基于内嵌式颗粒阻尼器的悬臂梁减振实验研究

张扬; 张万福; 田海洋; 彭佼飞; 李春

doi:10.13224/j.cnki.jasp.20230146

基于内嵌式颗粒阻尼器的悬臂梁减振实验研究

doi: 10.13224/j.cnki.jasp.20230146

上海理工大学能源与动力工程学院，上海 200093

基金项目: 国家自然科学基金（51875361）

详细信息

作者简介:
张扬（1998-），男，硕士生，研究方向为透平机械振动控制

通讯作者:
张万福(1986-)，男，教授，博士，研究方向为透平机械振动故障诊断及转子动力学。E-mail：wfzhang@usst.edu.cn

中图分类号: V216.2；TK263
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出版历程
- 收稿日期: 2023-03-12
- 网络出版日期: 2023-10-13

Experimental investigation of cantilever beam vibration based on embedded particle dampers

School of Energy and Power Engineering，University of Shanghai for Science and Technology，Shanghai 200093，China

摘要

摘要:
针对悬臂梁结构振动控制问题，开展基于内嵌式颗粒阻尼（embedded particle damper, EPD）减振方法的理论与实验研究。应用有限元法分析悬臂梁振动特性，围绕梁前三阶模态频率开展振动控制实验，通过改变填充颗粒的参数（粒径、填充率）和激励力，比较悬臂梁在不同填充情况下的振幅，并使用半功率法计算阻尼比。采用离散元法分析不同情况下颗粒的流变行为，以确定阻尼器最优设计参数。结果表明：颗粒填充率为90%时EPD减振效果最佳；填充颗粒的粒径与系统所受激励有关，本文模型中，激励振幅为80 μm时，梁前三阶模态频率下分别填充直径为8、6、1 mm颗粒时效果最好，减振率分别为47.5%、48.7%及71.2%，阻尼比分别提高1.7、3.1及2.1倍。
- 非阻塞性颗粒阻尼器 /
- 悬臂梁 /
- 颗粒填充率 /
- 内嵌式颗粒阻尼器 /
- 振动特性
Abstract:
Theoretical and experimental researches on embedded particle damper (EPD) damping method were carried out for vibration control of the cantilever beam structure. The finite element method was applied to analyze the vibration characteristics of the cantilever beam, and the vibration control experiments were carried out under the first, second and third order modal frequencies of the beam. By changing the parameters of the filled particles (particle size, filling rate) and the excitation force, the amplitudes of the cantilever beam under different filling conditions were compared, and the damping ratio was calculated using the half-power method. The discrete element method was used to analyze the rheological behavior of the particles in different cases to determine the optimal design parameters of the dampers. The results showed that: the best damping effect of EPD was achieved when the particle filling ratio was 90%; the particle size of the filled particles was related to the excitation of the system. In this model, when the excitation amplitude was 80 μm, the best effect was achieved when the beam was filled with 8, 6, 1 mm particles at these three modal frequencies, and the damping ratios were 47.5%, 48.7% and 71.2%, respectively, and the damping ratios increased by 1.7, 3.1 and 2.1 times, respectively.
- non-obstructive particle dampers /
- cantilever beams /
- particle filling rate /
- embedded particle dampers /
- vibration characteristics

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图 1 实验装置

Figure 1. Experimental device

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图 2 悬臂梁剖视图

Figure 2. Section view of cantilever beam

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图 3 不同直径颗粒

Figure 3. Particles with various diameters

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图 4 EPD振动控制模型

Figure 4. EPD vibration control model

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图 5 法向振动、切向振动及滑动模型

Figure 5. Model of normal vibration, tangential vibration and sliding

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图 6 悬臂梁模态振型

Figure 6. Modal of the cantilever beam

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图 7 不同颗粒填充率下悬臂梁振动响应

Figure 7. Response of cantilever beam with different particle filling rates

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图 8 不同填充率颗粒的动能分布

Figure 8. Kinetic energy of particles with different filling rates

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图 9 填充不同颗粒时悬臂梁振动情况

Figure 9. Vibration of cantilever beam when filled with different particles

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图 10 不同粒径颗粒的运动轨迹

Figure 10. Motion track of particles with different sizes

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图 11 不同填充情况下的频响函数图

Figure 11. Frequency response function for different filling cases

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图 12 不同激励振幅下颗粒的振幅衰减率和阻尼比

Figure 12. Amplitude decay rate and damping ratio of particles with different excitation amplitudes

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图 13 梁填充各颗粒在不同激励振幅下的阻尼比

Figure 13. Damping ratios of beams filled with different particles at different excitation amplitudes

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图 14 γ=90%时各颗粒堆积情况

Figure 14. Accumulation of each particle when γ=90%

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图 15 不同振动频率下的振幅和阻尼比

Figure 15. Amplitude and damping ratio at different vibration frequencies

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表 1 悬臂梁结构参数

Table 1. Structural parameters of cantilever beam

参数	数值
长×宽×高/（mm×mm×mm）	400×38.1×12.7
质量/g	600
孔直径/mm	8.5
孔深度/mm	240
密度/（kg/m³）	2700
剪切模量/10¹⁰ Pa	2.654
泊松比	0.3
碰撞恢复系数	0.65

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表 2 实验工况

Table 2. Experimental conditions

实验变量	数值
颗粒填充率γ/%	50, 70, 90, 100
颗粒直径D/mm	1, 2, 3, 4, 5, 6, 7, 8
激励振幅A/μm	80, 200, 600, 1000
激励频率f/Hz	63, 150, 410

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表 3 EDEM仿真参数

Table 3. EDEM simulation parameters

参数	数值
颗粒间动摩擦因数	0.01
颗粒间静摩擦因数	0.2
颗粒-壁面动摩擦因数	0.01
颗粒-壁面静摩擦因数	0.5
颗粒材料弹性模量/10¹¹ Pa	2
仿真步长/10⁻⁷	3
仿真时间/s	3

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表 4 颗粒间有效碰撞次数

Table 4. Effective collisions between particles

D/mm	γ=50%	γ=70%	γ=90%	γ=100%
1	0	8132	205417	29756
2	1554	5481	52887	38963
3	1093	2870	5343	3814

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表 5 颗粒与壁面间有效碰撞次数

Table 5. Effective collisions between particles and wall

D/mm	γ=50%	γ=70%	γ=90%	γ=100%
1	0	216	6484	1915
2	146	549	2541	1314
3	718	1169	1841	897

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