特殊对称铺设复合材料层合矩形板的全局动力学研究

Global dynamics of a special symmetrically laid composite laminated rectangular plate

应用广义Melnikov方法首次研究了四边简支正交异性对称铺设复合材料层合矩形板的全局分岔和混沌动力学。通过坐标变换理论得到复合材料层合矩形板的五维非线性动力系统,由广义Melnikov理论计算出系统的k-脉冲Melnikov函数,得到复合材料层合矩形板系统的混沌阈值区间。利用Matlab软件,对理论结果进行数值模拟,得到复合材料层合矩形板的分岔图、相图和时间历程图来验证理论分析的正确性。最后,通过理论分析和数值模拟进一步表明复合材料层合矩形板存在多脉冲混沌运动。

The global bifurcation and chaotic dynamics of simply supported orthotropic symmetrically laminated composite rectangular plate is studied for the first time by using the generalized Melnikov method.The five-dimensional nonlinear dynamic system of composite laminated rectangular plate is obtained by coordinate transformation theory.The k-pulse Melnikov function of the system is calculated by the generalized Melnikov theory,and the chaotic threshold interval of composite laminated rectangular plate system is obtained.Using MATLAB software,the theoretical results are numerically simulated to obtain the bifurcation diagram,phase diagram and time history diagram of the composite laminated rectangular plate to verify the correctness of the theoretical analysis.Finally,the theoretical analysis and numerical simulation further show that there is multi-pulse chaotic motion in the composite laminated rectangular plate.