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姚志刚 张伟 陈丽华. 压电复合材料层合梁的分岔、混沌动力学与控制[J]. 力学学报, 2009, 41(1): 129-140. DOI: 10.6052/0459-1879-2009-1-2008-250
引用本文: 姚志刚 张伟 陈丽华. 压电复合材料层合梁的分岔、混沌动力学与控制[J]. 力学学报, 2009, 41(1): 129-140. DOI: 10.6052/0459-1879-2009-1-2008-250
Z. G. Yao. Bifurcation, chaotic dynamics and control of piezoelectric laminated composite beam[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 129-140. DOI: 10.6052/0459-1879-2009-1-2008-250
Citation: Z. G. Yao. Bifurcation, chaotic dynamics and control of piezoelectric laminated composite beam[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 129-140. DOI: 10.6052/0459-1879-2009-1-2008-250

压电复合材料层合梁的分岔、混沌动力学与控制

Bifurcation, chaotic dynamics and control of piezoelectric laminated composite beam

  • 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、分岔和混沌动力学响应. 基于vonKarman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,得到两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动态分岔,分析了系统各种参数对倍周期分岔的影响及变化规律. 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岔解,从而阻止系统通过倍周期分岔进入混沌运动,并给出了控制分岔图.

     

    Abstract: The paper investigated the nonlinear dynamics, bifurcation and chaoticdynamics of simply supported laminated piezoelectric composite beam withaxial and transverse loading. The nonlinear equations of motions of the beamare first derived based on the general von Karman-type equations and theReddy third-order shear deformation plate theory. The partial differentialequations are discretized to the ordinary differential equations using theGalerkin approach. The averaged equations are obtained with the method ofmultiple scales. Numerical simulation is carried out to investigate theperiodic and chaotic motions of the beam. The results show that the chaoticresponses of the beam are sensitive to the piezoelectric excitations.Furthermore, the oscillation of the piezoelectric laminated composite beamcan be controlled with the piezoelectric excitation.

     

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