一类弦-梁耦合非线性振动系统的动力学数值模拟研究
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国家自然科学基金项目资助(11572288)


Numerical simulation research on dynamics of a string-beam coupled nonlinear vibration system
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    摘要:

    本文研究了一类具有参数激励和外激励弦-梁耦合非线性系统.首先,运用多尺度法分析弦-梁耦合非线性系统的响应,求得系统平均方程.其次,基于求得的方程,以系统的阻尼系数作为分叉参数,并对系统平衡点的稳定性进行分析,得到平衡点的分叉曲线.为了验证理论预测的正确性数值模拟了不同分叉参数下的相空间轨线.利用四阶龙格库塔方法验证了弦-梁耦合非线性系统混沌运动的存在性,从数值模拟看出系统存在单倍周期运动、多倍周期运动和混沌运动.

    Abstract:

    This paper studies nonlinear dynamic behavior of a stringbeam coupled system subjected to parametric and external excitations. Firstly, the method of multiple scales is used to analyze the nonlinear responses of the string-beam system coupled system. Secondly, based on the average equation and taking the damping coefficient of the system as the bifurcation parameter, the stability of the equilibrium point of the system is analyzed and the bifurcation curve of the equilibrium point is obtained. In order to verify the correctness of theoretical prediction, the trajectories in phase space under different bifurcation parameters are simulated. Finally, the fourth-order Runge-Kutta method is utilized to verify the existence of the chaotic motions in the stringbeam coupled system. From the results of numerical simulation, it is clearly found that the system exists period-1 motion, multi-periodic motion and chaotic motion.

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吴娟,钱有华.一类弦-梁耦合非线性振动系统的动力学数值模拟研究[J].动力学与控制学报,2018,16(5):403~410; Wu Juan, Qian Youhua. Numerical simulation research on dynamics of a string-beam coupled nonlinear vibration system[J]. Journal of Dynamics and Control,2018,16(5):403-410.

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  • 收稿日期:2017-10-09
  • 最后修改日期:2017-11-10
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  • 在线发布日期: 2018-06-29
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