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研究了简支压电复合材料层合梁在轴向、横向载荷共同作用下的非线性动力学、分叉和混沌动力学响应.基于von Karman理论和Reddy高阶剪切变形理论,推导出了压电复合层合梁的动力学方程.利用Galerkin法离散偏微分方程,得到二个自由度非线性控制方程,并且利用多尺度法得到了平均方程.基于平均方程,研究了压电层合梁系统的全局动力学分析、动态分叉,分析了系统各种参数对倍周期分叉的影响及变化规律.结果表明,压电复合材料层合梁周期运动的稳定性和混沌运动对外激励的变化非常敏感,通过控制压电激励,可以控制压电复合材料层合梁的振动,保持系统的稳定性,即控制系统产生倍周期分叉解,从而阻止系统通过倍周期分叉进入混沌运动,并给出了控制分叉图.
The nonlinear dynamic, bifurcation and chaotic dynamic response of a simply supported composite piezoelectric composite beam subjected to axial and transverse loads are studied. Based on von Karman theory and Reddy’s high-order shear deformation theory, The dynamic equations of the piezoelectric composite laminated beam are obtained. The two-degree-of-freedom nonlinear governing equations are obtained by the Galerkin method and the average equation is obtained by the multi-scale method. Based on the mean equation, the piezoelectric laminated beam The global dynamic analysis and dynamic bifurcation of the system are carried out to analyze the influence of various parameters of the system on the period bifurcation and the variation law.The results show that the stability of the periodic motion of the piezoelectric composite beam and the change of the external excitation Is very sensitive. By controlling the piezoelectric excitation, the vibration of the piezoelectric composite laminated beam can be controlled and the stability of the system can be maintained. That is to say, the control system produces a doubling period bifurcation solution so as to prevent the system from bifurcation into chaos through doubling period. The control bifurcation is given.