压电复合材料层合板的混沌动力学研究

压电复合材料具有独特的机电耦合性、比强度高、比刚度大和抗疲劳性能好等优点，越来越广泛地被应用于航空航天等工程领域中。根据Reddy的三阶剪切变形层合板理论，研究了受面内横向外激励力、面内纵向参数激励和面外参数激励以及压电参数激励联合作用下四边简支矩形复合材料层合板在1:2:4内共振情况下的六维平均方程。考虑平均方程存在一对双零特征值和两对纯虚特征值的情况，利用规范形理论进行化简，得到与原方程拓扑等价的最简规范形，然后在此基础上利用能量相位法从理论上分析得到系统会产生同宿的多脉冲跳跃现象；同时，基于平均方程，通过数值仿真，发现系统会产生混沌运动，具有跳跃现象。

Chaotic dynamics for laminated composite piezoelectric rectangular plates

Composite laminated plates have many advantages such as unique electromechanical coupling, light weight, high strength, fatigue resistance, and it is widely used in modern engineering and especially in the aerospace industry. In the present study, based on the third-order shear deformation laminate theory of Reddy, we study the six-dimensional nonlinear system for the simply supported at the four-edge rectangular laminated composite piezoelectric rectangular plates, which are subjected to in-plane excitations, out-plane loads, thermal loads and piezoelectric excitations. Taking into account that the averaged equation has a double zero and two pairs of pure imaginary eigenvalues, we use the theory of normal form to simplify the six-dimensional averaged equation to a simpler form. The energy-phase method is employed to study the global bifurcations and chaotic dynamics of the six-dimensional nonlinear system for a composite laminated plate. The global analysis indicates that there exists the multi-pulse jumping of homoclinic orbits in the system. At the same time, numerical simulation is used to investigate the nonlinear characteristic of the plate. The results of numerical simulation demonstrate that the jumping phenomena of orbits can occur for the composite laminated plate.