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Article(id=1243896353676444586, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.09.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1742227200000, receivedDateStr=2025-03-18, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774497601193, onlineDateStr=2026-03-26, pubDate=1758297600000, pubDateStr=2025-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774497601193, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774497601193, creator=13701087609, updateTime=1774497601193, updator=13701087609, issue=Issue{id=1243896350367134664, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='9', pageStart='1343', pageEnd='1498', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774497600404, creator=13701087609, updateTime=1774501609474, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243913165692584796, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243913165692584797, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896350367134664, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1484, endPage=1491, ext={EN=ArticleExt(id=1243896353999405995, articleId=1243896353676444586, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Research on vibration equivalent mass characteristics of particle damping vibration absorber with obstacle network, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

Particle damping vibration absorber is a dynamic vibration absorber that uses a mass block containing several particles as the mass element. It has the effect of broadening the effective frequency band of dynamic vibration absorbers and suppressing the secondary line spectrum of dynamic vibration absorbers. However, dynamic vibration absorber control techniques are sensitive to parameter selection, and the vibration equivalent mass of particle damping vibration absorbers changes with variations in excitation amplitude, affecting their vibration absorption performance and practical engineering applications. The method of building a 3D network into the mass block was proposed to improve the above defects. The influence of adding obstacle network into the mass block of particle damping vibration absorber was studied by experiment and simulation in this paper. The results show that when the vibration intensity of the particle damping vibration absorber is high, a part of the particles in the mass block enter a suspended flow state, leading to these particles not participating in the vibration process. As a result, equivalent mass of particle damping vibration absorber is changed, and the vibration absorption frequency has shifted. And the 3D network can keep the vibrational equivalent mass stable by breaking up the suspended flow state of the particles. And the vibration reduction effect is effectively improved on the specific vibration amplitude.

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颗粒阻尼吸振器是将含颗粒的质量块作为质量元件的动力吸振器，具有拓宽动力吸振有效频带及抑制动力吸振器二次线谱的作用。但动力吸振技术对于参数选取较为敏感，颗粒阻尼吸振器的振动等效质量会随激振幅值的变化而变化，影响其吸振性能及实际工程应用。因此，本文引入三维网络结构，构建障碍网络颗粒阻尼吸振器解决该问题，并通过试验和仿真研究障碍网络颗粒阻尼吸振器振动等效质量特性。研究结果表明：对于颗粒阻尼吸振器而言，一定的振动幅值会引起颗粒产生悬浮流态，导致其振动等效质量减小，而三维网络结构会打散颗粒悬浮流态，使其振动等效质量保持稳定，并在特定的振动幅值上有效提升减振效果。

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通讯作者，E-mail：
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蒋捷（1999-），男，硕士研究生

昝浩（1987-），男，博士，硕士研究生导师，通讯作者，E-mail：。

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蒋捷（1999-），男，硕士研究生

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蒋捷（1999-），男，硕士研究生

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昝浩（1987-），男，博士，硕士研究生导师，通讯作者，E-mail：。

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昝浩（1987-），男，博士，硕士研究生导师，通讯作者，E-mail：。

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Physical parameters of particle dampers

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组成密度/（kg·m−3）泊松比弹性模量/Pa恢复系数静摩擦因子滚动摩擦因子
颗粒79300.32.06×10110.740.20.01
壳体11900.323.3×1090.30.1540.01
网络11200.232.46×1090.70.30.01
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颗粒阻尼器接触参数

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组成密度/（kg·m−3）泊松比弹性模量/Pa恢复系数静摩擦因子滚动摩擦因子
颗粒79300.32.06×10110.740.20.01
壳体11900.323.3×1090.30.1540.01
网络11200.232.46×1090.70.30.01
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障碍网络颗粒阻尼吸振器振动等效质量特性研究
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蒋捷 1 , 陈本兰 2 , 汪冰 3 , 薛一帆 1 , 夏兆旺 1 , 陆金铭 1 , 昝浩 1
船舶力学 | 流体与结构声学 2025,29(9): 1484-1491
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船舶力学 | 流体与结构声学 2025, 29(9): 1484-1491
障碍网络颗粒阻尼吸振器振动等效质量特性研究
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蒋捷1, 陈本兰2, 汪冰3, 薛一帆1, 夏兆旺1, 陆金铭1, 昝浩1
作者信息
  • 1.江苏科技大学　能源与动力学院，江苏　镇江　212003
  • 2.中国舰船研究设计中心，武汉　430064
  • 3.宁波杜亚机电技术有限公司，浙江　宁波　315202

