时滞反馈对非线性黏弹性隔振系统的竖向振动控制研究

王道航; 孙博; 刘春霞; 周紫怡; 刘羽

doi:10.21656/1000-0887.450037

时滞反馈对非线性黏弹性隔振系统的竖向振动控制研究

doi: 10.21656/1000-0887.450037

王道航^1,,
孙博¹,
刘春霞^2, ,,
周紫怡¹,
刘羽¹

1.
昆明理工大学公共安全与应急管理学院, 昆明 650000
2.
云南财经大学统计与数学学院数学系, 昆明 650000

基金项目:

云南省基础研究计划(青年项目) 202201AU070227

详细信息

作者简介:
王道航(1983—)，男，讲师，博士(E-mail: wang_daohang@163.com)

通讯作者:
刘春霞(1989—)，女，讲师，博士(通讯作者. E-mail: lcx13099971218@163.com)

中图分类号: O322
计量
- 文章访问数: 70
- HTML全文浏览量: 34
- PDF下载量: 11
- 被引次数: 0
出版历程
- 收稿日期: 2024-02-22
- 修回日期: 2024-05-10
- 刊出日期: 2025-02-01

Vertical Vibration Control of Nonlinear Viscoelastic Isolation Systems With Time Delay Feedback

WANG Daohang^1
,,
SUN Bo¹,
LIU Chunxia^{2
, ,},
ZHOU Ziyi¹,
LIU Yu¹

1.
Faculty of Public Security and Emergency Management, Kunming University of Science and Technology, Kunming 650000, P.R.China
2.
Department of Mathematics, School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650000, P.R.China

摘要

摘要: 研究了时滞反馈对非线性黏弹性隔振系统的竖向振动控制情况. 基于黏弹性非线性Zener模型，引入时滞控制器，建立了时滞反馈黏弹性隔振系统数学模型；采用多尺度法得到了主共振条件下的近似解析解，并根据Routh-Hurwitz理论获取了系统的稳定性条件；最后，分析了时滞参数与黏弹性隔振系统振动行为的相关性. 研究结果表明，时滞控制器能够有效地对黏弹性竖向振动系统的不稳定行为和振动幅值进行控制，且时滞参数可作为独立变量调控系统振动特性. 研究结果可为利用时滞控制提高黏弹性隔振系统竖向振动稳定性的应用提供理论指导.
- 黏弹性隔振器 /
- 非线性振动 /
- 时滞反馈控制 /
- Zener模型 /
- 多尺度法 /
- 稳定性
Abstract: The vertical vibration control of nonlinear viscoelastic vibration isolation systems with time delay feedback was studied. Based on the viscoelastic nonlinear Zener model, a time delay controller was introduced to establish the mathematical model for time delay feedback viscoelastic vibration isolation system. The approximate analytical solution under the condition of primary resonance was obtained with the multiscale method. The stability conditions of the system were obtained based on the Routh-Hurwitz theory. Finally, the correlation between the time delay parameters and the vibration behavior of the viscoelastic vibration isolation system was analyzed. The results show that, the time delay controller can effectively control the unstable behaviors and vibration amplitudes of the viscoelastic vertical vibration system, and the time delay parameters can be used as independent variables to regulate the vibration characteristics of the system. The work provides a theoretical guidance for the application of time delay control to improve the vertical vibration stability of viscoelastic vibration isolation systems.
- viscoelastic isolator /
- nonlinear vibration /
- time delay feedback control /
- Zener model /
- multiscale method /
- stability

HTML全文

图 1 黏弹性隔振系统等效力学模型

Figure 1. The equivalent mechanical model for the viscoelastic isolation system

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图 2 数值解与解析解对比

Figure 2. Comparison between numerical and analytical solutions

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图 3 系统衰减率随时滞的变化(c=0.07)

Figure 3. The decay rates of the system varying with the time delay (c=0.07)

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图 4 不同反馈增益系数下时滞-振幅曲线

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. Delay-amplitude curves under different feedback gain coefficients

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图 5 不同反馈增益系数下的幅频曲线

Figure 5. Amplitude frequency curves under different feedback gain coefficients

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图 6 不同时滞量下的幅频曲线

Figure 6. Amplitude frequency curves under different time delays

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图 7 与τ₁和τ₂有关的稳定区域和不稳定区域

Figure 7. Stable and unstable regions related to τ₁ and τ₂

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图 8 不同时滞参数下外激励-振幅曲线

Figure 8. External excitation-amplitude curves under different time delay parameters

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