotic vibrations easily.