    • 蒋捷（1999-），男，硕士研究生

    昝浩（1987-），男，博士，硕士研究生导师，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Research on vibration equivalent mass characteristics of particle damping vibration absorber with obstacle network
Jie JIANG1, Ben-lan CHEN2, Bing WANG3, Yi-fan XUE1, Zhao-wang XIA1, Jin-ming LU1, Hao ZAN1
Affiliations
  • 1.School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • 2.China Ship Development and Design Center, Wuhan 430064, China
  • 3.Ningbo Dooya Mechanic & Electronic Technology Co., Ltd, Ningbo 315202, China
出版时间: 2025-09-20 doi: 10.3969/j.issn.1007-7294.2025.09.014
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颗粒阻尼吸振器是将含颗粒的质量块作为质量元件的动力吸振器，具有拓宽动力吸振有效频带及抑制动力吸振器二次线谱的作用。但动力吸振技术对于参数选取较为敏感，颗粒阻尼吸振器的振动等效质量会随激振幅值的变化而变化，影响其吸振性能及实际工程应用。因此，本文引入三维网络结构，构建障碍网络颗粒阻尼吸振器解决该问题，并通过试验和仿真研究障碍网络颗粒阻尼吸振器振动等效质量特性。研究结果表明：对于颗粒阻尼吸振器而言，一定的振动幅值会引起颗粒产生悬浮流态，导致其振动等效质量减小，而三维网络结构会打散颗粒悬浮流态，使其振动等效质量保持稳定，并在特定的振动幅值上有效提升减振效果。

颗粒阻尼吸振器  /  障碍网络  /  振动等效质量  /  离散元仿真

Particle damping vibration absorber is a dynamic vibration absorber that uses a mass block containing several particles as the mass element. It has the effect of broadening the effective frequency band of dynamic vibration absorbers and suppressing the secondary line spectrum of dynamic vibration absorbers. However, dynamic vibration absorber control techniques are sensitive to parameter selection, and the vibration equivalent mass of particle damping vibration absorbers changes with variations in excitation amplitude, affecting their vibration absorption performance and practical engineering applications. The method of building a 3D network into the mass block was proposed to improve the above defects. The influence of adding obstacle network into the mass block of particle damping vibration absorber was studied by experiment and simulation in this paper. The results show that when the vibration intensity of the particle damping vibration absorber is high, a part of the particles in the mass block enter a suspended flow state, leading to these particles not participating in the vibration process. As a result, equivalent mass of particle damping vibration absorber is changed, and the vibration absorption frequency has shifted. And the 3D network can keep the vibrational equivalent mass stable by breaking up the suspended flow state of the particles. And the vibration reduction effect is effectively improved on the specific vibration amplitude.

