Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation  

作　　者：GUO Xiang Ying,ZHANG Wei & YAO MingHui College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China 

出　　处：《Science China(Technological Sciences)》2010年第3期612-622,共11页中国科学（技术科学英文版）

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)

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.

关 键 词：ANGLE-PLY composite LAMINATED plate THIRD-ORDER SHEAR deformation theory PARAMETRIC excitation CHAOTIC motion 

分 类 号：TB33[一般工业技术—材料科学与工程]