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Article(id=1228295392702428059, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228295387077866291, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2025.01.001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1670947200000, receivedDateStr=2022-12-14, revisedDate=1678291200000, revisedDateStr=2023-03-09, acceptedDate=null, acceptedDateStr=null, onlineDate=1770778042245, onlineDateStr=2026-02-11, pubDate=1736438400000, pubDateStr=2025-01-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770778042245, onlineIssueDateStr=2026-02-11, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770778042245, creator=13701087609, updateTime=1770778042245, updator=13701087609, issue=Issue{id=1228295387077866291, tenantId=1146029695717560320, journalId=1225147924628267009, year='2025', volume='38', issue='1', pageStart='1', pageEnd='222', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770778040904, creator=13701087609, updateTime=1770949073977, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1229012751838802169, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228295387077866291, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1229012751838802170, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228295387077866291, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1, endPage=7, ext={EN=ArticleExt(id=1228295392949892003, articleId=1228295392702428059, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Research on the influence of structural vibration of energy-manipulated piezoelectric shunt branch, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Piezoelectric materials are often used in the fields of vibration energy harvesting and structural vibration suppression due to the excellent electromechanical coupling characteristics. This paper introduces a new shunt with switchable and manipulable force (mechanical) and electrical energy, using the primary and secondary energy conversion function of the flyback transformer based on the existing switching piezoelectric shunt. Based on the positive and negative piezoelectric effects, this paper designs the branch circuits for absorbing energy to suppress vibration and injecting energy to control vibration respectively, resulting in a highly efficient and stable structural vibration control system. The paper introduces the operating principles of the proposed new piezoelectric shunt branch and derives the decay rate models of structural amplitude under different energy manipulation conditions. The relationship between the effect of different energy manipulation methods and the amplitude of the structure is discussed through experiments. Results show that the introduced energy-manipulated shunt branch can realize highly efficient structural vibration suppression depending on the damping requirements of actual scenarios.

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压电材料具有良好的机电耦合特性，常被用于振动系统中的能量俘获和振动抑制。在已有开关型压电分流支路的基础上，利用反激变压器的原、副边能量转换功能，提出一种力（机械）-电能量可切换并操控的分流支路，基于正、逆压电效应分别设计支路的吸能抑振和注能控振两种功能，实现高能效且稳定的结构振动控制系统。介绍了所述压电分流支路的工作原理，推导了不同能量操控条件下结构振幅的衰减率模型，通过试验讨论了不同能量操控方法对结构振幅的影响。研究结果表明，所述能量操控型分流支路能够根据实际场景的减振需求实现高能效的结构振动抑制。

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吴义鹏（1986—），男，博士，副教授。E-mail：
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裴万鹏（1998—），男，硕士研究生。E-mail：

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裴万鹏（1998—），男，硕士研究生。E-mail：

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裴万鹏（1998—），男，硕士研究生。E-mail：

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of the energy and vibration amplitude under different control modes with the load resistance and switch time coefficient, figureFileSmall=LVecyOtDfEUEQDTTywSNwQ==, figureFileBig=FLFJJ/lBBXAmKKgHffsw/g==, tableContent=null), ArticleFig(id=1228299344965730412, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228295392702428059, language=CN, label=图8, caption=不同控制模式下能量和振幅随负载和开关时间系数的变化关系, figureFileSmall=LVecyOtDfEUEQDTTywSNwQ==, figureFileBig=FLFJJ/lBBXAmKKgHffsw/g==, tableContent=null), ArticleFig(id=1228299345066393716, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228295392702428059, language=EN, label=Tab. 1, caption=

Actual measurement parameters of the controlled piezoelectric cantilever beam

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参数符号数值
短路共振频率/Hzfs15.42
开路共振频率/Hzfo15.54
机械品质因子Qm20.41
开路电压与振动位移之比/(V•m-1)β12368
压电片等效电容/nFCP30
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被控压电悬臂梁的实际测量参数

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参数符号数值
短路共振频率/Hzfs15.42
开路共振频率/Hzfo15.54
机械品质因子Qm20.41
开路电压与振动位移之比/(V•m-1)β12368
压电片等效电容/nFCP30
), ArticleFig(id=1228299345292886144, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228295392702428059, language=EN, label=Tab. 2, caption=

Key parameters in the equivalent model of piezoelectric cantilever beam

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参数符号数值
力-电耦合因子/(N•V-1)α3.71×10-4
等效刚度/(N•m-1)K2.94×102
等效质量/gM31.3
等效阻尼/(N•s•m-1)D0.15
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压电悬臂梁等效模型中的关键参数