particle damping vibration absorber  /  obstacle network  /  vibration equivalent mass  /  discrete element simulation
蒋捷, 陈本兰, 汪冰, 薛一帆, 夏兆旺, 陆金铭, 昝浩. 障碍网络颗粒阻尼吸振器振动等效质量特性研究. 船舶力学, 2025 , 29 (9) : 1484 -1491 . DOI: 10.3969/j.issn.1007-7294.2025.09.014
Jie JIANG, Ben-lan CHEN, Bing WANG, Yi-fan XUE, Zhao-wang XIA, Jin-ming LU, Hao ZAN. Research on vibration equivalent mass characteristics of particle damping vibration absorber with obstacle network[J]. Journal of Ship Mechanics, 2025 , 29 (9) : 1484 -1491 . DOI: 10.3969/j.issn.1007-7294.2025.09.014
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0　引言
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动力吸振器具有结构简单、可靠性高、且不需外界能量等优点，在船舶动力设备的振动抑制中获得广泛的应用。动力吸振器可以针对某一特定频率起到有效抑制主系统振动的作用，但存在有效减振频带窄、鲁棒性差等缺点，而颗粒阻尼具有布置灵活、安装方便、减振频带宽、鲁棒性较强和成本低等优点。因此我们考虑结合颗粒阻尼技术，以含颗粒的质量块代替动力吸振器的质量元件，形成颗粒阻尼吸振器，以期拓宽动力吸振的有效频带，并利用颗粒阻尼的阻尼效应来抑制动力吸振器的二次线谱。
由于颗粒阻尼具有高度非线性和参数影响的多样性，颗粒阻尼的模型与预估理论工作一直没有停止过[1]。离散元法的提出[2-5]实现了对颗粒阻尼进行数值模拟和表征。其次，Hu等[6]通过建立粉体力学模型分析了颗粒阻尼器的不同几何参数对颗粒阻尼特性的影响，揭示了颗粒阻尼的非线性特性。随着研究的深入，研究人员提出了一种在深度神经网络框架下基于迁移学习的多保真建模方法[7]，用于表征颗粒阻尼器的动态阻尼性能。而遗传算法-支持向量回归模型[8]则可以用来预测颗粒阻尼器的阻尼性能。目前，离散元法作为颗粒阻尼研究的主要理论分析方法，由于其揭示了颗粒-颗粒之间以及颗粒-壁面之间的相互作用，因此被用来研究颗粒阻尼的耗能机理和力学现象。夏兆旺等人[9]将颗粒阻尼应用于海洋平台的结构减振，发现颗粒密度和填充率对系统的减振效果影响明显，且颗粒直径只在高频振动时对桁架的振动有影响。在最近的研究中发现，颗粒阻尼器在较高振动幅值的情况下其减振效果并不理想[10]，但通过在颗粒阻尼器的空腔中嵌入障碍结构[11]，可以影响颗粒的运动状态并提高颗粒阻尼器的能量耗散。在Gnanasambandham等[12]的研究中，通过引入三维网络，使带网络颗粒阻尼器的阻尼性能达到传统颗粒阻尼器的两倍。再进一步，Hu等人[13]通过试验验证了三维网络可以改善颗粒阻尼器的耗能，采用离散元法仿真分析了振动参数和填充率对耗能的影响，并总结了颗粒阻尼器的耗能特征。其次，研究人员将障碍网络颗粒阻尼器置于悬臂梁结构[14]，研究了障碍网络颗粒阻尼器的各项参数对悬臂梁振动的影响并与传统颗粒阻尼器对比，结果表明障碍网络能有效地提高颗粒阻尼器的阻尼性能。
随着障碍网络颗粒阻尼器的研究往低频、低振动幅值方向的深入，学者[15]发现颗粒阻尼器和障碍网络颗粒阻尼器在此情况下并没有良好的减振效果。图1所示为根据试验测得的颗粒阻尼器与障碍网络颗粒阻尼器的损耗因子云图，能明显看出在低频低振动幅值情况下两者的损耗因子较低。因此，将颗粒阻尼与动力吸振相结合[16]，将吸振器子系统的质量块用颗粒阻尼器来代替，使得颗粒阻尼吸振器既能够吸收主系统能量，又能够发挥颗粒阻尼在低振动加速度环境中的阻尼作用。其次，Liu[17]在研究中发现，颗粒阻尼器在振动过程中会出现振动等效质量随激振幅值增大而减小的现象，表现为共振峰会随激振幅值的变化而变化，当激振幅值达到一定值时，颗粒阻尼器的等效质量将趋于无颗粒填充的容器，但该现象产生的机理并无研究，并且对于等效质量变化问题的解决措施也存在空缺。
