简支压电复合材料层合梁Neimark-Sacker分岔
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    摘要:

    研究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。该模型的动力学方程为受参数和外激励共同作用下的两自由度非线性控制方程。针对在1∶9条件下的平均方程,先用数值方法研究在刚度系数变化时的动力学行为,发现存在周期、概周期和混沌等响应以及周期解的分岔现象。针对发生分岔的临界周期响应,计算 Poincaré映射的单值矩阵,由Floquet乘子可以判断该分岔为Neimark-Sacker分岔。

    Abstract:

    A simply supported symmetric cross-ply laminated piezoelectric rectangular beam which is simultaneously forced by the transverse, axial excitations an d the excitation loaded by piezoelectric layers is considered. The model of which is a two-degree-of -freedom nonlinear system under the combination of the parametric and external excitations. Attention is paid to the averaged equation which is obtained in the case of 1:9 internal resonance. First, the bifurcations and chaotic dynamics by varying the coefficient of stiffness are found by simulation . Then the critical periodic solution which is undergoing the bifurcation scenarios is analyzed by Poincaré map. The Floquet multipliers verify the numerical prediction and show that the former bifurcation scenario is Neimark -Sacker bifurcation.

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  • 在线发布日期: 2012-05-16
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