| 时滞反馈及轴力作用下弹性梁的非线性振动 |
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| 引用本文： | 彭 剑,赵珧冰,王连华.时滞反馈及轴力作用下弹性梁的非线性振动[J].湖南农业大学学报(自然科学版),2013,40(9):30-36. |
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| 作者姓名： | 彭 剑 赵珧冰 王连华 |
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| 作者单位： | （1.湖南大学 机械与运载工程学院，湖南 长沙 410082； 2.湖南大学 土木工程学院，湖南 长沙 410082） |
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| 摘 要： | 基于时滞反馈控制策略及Euler-Bernoulli梁理论，建立了轴力作用下弹性支座压电耦合梁的非线性动力学模型.通过模态分析和线性稳定性分析，得到了压电耦合作用时滞反馈条件下的系统稳定性条件.采用Galerkin方法和非线性振动的多尺度法，从理论上推导出时滞动力系统的分岔响应.结果表明，对于某一确定的时滞，控制增益的变化可能会导致周期运动、拟周期运动以及混沌运动.
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| 关 键 词： | 轴力 Euler-Bernoulli梁 时滞反馈控制 稳定性 分岔 |
Nonlinear Vibrations of Elastic Beams Subjected to Axial Force and Delayed-feedback |
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| PENG Jian,ZHAO Yao-bing,WANG Lian-hua.Nonlinear Vibrations of Elastic Beams Subjected to Axial Force and Delayed-feedback[J].Journal of Hunan Agricultural University,2013,40(9):30-36. |
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| Authors: | PENG Jian ZHAO Yao-bing WANG Lian-hua |
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| Abstract: | Based on the Euler-Bernoulli beam theory, a dynamical model of piezoelectric coupling beam subjected to axial force and delayed-feedback was derived. The stability conditions of the system under piezoelectric coupling and delayed feedback was investigated through modal analysis and linear stability analysis. The Galerkin method and multi-scale method were used to study the bifurcation response of the time delay system. Numerical simulation was employed to study the effects of control gain on the dynamics of the system, i.e., stability and bifurcation of an equilibrium point, periodic solution, period-doubling, quasi-periodic motion and even chaos. |
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| Keywords: | axial force Euler-Bernoulli beam time-delay feedback stability bifurcation |
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