橡胶四元件模型动力学特性分析

俞力洋; 黄然; 吴少培; 丁旺才; 李国芳; 屈鸣鹤

doi:10.13433/j.cnki.1003-8728.20220209

橡胶四元件模型动力学特性分析

doi: 10.13433/j.cnki.1003-8728.20220209

兰州交通大学机电工程学院，兰州　730070

基金项目: 国家自然科学基金项目（11962013，11732014，12162020）、甘肃省优秀研究生“创新之星”项目（2021CXZX-543）、甘肃省教育厅高校大学生就业创业能力提升工程项目（2021）及甘肃省青年科技基金项目（21JR7RA328，21JR7RA335）

详细信息

作者简介:
俞力洋（1995−），博士研究生，研究方向为非线性动力学，yuly1101@163.com

通讯作者:
丁旺才，教授，博士生导师，dingdd@163.com

中图分类号: O321; O328
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- 文章访问数: 63
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- 被引次数: 0
出版历程
- 收稿日期: 2021-12-01
- 修回日期: 2022-01-04
- 刊出日期: 2023-02-04

Dynamic Characteristics Analysis of Rubber Four-element Model

School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 采用四元件模型表征橡胶等黏弹隔振系统的动力学特性，利用谐波平衡法求解了系统的无量纲运动微分方程，分析了参数对系统幅频特性与力传递率的影响规律，推导了系统单频激励与多频激励下最优阻尼系数的计算方法。结果表明：增大阻尼系数或刚度比会使系统共振峰向高频方向偏移，同时也会拓宽系统在低频区的有效隔振范围；刚度比的合理设计可使系统共振峰远离被隔振系统工作主频，而在不降低系统静挠度的条件下，还可通过调整阻尼系数实现系统共振频率的小范围微调；确定刚度比时，系统不同阻尼系数下的幅频响应曲线与力传递率曲线各有一个公共点，基于这一典型特征可计算出系统既定参数下的最优阻尼系数，使系统共振峰值最小、隔振性能最佳；该方法同样适用于多频激励作用下系统最优阻尼系数的计算。
- 橡胶隔振系统 /
- 幅频特性 /
- 力传递率 /
- 最优阻尼系数
Abstract: A four-component model was used to characterize the dynamic characteristics of rubber viscoelastic vibration isolation system, and the dimensionless differential equation of the system was solved by harmonic balance method. The influence of parameters on the amplitude-frequency characteristics and force transmissibility of the system was analyzed, and the calculation method of the optimal damping coefficient under single frequency excitation and multiple frequency excitation was derived. The results show that increasing the damping coefficient or stiffness ratio will shift the system′s resonance peak to the high frequency direction, and also broaden the effective vibration isolation range in the low frequency region. The reasonable design of the stiffness ratio can make the resonance peak of the system far away from the main frequency of the vibration isolation system, and under the condition of not reducing the static deflection of the system, the resonance frequency of the system can be fine-tuned in a small range by adjusting the damping coefficient. When the stiffness ratio is determined, the amplitude-frequency response curves and force transfer curves have a common point under different damping coefficients. Based on this characteristic, the optimal damping coefficient under given parameters can be calculated, which minimizes the resonance peak and optimizes the vibration isolation performance of the system. The method can also be used to calculate the optimal damping coefficient of the system under multi-frequency excitation.
- rubber vibration isolation system /
- amplitude frequency characteristic /
- force transmissibility /
- optimal damping ratio

HTML全文

图 1 四元件橡胶隔振系统

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图 2 质量块幅频响应对比图

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图 3 不同参数条件下阻尼系数对质量块幅频响应的影响

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图 4 $ {\mu _{{K1}}} = 1,{\mu _{K2}} = 0.01 $时质量块的最佳幅频响应

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图 5 $ {\mu _{K1}} = 3,{\mu _{K2}} = 0.01 $时质量块的最佳幅频响应

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图 6 双频率激励下质量块最佳幅频响应

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图 7 $ {\mu _{K1}} = 1,{\mu _{K2}} = 0.01 $时$\, \beta $在$ (\omega ,\xi ) $参数平面的分布

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图 8 $ \xi = 0.2,{\mu _{K2}} = 0.01 $时$ \,\beta $在$ (\omega ,{\mu _{K1}}) $参数平面的分布

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图 9 参数对系统力传递率的影响

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图 10 $ {\mu _{{\text{k1}}}} = 1,\;{\mu _{{\text{k2}}}} = 0.01 $时系统的最佳力传递率

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