弹性梁中端惯容型非线性能量汇振动抑制研究

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摘要欧拉-伯努利梁作为许多航空航天结构的简化模型，对其振动抑制研究具有重要的工程意义。本文提出利用惯容型非线性能量汇抑制弹性梁的横向振动。应用广义哈密顿原理，建立弹性梁的动力学控制方程。通过伽辽金截断方法离散系统的偏微分控制方程。应用谐波平衡方法得到系统非线性振动的稳态响应，并对其进行数值验证。研究结果表明，惯容型非线性能量汇可以有效抑制弹性梁的横向振动。此外，讨论了惯容型非线性能量汇的阻尼、惯性质量和立方非线性刚度的变化对其减振效果的影响。最后，讨论了在不同激励和梁不同弯曲刚度下参数的最优取值范围。结果表明，优化后的惯容型非线性能量汇的减振效果可高达99%。

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	高志通
	方勃
	张振

关键词 ：惯容型非线性能量汇, 幅频响应, 稳态响应, 减振效果

Abstract：As a simplified model of many aerospace structures, the vibration suppression research about Euler Bernoulli beam has important engineering significance. In this paper, the inertial nonlinear energy sink was used to suppress the lateral vibration of elastic beam. With Hamilton’s principle, the dynamic governing equations of elastic beams were established. The partial differential control equations of the system were discretized by Galerkin truncation method. The steady-state response of nonlinear vibration was obtained by harmonic balance method and verified by numerical solutions. The results showed that the inertial nonlinear energy sink can effectively suppress the lateral vibration of the elastic beam. In addition, the influence of damping, inertial mass and cubic nonlinear stiffness on the vibration suppression effect was discussed. Finally, the optimal range of parameters under different excitation and bending stiffness was discussed. The results showed that the vibration suppression effect of the optimized inertial nonlinear energy sink can reach 99%.

Key words： Inertial nonlinear energy sink amplitude-frequency response steady-state response vibration reduction effect

收稿日期: 2020-11-16 出版日期: 2022-04-28

引用本文:

高志通，方勃，张振. 弹性梁中端惯容型非线性能量汇振动抑制研究[J]. 振动与冲击, 2022, 41(8): 311-322.
GAO Zhitong，FANG Bo，ZHANG Zhen. A study on nonlinear energy sink of inertia capacity in the middle of an elastic beam. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(8): 311-322.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I8/311

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