郭翔鹰张伟陈丽华.doc

高阶剪切复合材料层合板的非线性动力学分析eriodic and chaotic oscillations of laminated composite plates Xiangying Guo, Wei Zhang，Lihua Chen College of Mechanical Engineering, Beijing University of Technology, 100022 [Abstract] In this paper, it is presented the nonlinear vibration of a simply-supported laminated composite rectangular plate with parametrical excitation and forcing excitation. Based on the Reddy’s high-order shear deformation theory and the model of von Karman type geometric nonlinearity, nonlinear governing partial differential equations of motion are derived by using Hamilton’s principle. The Galerkin method is utilized to discretize the governing partial equations to a three-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The case of 1:3:3 internal resonances and fundamental parametric resonance of a simply-supported laminated composite rectangular plate is studied by using the multiple scales method. Then, numerical method is used to investigate periodic and chaotic motions in the nonlinear oscillation of the laminated composite plates. The results of numerical simulation demonstrate that there exist the periodic motion and different kinds of chaotic motions in the laminated composite plates under certain conditions. [key word] laminated composite plates, High-order shear deformation, multiple scale method, chaotic motion 一.引言 复合材料层合板因其具有重量轻，高的比强度和轻刚度以及良好的可设计性等优点，越来越广泛地用于现代工程结构中。Kim[1]在2002年应用有限元和多尺度法研究了粘弹性复合材料层合板的动力学特性，讨论了系统的振动频率以及频率对幅值的影响但他没有考虑高阶剪切的影响。2003年Ishihara[2]分析了各相异性层合板的非线性动力特性，讨论了同时受到面内和面外载荷作用下的大静力变形，在静力平衡状态下的极小振动的固有频率和有限振幅的固有频率。2004年Shukla[3]研究了在各边带有空间导向短纤维的层合板的非线性动力响应Harras 等[4]研究了对称夹层复合板的非线性自由振动讨论了非线性特性对振动频率的影响。Elbeyli 等[5,6]用多尺度方法研究了受横向简谐力作用的矩形板的非线性振动.2001年Zhang[7]研究了带有参数激励的简支正方形板的全局分岔和混沌动力学，用数值模拟薄板混沌运动. Zhang[8,9]等还研究了对称和反对称形式的复合材料层合板在参数激励下的非线性振动，数值模拟了其混沌运动. 胡浩等[10]分析了几何非线性粘弹性正交各向异性对称层合矩形板的非线性动力响应问题.以三层(单层各向同性) 对称矩形层合板为例进行数值计算,得到不同材料性质对频谱曲线以及时间-位移曲线的影响. 傅衣铭等[11]研究了层合板的结构损伤对非线性动力响应的影响. 二.力学模型 以飞机飞行中机翼的颤振为