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参数符号数值
力-电耦合因子/(N•V-1)α3.71×10-4
等效刚度/(N•m-1)K2.94×102
等效质量/gM31.3
等效阻尼/(N•s•m-1)D0.15
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能量操控式压电分流支路对结构振动的影响研究
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裴万鹏 1 , 刘轩 2 , 马少飞 1 , 虞丽塬 1 , 吴义鹏 1 , 季宏丽 1 , 裘进浩 1
振动工程学报 | 2025,38(1): 1-7
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振动工程学报 | 2025, 38(1): 1-7
能量操控式压电分流支路对结构振动的影响研究
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裴万鹏1 , 刘轩2, 马少飞1, 虞丽塬1, 吴义鹏1 , 季宏丽1, 裘进浩1
作者信息
  • 1.南京航空航天大学航空航天结构力学及控制全国重点实验室，江苏 南京 210016
  • 2.航空工业成都飞机工业（集团）有限责任公司，四川 成都 610073

    • 裴万鹏（1998—），男，硕士研究生。E-mail：

通讯作者:

吴义鹏（1986—），男，博士，副教授。E-mail：
Research on the influence of structural vibration of energy-manipulated piezoelectric shunt branch
Wanpeng PEI1 , Xuan LIU2, Shaofei MA1, Liyuan YU1, Yipeng WU1 , Hongli JI1, Jinhao QIU1
Affiliations
  • 1.State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 2.AVIC Chengdu Aircraft Industrial (Group) Co., Ltd., Chengdu 610073, China
出版时间: 2025-01-10 doi: 10.16385/j.cnki.issn.1004-4523.2025.01.001
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摘要
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压电材料具有良好的机电耦合特性，常被用于振动系统中的能量俘获和振动抑制。在已有开关型压电分流支路的基础上，利用反激变压器的原、副边能量转换功能，提出一种力（机械）-电能量可切换并操控的分流支路，基于正、逆压电效应分别设计支路的吸能抑振和注能控振两种功能，实现高能效且稳定的结构振动控制系统。介绍了所述压电分流支路的工作原理，推导了不同能量操控条件下结构振幅的衰减率模型，通过试验讨论了不同能量操控方法对结构振幅的影响。研究结果表明，所述能量操控型分流支路能够根据实际场景的减振需求实现高能效的结构振动抑制。

振动控制  /  振动能量收集  /  压电分流支路  /  反激变压器  /  压电悬臂梁

Piezoelectric materials are often used in the fields of vibration energy harvesting and structural vibration suppression due to the excellent electromechanical coupling characteristics. This paper introduces a new shunt with switchable and manipulable force (mechanical) and electrical energy, using the primary and secondary energy conversion function of the flyback transformer based on the existing switching piezoelectric shunt. Based on the positive and negative piezoelectric effects, this paper designs the branch circuits for absorbing energy to suppress vibration and injecting energy to control vibration respectively, resulting in a highly efficient and stable structural vibration control system. The paper introduces the operating principles of the proposed new piezoelectric shunt branch and derives the decay rate models of structural amplitude under different energy manipulation conditions. The relationship between the effect of different energy manipulation methods and the amplitude of the structure is discussed through experiments. Results show that the introduced energy-manipulated shunt branch can realize highly efficient structural vibration suppression depending on the damping requirements of actual scenarios.

