Nonlinear combination resonances and bifurcation of orthotropic laminated plates

Considering the effects of geometrical nonlinearity and damping, the vibration differential equation of simply supported rectangular orthotropic laminated plate excited by two-term harmonic forces was established. The non-dimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method. The amplitude frequency response equation of system steady motion under combination resonance was obtained by the method of multiple scales. Based on Lyapunov stable theory, the critical conditions of steady-state solutionsp stability were got. By some examples, the influence of different parameters on nonlinear combination resonances and bifurcation properties of system was analyzed. The results show that the detuning parameter, thickness of plate, damping and amplitude of excitation have different influences on combination resonance and bifurcation. With the change of parameters, the jump phenomenon, hysteresis phenomenon and unstable solutions will occur. It is also shown that the system presents relatively complicated dynamics behaviors, and there exists multi-valued phenomenon, and the dynamics behaviors will change in some values.