双稳态余弦梁非线性隔振器的动力学与隔振特性研究

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摘要为了隔离航空器上的低频振动，提出一种具有准零刚度特性的非线性隔振器，其由线性正刚度弹簧并联双稳态余弦梁负刚度元件而成。首先，通过对余弦梁非线性隔振器的静力学分析，给出了隔振器在准零刚度平衡点时的结构参数需要满足的条件。其次，建立谐波力作用下的系统动力学模型，通过未扰系统的分析，得其存在平衡点分岔行为和满足稳定准零刚度的条件。最后，通过数值方法和有限元软件动力学仿真分析扰动系统的隔振性能，得余弦梁非线性隔振器的起始隔振频率。进一步与线性隔振系统相比可知，引入余弦梁的非线性隔振系统有效降低了起始隔振频率。因此，余弦梁非线性隔振器具有优异的低频隔振性能，这为低频非线性隔振器设计提供了理论基础。

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	张威1
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	王文波1
	李双宝3

关键词 ：双稳态余弦梁, 平衡点分岔, 起始隔振频率, 准零刚度

Abstract：In order to isolate the low frequency vibrations in aircraft, a quasi-zero stiffness nonlinear vibration isolator is proposed, which is composed of a linear positive stiffness spring in parallel with a bistable cosine-shaped beam with negative stiffness. Firstly, through the static analysis of the cosine-shaped beam nonlinear vibration isolator, the structure parameters of the isolator at the quasi-zero-stiffness equilibrium point are given. Secondly, the dynamical model of a harmonically excited nonlinear vibration isolator with a bistable cosine-shaped beam is established. Through the analysis of the unperturbed system, the existence of bifurcation behavior of equilibrium point and the condition of stable-quasi-zero-stiffness are obtained. Finally, the isolation performance of the cosine-shaped beam nonlinear isolator under the excitation force is analyzed to obtain the initial vibration isolation frequency by using numerical analysis method and Finite Element Analysis(FEA). Moreover, compared with the linear vibration isolation system, it is shown that the initial vibration isolation frequency can be effectively reduced for the proposed quasi-zero stiffness nonlinear vibration isolation with cosine beam. Therefore, the nonlinear vibration isolator with cosine-shaped beam has excellent low frequency vibration isolation performance, which provides a theoretical basis for the optimal design of low frequency nonlinear vibration isolator.

Key words： bistable cosine-shaped beam equilibrium bifurcation initial vibration isolation frequency quasi- zero-stiffness

收稿日期: 2020-07-23 出版日期: 2022-01-28

引用本文:

张威1,2，王文波1，李双宝3. 双稳态余弦梁非线性隔振器的动力学与隔振特性研究[J]. 振动与冲击, 2022, 41(2): 113-122.
ZHANG Wei1,2，WANG Wenbo1，LI Shuangbao3. Dynamics and isolation performance of a nonlinear vibration isolator with a bistable cosine-shaped beam. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(2): 113-122.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I2/113

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