混联Ⅱ型惯容非线性能量阱的动力学特性研究

吴子英; 朱荣贤; 姜东贵; 晁国强; 张禹轩

doi:10.21656/1000-0887.440350

混联Ⅱ型惯容非线性能量阱的动力学特性研究

doi: 10.21656/1000-0887.440350

西安理工大学机械与精密仪器工程学院, 西安 710048

基金项目:

国家自然科学基金 11572243

详细信息

通讯作者:
吴子英(1975—)，男，副教授，博士(通讯作者. E-mail: ziyingwu@163.com)

中图分类号: O322;TP113
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- 文章访问数: 93
- HTML全文浏览量: 42
- PDF下载量: 22
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-08
- 修回日期: 2024-02-17
- 刊出日期: 2024-07-01

Research on Dynamic Characteristics of Serial-Parallel-Ⅱ Inerter Nonlinear Energy Sink

School of Mechanical and Precision Instrument Engineering, Xi'an Univercity of Technology, Xi'an 710048, P.R.China

摘要

摘要: 分别使用非线性恢复力、非线性阻尼替代惯容减振系统中的线性恢复力、线性阻尼，并考虑摩擦力的影响，提出了混联Ⅱ型惯容非线性能量阱. 建立了主系统的动力学方程，利用谐波平衡法求解系统在简谐激励下的幅频响应曲线. 采用弧长算法和数值法相结合的方法研究了系统的惯质比、非线性阻尼、非线性刚度和摩擦力单个参数对其减振性能的影响. 发现非线性刚度和非线性阻尼数值的增大会使峰值先减小后增大，不同的是，前者幅频响应曲线逐渐向右上方向弯曲，后者产生峰值的位置向低频段转移. 分析了惯质比、非线性阻尼、非线性刚度3种参数两两组合下对系统减振效果的影响. 研究表明，在激励幅值为0.005 m时，惯质比和阻尼同时变化减振效果最好：当ε=0.1时，系统主结构位移峰值的最小值约为0.01 m；而在参数ε=0.001时，整体取值范围内其最大值约为0.061 m；当惯质比取得最佳值0.1时，非线性阻尼和非线性刚度κ₂₁的取值范围变大. 在摩擦力的作用下，系统的最大幅值都有不同程度的增加. 上述研究可为振动系统减振的研究提供参考.
- 谐波平衡法 /
- 非线性 /
- 惯容器 /
- 振动控制
Abstract: A serial-parallel-Ⅱ inerter nonlinear energy sink was proposed through replacement of the linear restoring force and linear damping with the nonlinear restoring force and nonlinear damping in inertial vibration reduction systems, in view of the effects of friction. The dynamic equation for the main system was established, the amplitude-frequency response curves of the system under the base simple harmonic excitation were solved with the harmonic balance method. The effects of the inertia ratio, nonlinear damping, nonlinear stiffness and friction on the vibration damping performance of the system were studied with the arc length algorithm and the numerical method. The results show that, with the increase of the nonlinear stiffness and nonlinear damping, the peak value will first decrease and then increase. The difference is that the amplitude-frequency response curve of the former gradually bends to the upper right direction, and the position of the peak value of the latter shifts to the lower frequency band. The actions of 3 parameters of the inertial ratio, nonlinear damping and nonlinear stiffness, on the damping effects of the system were analyzed. The research indicates that, with an excitation amplitude of 0.005 m, the vibration reduction effect will be the best when the inertia ratio and damping change simultaneously. For ε=0.1, the minimum value of the peak displacement of the main structure of the system will be about 0.01 m, while for ε=0.001, the maximum value within the overall value range will be approximately 0.061 m, and the amplitude damping ratio will be 97.1% and 82.1%, respectively. When the inertia ratio reaches optimal value 0.1, the nonlinear damping range and nonlinear stiffness κ₂₁ will grow larger. Under friction, the maximum amplitude of the system will have different degrees of increases. The research results provide a reference for the study on structural vibration reduction.
- harmonic balance method /
- nonlinear /
- inerter /
- vibration control

HTML全文

图 1 新型混联Ⅱ型惯容NES力学模型

Figure 1. Mechanical modeling of a new serial-parallel-Ⅱ inerter NES

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图 2 滚珠丝杠惯容器的工作原理图

Figure 2. The ball screw inerter working principle diagram

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图 3 单自由度主系统的力学模型

Figure 3. Mechanical modeling of a 1-DOF primary system

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图 4 弧长算法求解示意图

Figure 4. Schematic diagram of the arc-length algorithm solution

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图 5 系统幅频响应曲线对比(ε=0.1, A=0.005 m)

