一类阻尼控制半主动隔振系统的解析研究

张婉洁; 牛江川; 申永军; 杨绍普; 王丽

doi:10.6052/0459-1879-20-147

一类阻尼控制半主动隔振系统的解析研究

张婉洁^*,†,
牛江川^*,†,2), ,,
申永军^*,†,
杨绍普^*,
王丽^†

^*石家庄铁道大学交通工程结构力学行为与系统安全国家重点实验室,石家庄 050043
^†石家庄铁道大学机械工程学院,石家庄 050043

基金项目: 1) 国家自然科学基金资助项目(11872254);国家自然科学基金资助项目(U1934201);国家自然科学基金资助项目(11790282)

详细信息

作者简介:
2) 牛江川,教授,主要研究方向：机械系统动力学与振动控制. E-mail： menjc@163.com

通讯作者:
牛江川

中图分类号: O322,O328
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出版历程
- 收稿日期: 2020-05-05
- 刊出日期: 2020-12-09

DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL

Zhang Wanjie^*,†,
Niu Jiangchuan^*,†,2), ,,
Shen Yongjun^*,†,
Yang Shaopu^*,
Wang Li^†

^*State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043,China
^†School of Mechanical Engineering, Shijiazhuang Tiedao University,Shijiazhuang 050043,China

摘要

摘要: 研究了一类基于相对速度反馈的含立方刚度的单自由度非线性半主动隔振系统.通过平均法得到了系统分别在基于加速度-相对速度反馈的加速度驱动阻尼控制策略、速度-相对速度反馈的天棚阻尼控制策略和位移-相对速度反馈的地棚阻尼控制策略下主共振响应的近似解析解,并利用数值解验证了近似解析解的准确性.通过 Lyapunov 理论对不同控制策略下系统的稳定性进行了分析,讨论了系统参数对控制效果的影响.分析结果表明,对 3 种基于相对速度反馈的控制策略进行解析研究时,切换条件中的控制参数具有相同的表达式;在抑制共振响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略在低频时的减振效果最好,而基于加速度-相对速度反馈的加速度驱动阻尼控制策略在高频时的减振效果最优;在抑制瞬态响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略的减振效果最好.此类解析研究方法可应用到其他半主动开关控制策略中,为半主动隔振系统的控制策略研究提供了有效的方法和手段.
- 隔振系统 /
- 半主动控制 /
- 主共振 /
- 平均法 /
- 近似解析解
Abstract: A series of single-degree-of-freedom semi-active nonlinear vibration isolation system with cubic stiffness based on relative velocity feedback on-off control is studied. By using the averaging method, the approximate analytical solutions of the primary resonance of the system are obtained, which is controlled by the acceleration and relative velocity based acceleration drive damping control, the velocity and relative velocity based sky-hook damping control, and the displacement and relative velocity based ground-hook damping control, respectively. A further comparison between the numerical solutions and the approximate analytical solutions under different control strategies is fulfilled. And such comparison results suggest that the approximate analytical results are quite consistent with the numerical solutions, which verifies the effectiveness of the approximate analytical solutions. Moreover, the stability conditions of the steady-state solution of the system under different control strategies are analyzed by Lyapunov theory, and the influences of system parameters on the control effect are discussed. In order to compare the control performances in the three different control approaches, the amplitude-frequency response equation is conducted. The results show that the similar expressions can be found in the switching conditions in the process of the analytical analysis of the three relative velocity feedback control strategies. In the aspect of suppressing resonance response amplitude, the sky-hook damping control strategy based on velocity and relative velocity feedback has the best damping effect in low frequency band, while the acceleration drive damping control strategy based on acceleration and relative velocity feedback has the best damping effect in high frequency band. The sky-hook damping control strategy also shows good performance in reducing the amplitude response of transient response. This analytical research method can also be applied to the system with other semi-active on-off control strategies, and it provides an effective way for the control strategy research of semi-active vibration isolation system.
- vibration isolation system /
- semi-active control /
- primary resonance /
- averaging method /
- approximate analytical solution

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