六层非对称正交双稳态复合材料层合板的动态跳跃研究1)

STUDY ON DYNAMIC SNAP-THROUGH OF A SIX-LAYER ASYMMETRIC CROSS-PLY BISTABLE COMPOSITE LAMINATED PLATE1)

  • 摘要: 本文研究了中心固支,四边自由的六层非对称正交双稳态复合材料层合板(0/0/0/90/90/90)的动态跳跃现象,并展示了双稳态复合材料层合板在动态跳跃前后和过程中的非线性振动。考虑冯卡门大变形,利用Reddy三阶剪切变形理论和哈密顿原理,建立了动力学与控制方程。利用动力学与控制方程,得到了李雅普诺夫指数图、庞加莱截面图和时间历程图,分析了双稳态复合材料层合板的周期振动、概周期振动、混沌振动和动态跳跃现象。

     

    Abstract: In this paper, the dynamic snap-through phenomenon of a six-layer asymmetric cross-ply bistable composite laminated plate (0/0/0/90/90/90) is studied and the nonlinear vibrations before, after and during the dynamic snap-through are demonstrated. The boundary conditions are fixed at the center and free at the four sides. From the von Kármán's large deflection theory, the dynamic and governing equations of the six-layer asymmetric cross-ply bistable composite laminated plate are established by using the Reddy's third-order shear deformation theory and the Hamilton's principle. Taking the base excitation amplitude as the control parameter, the diagram for the maximum Lyapunov exponents, the Poincaré maps and the time-history for the dynamic snap-through are obtained. Based on the maximum Lyapunov exponents and the Poincaré maps, the periodic vibration, the quasi-periodic vibration, the chaotic vibration and the dynamic snap-through of the six-layer asymmetric cross-ply bistable composite laminated plate are analyzed. It is found that the chaotic vibration is a favorable condition for the dynamic snap-through.

     

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