针对上述研究，本文将颗粒阻尼与动力吸振相结合，用含颗粒质量块代替动力吸振的质量元件，以构成颗粒阻尼吸振器解决船舶动力设备低频多线谱振动控制的难题。但由于动力吸振技术对于参数的选取较为敏感，而含颗粒质量元件的振动等效质量会随激振幅值的变化而改变，使吸振频率发生偏移，影响颗粒阻尼吸振器的减振效果。因此，我们通过内置三维网络，研究障碍网络颗粒阻尼吸振器的振动等效质量特性以寻求解决方法。本文依据动力吸振原理，研究单自由度颗粒阻尼-弹簧系统的固有频率以及障碍网络颗粒阻尼吸振器的减振效果，为障碍网络颗粒阻尼吸振器的实际工程应用提供一定的参考。
1　试验装置与测试系统
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颗粒阻尼吸振器振动试验装置如图2所示，其中含颗粒质量块由亚克力透明材料制成空腔结构，以便于开展可视化试验研究，将直径为2 mm的不锈钢颗粒按照质量填充比90%填充进质量块的空腔中，空腔的尺寸为L×W×H=30 mm×30 mm×50 mm。所用的障碍网络通过光敏树脂3D打印技术加工而成，障碍网络的结构单元间距为5 mm，网络直径为1 mm，障碍网络外形尺寸略小于质量块空腔尺寸以便嵌入。在颗粒阻尼器下端连接弹簧，经B&K力传感器固定在振动台上，其中弹簧刚度为82 500 N/m。其次，在颗粒阻尼器上端盖处与振动台上布置B&K加速度传感器，将采集到的力信号与两个加速度信号经DASP数据采集和分析系统进行处理分析。试验通过振动台输出一个正弦扫频激励，频率为10~120 Hz，加速度分别为0.2g、0.5g、0.8g。其中，g表示重力加速度常数，在本研究中取9.81 m/s2。若无特别说明，后文均以该定义为准。
2　试验结果
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试验填充的颗粒为粒径2 mm的304不锈钢钢球，分别对有无障碍网络的颗粒阻尼吸振器按质量填充比90%进行填充，然后依次在10~120 Hz的频段上，以振动加速度为0.2g、0.5g、0.8g进行振动试验。加速度为0.2g时，振动响应如图3所示，动力吸振器（300g）的固有频率为83.5 Hz，颗粒阻尼吸振器（330g）的固有频率为78 Hz，障碍网络颗粒阻尼吸振器（310g）的固有频率为81.5 Hz。此时有/无网络的颗粒阻尼吸振器的加速度峰值均小于动力吸振器，即吸振效果较动力吸振器而言更好。由于此时加速度较小，障碍网络会影响颗粒阻尼器的阻尼特性，在时域图上表现为障碍网络颗粒阻尼吸振器的加速度幅值较大，即此时颗粒阻尼吸振器的吸振效果优于障碍网络颗粒阻尼吸振器。
随着振动加速度的增大，即振动加速度为0.5g、0.8g时，颗粒阻尼吸振器固有频率变化如图4所示。颗粒阻尼吸振器的固有频率随振动加速度的增大而增大，其中，当振动幅值为0.5g时，颗粒阻尼吸振器的固有频率为84.5 Hz，其振动等效质量为292.67 g，减少了11.3%。对于障碍网络颗粒阻尼吸振器而言，在振动幅值增大的过程中，固有频率为81.5 Hz并未出现明显变化，即障碍网络颗粒阻尼吸振器的振动等效质量几乎不发生变化。当振动幅值为0.8g时，颗粒阻尼吸振器固有频率为90 Hz，其振动等效质量为257.99 g，减少了21.8%。对于障碍网络颗粒阻尼吸振器而言，此时固有频率仍为81.5 Hz，并未出现变化，即障碍网络颗粒阻尼吸振器振动等效质量几乎不变。由此得出，障碍网络的引入能够有效地防止在振动幅值变化时引起颗粒阻尼振动等效质量变化，从而避免对吸振效果的影响。其次，如图4（c）所示，此时障碍网络颗粒阻尼吸振器的加速度幅值要明显小于颗粒阻尼吸振器，即障碍网络颗粒阻尼吸振器具有更好的吸振效果。
3　离散元仿真
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由于颗粒阻尼受振动幅值的影响较大，在不同激励条件下颗粒运动会呈现出许多不同的运动状态。颗粒在垂直振动的条件下，会呈现出类固态、局部流化、全局流化、蹦床、对流、莱登弗罗斯特效应流和浮力对流等运动状态[18]，颗粒的流态可能会引起颗粒阻尼振动等效质量的变化。因此，我们采用离散元仿真分析有/无网络的颗粒阻尼吸振器在流化运动状态下的颗粒运动规律，以寻求颗粒阻尼振动等效质量变化的原因。颗粒阻尼离散元仿真的颗粒接触参数如表1所示，各组成部分的密度、泊松比、弹性模量很容易得到，而恢复系数、静摩擦因子、滚动摩擦因子可参考Hu[13]的研究取值。
通过离散元仿真对颗粒阻尼吸振器进行垂直正弦振动仿真模拟，仿真中颗粒阻尼吸振器以粒径为2 mm的颗粒按照质量填充比90%进行填充。依据振动台加速度为0.5g情况下，颗粒阻尼吸振器固有频率84.5 Hz以及对应加速度作为激励条件，通过离散元仿真分析颗粒阻尼吸振器的颗粒流态，观察到在颗粒振动过程中存在颗粒悬浮状态，如图5所示。我们将颗粒进行剖分，分析右半边悬浮颗粒的占比，由此得到悬浮部分颗粒约占总体颗粒的12%，与试验结果（11.3%）相符。
