作　　者： ; ; ; ;

机构地区： 北京市工业技师学院

出　　处： 《动力学与控制学报》 2011年第3期207-213,共7页

摘　　要： 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 dynamics,bifurcation and chaotic dynamics of a simply supported laminated composite piezoelectric beam were analyzed. The beam was forced by an axial load and a transverse load. Based on the von Karmantype equations and the Reddy thirdorder shear deformation plate theory, the nonlinear equations of motions of the laminated composite piezoelectric beam were derived. The Galerkin’s approach was employed to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales was used to obtain the averaged equations. Based on the averaged equations, the bifurcation and chaotic motions of the beam were studied. The periodic and chaotic motions of the beam were found by using numerical simulation. It is concluded that the chaotic responses are sensitive to the piezoelectric excitations. Through changing the piezoelectric excitation, we can control the oscillation of the laminated composite piezoelectric beam.

关 键 词： 压电层合复合材料 全局动力学 混沌动力学

领　　域： [理学] [理学]