摘要
An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms.Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance.Furthermore,the stability analysis is given for the steady-state solutions of the averaged equation.Based on the averaged equation obtained by the asymptotic perturbation method,the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate.Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.
An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy’s third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton’s principle.Then,the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms.Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance.Furthermore,the stability analysis is given for the steady-state solutions of the averaged equation.Based on the averaged equation obtained by the asymptotic perturbation method,the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate.Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.
基金
supported by the National Natural Science Foundation of China (Grant Nos.10732020,10872010)
the National Science Fund for Distinguished Young Scholars (Grant No.10425209)