Figure 5. Comparison of amplitude-frequency response curves of the system(ε=0.1, A=0.005 m)

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图 6 系统幅频响应曲线对比(ε=1, κ₂₂=120)

Figure 6. Comparison of amplitude-frequency response curves of the system(ε=1, κ₂₂=120)

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图 7 3种减振系统的力学模型

Figure 7. Mechanical models of 3 vibration reduction systems

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图 8 不同减振系统和激励幅值下主结构的幅频响应曲线(ε=0.1)

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 8. The amplitude-frequency response curves of the main structure under different vibration reduction systems and excitation amplitudes(ε=0.1)

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图 9 NES的质量比与减振率的关系曲线

Figure 9. Relation curves between the mass ratio of NES and the vibration reduction rate

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图 10 不同刚度比κ₂₁下的系统最大幅值(ε=0.1, A=0.005 m)

Figure 10. Maximum amplitude of the system for different stiffness ratios κ₂₁ (ε=0.1, A=0.005 m)

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图 11 不同刚度比κ₂₂下的系统幅频响应曲线(ε=1, A=0.005 m)

Figure 11. Amplitude-frequency response curve of the system with different stiffness ratio κ₂₂ (ε=1, A=0.005 m)

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图 12 不同阻尼下的系统幅频响应曲线(ε=1, A=0.005 m)

Figure 12. Amplitude-frequency response curve of the system under different damping (ε=1, A=0.005 m)

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图 13 摩擦力对主系统的非线性特性的影响(ε=0.1, A=0.005 m)

Figure 13. The influence of friction on the nonlinear characteristics of the primary system (ε=0.1, A=0.005 m)

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图 14 摩擦力下的系统幅频响应曲线(ε=0.1, A=0.005 m)

Figure 14. Amplitude-frequency response curve of the system under friction force(ε=0.1, A=0.005 m)

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图 15 刚度和阻尼同时变化对主结构频响曲线峰值的影响

Figure 15. Influence of simultaneous stiffness and damping changes on the peak value of the frequency response curve of the main structure

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图 16 刚度和惯质比同时变化对主结构频响曲线峰值的影响

Figure 16. Influence of simultaneous stiffness and inertia ratio changes on the peak of the frequency response curve of the main structure

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图 17 惯质比和阻尼同时变化对主结构频响曲线峰值的影响

Figure 17. Influence of simultaneous inertia ratio and damping changes on the peak of the frequency response curve of the main structure

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表 1 混联Ⅱ型惯容NES系统的仿真参数

Table 1. Simulation parameters of the serial-parallel-Ⅱ inerter NES system

symbol	value
main structural mass m₁/kg	3.3
inerter parameter b/kg	0.33
main structure damping c₁/(N·s·m^-1)	1.4
linear stiffness k₁/(N/m)	2 814
linear coefficient of nonlinear damping c₂₁/(N·s·m^-1)	5
nonlinear coefficient of nonlinear damping c₂₂/(N·s³·m^-3)	5
linear coefficient of nonlinear stiffness k₂₁/(N/m)	4 814
nonlinear coefficient of nonlinear stiffness k₂₂/(N/m³)	199 980
excitation amplitude A/m	0.005
natural frequency ω₁/(rad/s)	29.2
inertia ratio ε	0.1

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表 2 3种减振系统减振效果的对比

Table 2. Comparison of vibration reduction effects of 3 vibration reduction systems

excitation amplitude A/m	system name	value
	system name	T-NES	SP-Ⅱ-Ⅰ	I-NES
	inertia ratio		ε_I=0.1	ε_I=0.1
	mass ratio	ε_m=0.1	ε_b=0.001	ε_b=0.001
0.002 5	A_i/m	0.021 9	0.033 0	0.025 2
0.002 5	R_i/%	87.2	80.71	85.27
0.005	A_i/m	0.230 1	0.066 0	0.038 8
0.005	R_i/%	40.63	80.70	88.66
0.001	A_i/m	0.574 6	0.132 1	0.056 6
0.001	R_i/%	15.61	80.60	91.69

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