vibration control  /  vibration energy harvesting  /  piezoelectric shunt branch  /  flyback transformer  /  piezoelectric cantilever beam
裴万鹏, 刘轩, 马少飞, 虞丽塬, 吴义鹏, 季宏丽, 裘进浩. 能量操控式压电分流支路对结构振动的影响研究. 振动工程学报, 2025 , 38 (1) : 1 -7 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.01.001
Wanpeng PEI, Xuan LIU, Shaofei MA, Liyuan YU, Yipeng WU, Hongli JI, Jinhao QIU. Research on the influence of structural vibration of energy-manipulated piezoelectric shunt branch[J]. Journal of Vibration Engineering, 2025 , 38 (1) : 1 -7 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.01.001
正文
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振动作为一种常见的物理现象普遍存在于工业生产和人们的日常生活中[1]，振动的控制[2]和利用[3-4]具有较高的研究价值。结构振动的控制一般通过隔振技术降低振动传递率[5]，振动阻尼技术减弱物体振动强度[6]，动力吸振器技术转移机械振动能[7]等几种方式实现。振动控制的基本方法主要有减小振动、防止共振和采取隔振措施三类[8-11]。其中，基于压电元件的结构振动控制方法主要为第一类[12]，即利用正、逆压电效应实现振动能与电能之间的相互转换，进而达到减小结构振动的目的[13]。
RICHARD等[14]提出的同步开关阻尼（synchronized switch damping，SSD）技术是一种经典的开关型压电分流方法，该方法通过对支路实施同步短路（SSD based on short-circuit）、LC振荡翻转（SSD based on inductor，SSDI）等方式实现控制系统的电致阻尼效应和对结构振动抑制的反向制动效应，高效地抑制结构振动[15]。为进一步提高结构振动抑制效果，LEFEUVRE等[16]在SSDI电路中增加了直流电压源，在压电电压同步翻转的瞬间通过电压源注入电能来提高压电致动力。JI等[17-18]则针对压电器件的基本特性提出了更为先进的SSD方法，极大地提高了压电作动器的工作性能，拓宽了此类振动控制方法的适用范围。
若在SSDI分流支路中接入负载电路，则该技术能将结构振动能转换成电能并利用起来，GUYOMAR等[19]基于该思路提出了基于电感的同步开关回收电路，不仅可以收集电能，还能在特定条件下抑制主结构振动。WU等[20-21]提出的优化型同步电荷提取（optimized synchronous electric charge extraction，OSECE）电路，其本质也是借助反激变压器在副边接入收集电能的负载，若副边电路断开不工作，OSECE就完全等效成了SSDI电路。若将变压器的原、副边能量转换方向切换，OSECE技术就变成了基于能量注入的SSD（SSD based on energy injection，SSDEI）技术[22]，达到类似LEFEUVRE等[16]提出的基于电压源SSD一样的控制效果，但SSDEI电路在自适应调节注能大小、系统控制精度等方面更具有优势。
本文在OSECE和SSDEI电路的基础上，提出了一种机械能-电能可切换并操控的压电分流支路，同样在分流支路中设计一反激变压器，利用变压器的原、副边能量转换功能和正、逆压电效应双向操控压电振动系统中的机电耦合能量，自适应改变控制系统能耗和主结构振动控制效果。本文详细介绍了该能量操控式分流支路的工作原理，并通过结构振动控制试验平台验证了该方法的可行性。
1　能量操控式压电分流支路
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1.1　SSDEI、OSECE与SSDI分流支路
理论上，SSDEI和OSEDE技术都是在SSDI技术的基础上衍生出来的，图1给出了这三种压电分流电路的原理图及其相互关系示意图。图1中左侧即为SSDI电路，当压电元件两端电压V达到极值时，闭合开关，压电元件（低频条件下可等效成电容）和电感组成了LC振荡电路，当振荡相位为π时开关断开，振荡电路“消失”，压电元件两端电压发生翻转。该技术可以让压电电压始终与振动速度反相位，最大化反相制动力做功；同时由于振荡电路品质因子的存在，压电元件在同步开关闭合的瞬间会通过输出电压及电流向支路做功消耗电能，引起耦合结构的电致阻尼效应。
OSECE技术通过在反激变压器副边接入负载，实现振动控制系统吸能抑振的功能。SSDEI技术则在反激变压器的副边接入注能电压源，通过在LC电路振荡之前提前注入电能再转移至压电元件中的方式，提高压电元件对振动结构的抑制力。
