复合干摩擦的准零刚度隔振系统的亚谐共振 -

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复合干摩擦的准零刚度隔振系统的亚谐共振

doi:10.6052/0459-1879-21-680

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:国家自然科学基金(11872254, U1934201, 11802183)和河北省自然科学基金(A2021210012)资助项目

详细信息

作者简介:
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@stdu.edu.cn

中图分类号:O322
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- 被引次数:0
出版历程
- 收稿日期:2021-12-21
- 录用日期:2022-02-10
- 网络出版日期:2022-02-11
- 刊出日期:2022-04-18

SUBHARMONIC RESONANCE OF QUASI-ZERO-STIFFNESS VIBRATION ISOLATION SYSTEM WITH DRY FRICTION DAMPER

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:利用增量平均法研究了复合干摩擦阻尼器的准零刚度非线性隔振系统在外部简谐激励作用下的1/3次亚谐共振. 首先利用平均法得到了复合干摩擦的准零刚度隔振系统的主共振近似解析解, 然后在系统主共振近似解析解的基础上将系统的亚谐共振响应看作增量, 并利用平均法得到了准零刚度隔振系统的亚谐共振近似解析解. 利用李雅普诺夫方法得到了准零刚度隔振系统主共振和亚谐共振稳态解的稳定性条件, 并推导了系统1/3次亚谐共振的存在条件. 根据近似解析解分别得到了复合干摩擦的准零刚度隔振系统的主共振和亚谐共振力传递率. 利用数值解验证了准零刚度隔振系统主共振和亚谐共振近似解析解的准确性. 利用系统的近似解析解详细分析了准零刚度参数和干摩擦力对系统主共振和亚谐共振的幅频响应以及力传递特性的影响. 分析结果表明, 通过选取合适的干摩擦力参数, 可以消除准零刚度隔振系统在主共振区域的亚谐共振. 通过复合干摩擦阻尼器不但可以提高准零刚度隔振系统在低频区域的振幅抑制效果, 而且可以降低准零刚度隔振系统的起始隔振频率, 但是会增大系统在有效隔振频带内的力传递率.
- 亚谐共振/
- 准零刚度/
- 隔振/
- 干摩擦
Abstract:The 1/3 subharmonic resonance of the quasi-zero-stiffness nonlinear vibration isolation system with dry friction damper is studied by using the incremental averaging method, which is subjected to external simple harmonic excitation. Firstly, the approximate analytical solution of the primary resonance of the quasi-zero-stiffness vibration isolation system with dry friction damper is obtained by using the averaging method. Then, based on the approximate analytical solution of the primary resonance of the system, the subharmonic resonance response of the system is regarded as an increment, and the approximate analytical solution of the subharmonic resonance of the quasi-zero-stiffness vibration isolation system is obtained by using the averaging method. The stability conditions of the steady-state solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system are obtained by using the Lyapunov method, and the existence condition of the 1/3 subharmonic resonance of the quasi-zero-stiffness vibration isolation system is deduced. According to the approximate analytical solution, the primary resonance and subharmonic resonance force transmissibility of the quasi-zero-stiffness vibration isolation system with dry friction damper are obtained respectively. Compared with the numerical solution, the accuracy of the approximate analytical solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system is verified. By using the approximate analytical solution of the system, the effects of quasi-zero stiffness parameters and dry friction force on the amplitude-frequency response and force transfer characteristics for the primary resonance and subharmonic resonance of the system are analyzed in detail. The results show that the subharmonic resonance of the quasi-zero-stiffness vibration isolation system in the primary resonance region can be eliminated by selecting appropriate dry friction force parameter. The addition of dry friction damper can not only improve the amplitude suppression effect of the quasi-zero-stiffness vibration isolation system in the low frequency region, but also reduce the initial vibration isolation frequency. However, it will increase the force transmissibility of the system in the vibration isolation frequency band with vibration isolation effect.
- subharmonic resonance/
- quasi-zero stiffness/
- vibration isolation/
- dry friction

HTML全文

图 1准零刚度隔振系统模型

Figure 1.Quasi-zero-stiffness vibration isolation system model

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图 2水平弹簧在垂直方向的弹性恢复力位移曲线

Figure 2.Restoring force-displacement curve of horizontal springs in vertical direction

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3幅频响应响应曲线对比

3.Comparison of amplitude-frequency response curves

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3幅频响应响应曲线对比(续)

3.Comparison of amplitude-frequency response curves (continued)

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4力传递率对比

4.Comparison of force transmissibility

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5不同准零刚度参数的振动控制效果

5.Effect of different quasi-zero-stiffness parameters

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5不同准零刚度参数的振动控制效果(续)

5.Effect of different quasi-zero-stiffness parameters (continued)

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6不同干摩擦力的振动控制效果

6.Effect of different dry friction force

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