其次，通过离散元仿真对障碍网络颗粒阻尼吸振器进行垂直正弦振动仿真模拟，仿真中障碍网络颗粒阻尼吸振器以粒径为2 mm的颗粒按照质量填充比90%进行填充。依据振动台加速度为0.5g情况下，障碍网络颗粒阻尼-弹簧系统固有频率81.5 Hz以及对应加速度作为激励条件，通过离散元仿真分析了障碍网络颗粒阻尼吸振器的颗粒流态，如图6所示。受到障碍网络的影响，颗粒的悬浮现象被打破，原本的颗粒流动转变成更为复杂的无序运动，此时障碍网络颗粒阻尼吸振器的振动等效质量并未发生变化。
除此之外，我们对颗粒阻尼吸振器和障碍网络颗粒阻尼吸振器的整体耗能进行了对比分析。图7（a）为颗粒阻尼吸振器和障碍网络颗粒阻尼吸振器的耗能时域变化图，颗粒阻尼吸振器在全时段主要呈现出间歇脉冲耗能的现象，且在较长时间里存在能量损耗趋近于零的情况，而障碍网络颗粒阻尼吸振器的耗能波动较为连续且时刻存在耗能的情况。对于总体耗能而言，障碍网络颗粒阻尼吸振器是颗粒阻尼吸振器的1.47倍，如图7（b）所示。
其次，在振动台加速度为0.8g的情况下，以颗粒阻尼-弹簧系统固有频率为90 Hz以及对应加速度作为激励条件，通过离散元仿真分析颗粒阻尼吸振器的颗粒流态，观察到在颗粒振动过程中存在颗粒悬浮状态，如图8所示。我们将颗粒进行剖分，分析右半边悬浮颗粒的占比，由此得到悬浮部分颗粒约占总体颗粒的21.2%，与试验结果（21.8%）相符。
同样地，在振动台加速度为0.8g的情况下，以障碍网络颗粒阻尼-弹簧系统固有频率为81.5 Hz以及对应加速度作为激励条件，通过离散元仿真分析了障碍网络颗粒阻尼吸振器的颗粒流态，如图9所示。类似地，受到障碍网络的影响，颗粒并未出现悬浮流态，此时障碍网络颗粒阻尼吸振器的振动等效质量并未发生变化。
其次，对颗粒阻尼吸振器和障碍网络颗粒阻尼吸振器的整体耗能进行对比分析，图10（a）为颗粒阻尼吸振器和障碍网络颗粒阻尼吸振器的耗能时域变化图，颗粒阻尼吸振器在全时段里主要呈现出间歇脉冲耗能的现象，且在较长时间内存在能量损耗趋近于零的情况，而障碍网络颗粒阻尼吸振器耗能波动较为连续，呈现周期性耗能的规律且时刻存在耗能的情况，并随着时间的推移有上升的趋势。对于总体耗能而言，障碍网络颗粒阻尼吸振器是颗粒阻尼吸振器的4.33倍，如图10（b）所示。
4　结论
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本文将障碍网络颗粒阻尼器与动力吸振技术相结合，通过研究颗粒阻尼吸振器与障碍网络颗粒阻尼吸振器的振动等效质量变化，显示了障碍网络颗粒阻尼吸振器的优越性。并采用离散元仿真方法分别对有/无障碍网络颗粒阻尼器吸振器进行仿真模拟，定量分析了颗粒阻尼吸振器与障碍网络颗粒阻尼吸振器的等效质量变化，可以得出以下结论：
（1）在颗粒阻尼吸振器中，随着振动加速度的增大，颗粒流态会引起部分颗粒的悬浮，导致其整体的振动等效质量降低，表现为颗粒阻尼吸振器的固有频率随振动加速度的增大而增大；
（2）对于障碍网络颗粒阻尼吸振器而言，由于障碍网络的引入会打散颗粒的悬浮流态，随着振动增大颗粒很难出现悬浮状态，因此障碍网络颗粒阻尼吸振器的振动等效质量保持稳定，并在特定的振动幅值上有效提升减振效果。
基金
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  • 预研项目(70203050106; 50910050102)
  • 精密电机柔性制造关键技术与装备研发(2024Z173)
文献
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2025年第29卷第9期
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doi: 10.3969/j.issn.1007-7294.2025.09.014
  • 接收时间：2025-03-18
  • 首发时间：2026-03-26
  • 出版时间：2025-09-20
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  • 收稿日期：2025-03-18
基金
预研项目(70203050106; 50910050102)
精密电机柔性制造关键技术与装备研发(2024Z173)
作者信息
    1.江苏科技大学　能源与动力学院，江苏　镇江　212003
    2.中国舰船研究设计中心，武汉　430064
    3.宁波杜亚机电技术有限公司，浙江　宁波　315202

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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