1.2　能量操控式分流支路
为了将上述两种功能结合起来，实现注能控振和吸能抑振之间的自适应切换，本文提出一种能量操控式分流支路，如图2所示，通过反激变压器实现上述能量操控，变压器副边的吸能与注能支路共用一个线圈，通过控制电子开关实现功能切换。
能量操控式分流支路在注能控振功能下的电路工作原理图如图3所示。图3中（1）为第一阶段，控制信号Sig1为低电平，开关S1断开，开关S2闭合。但此时压电元件电压为正，所以二极管D2反向截止，压电元件处于开路状态，电压随着结构位移的增大而增大。副边电路中开关控制信号Sig2为低电平，开关S4和S5断开，因此处于断路状态。
开关S4和S5在Sig2控制下闭合，开启了如图3中（2）所示的第二阶段。二极管D4导通，电压源VDC与线圈L3相连接，回路中出现充电电流Ipri，部分电能预先存储到了变压器绕组L3中。
结构振动位移达到最大值时，Sig2变为低电平，开关S4和S5断开，Sig1切换为高电平，开关S1导通，S2断开，电路处于如图3中（3）所示的第三阶段。此时二极管D1正向导通，使电感L1与压电元件之间产生了LC振荡，回路中出现振荡电流Isec，当该电流为零时，二极管D1反向截止结束第三阶段，压电电压发生翻转。定义λ为电压翻转因子[22]，则有：
式中，VM为翻转前的电压；Vm为翻转后的电压；Cp为压电元件的等效电容；α为力-电耦合因子；uM为结构振幅。
二极管D1反向截止后，压电元件重新处于开路状态，如图3中（4）所示的第四阶段。
定义fe为外加电压源VDC，α以及结构振动加速度共同决定的控制力系数，为机电耦合结构的品质因数，得到归一化的翻转因子λ和翻转相位ωet的表达式[22]：
式中，Qe为振荡电路的品质因子。
由式（2）可知，开关S4和S5闭合的时间系数τ与外加电压源VDC的大小最终共同决定了注入能量的多少。注入能量与翻转相位又成反比关系。若τ=0，则没有注入能量，翻转相位为π。
通过调整开关控制策略可以进行功能切换，即转换至吸能抑振功能。由实时控制系统发出阶跃信号控制开关S3闭合，S4和S5断开，该功能与注能控振功能共用线圈L3。需要说明的是，此功能下电路的工作步骤和电压电流波形图与优化同步电荷提取电路[20]一致，在此不加赘述。相应地，可以推导出吸能抑振功能的翻转因子η和翻转相位ωet的表达式：
式中，ξR为等效负载系数，即负载阻抗RL与压电元件等效输出阻抗（1/Cpω）的比值，其中ω为结构的振动角频率[20]。
1.3　分流支路作用下结构振动衰减率模型
假设被控结构等效为单自由度的质量-弹簧-阻尼系统，则在压电分流支路作用下，其等效机电耦合模型如图4所示。图4中，M、K和D分别为模型的等效质量、刚度和阻尼，x1为外部激励加速度等于a时的振动位移，x2为惯性质量的振动位移，V和I分别为压电元件电极面之间的电压和电流的正方向。
当机电耦合结构处于稳态时，外界输入系统的总能量可分为动能、弹性势能、阻尼导致的机械能损耗以及机电转换能[22]。机电转化能又分为储存在压电元件上的电能和分流支路操控的电能。因此可推得系统半个振动周期内的能量表达式：
式中，t0为结构稳态振动过程中的任意时刻；T为结构稳态振动周期；F为外界激振力；u=x2-x1，为相对振动位移。
根据各个分流支路的工作原理，可知SSDI支路控制下结构位移响应为[22]：
式中，FM为外界激振力幅值；γ为SSDI技术中电压的翻转因子。
引入归一化参数，结构的振动衰减率为[22]：
将式（1）代入式（4），注能控振功能（即SSDEI）下结构的位移响应为[22]：
结构振动衰减率为[22]：
相应地，吸能抑振功能（即OSECE）控制下的位移幅值uM的表达式为[20]：
类似地，结构振动衰减率为：
2　试验结果分析与讨论
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2.1　试验平台介绍
为验证所述能量操控式分流支路所具备的注能控振、吸能抑振以及两者之间的切换功能，搭建了如图5所示的压电悬臂梁试验平台，同时可以研究两种工作模式下结构的实际减振效果及能量操控关系。试验平台中，悬臂梁采用弹簧钢材料，尺寸为（200×24×0.8） mm3，两片PZT-5压电陶瓷片并联在一起，尺寸为（40×20×0.5） mm3。悬臂梁固定端通过夹持装置连接在激振器上。实验使用的激振器和配套功放为东华公司的DH40200和DH5872，采用基恩士公司的激光位移传感器IL-100测量悬臂梁自由端的振动位移。实验控制系统硬件为Speedgoat公司的实时控制系统，控制程序则在MATLAB/Simulink平台上搭建。分流支路中变压器原、副边绕组电感均为22.16 mH，直流电压源VDC为3 V，控制开关信号均通过光耦隔离芯片驱动电子场效应管开关。
2.2　被控结构实际参数
实际被控结构模型比理想状态下复杂得多，这里采用文献[20]所述的结构参数识别方法，再结合实验结果（压电悬臂梁在无任何接口电路条件下直接接负载测试得到的输出功率与理论计算功率对比）修正，得到所述被控结构的实际测量参数，如表1所示（表中对机械品质因子、压电开路与短路条件下的共振频率均进行了修正）。结合表1中的参数值，即可根据文献[20]提供的参数识别计算公式推导得到相应等效模型中的关键参数，如表2所示。
图6所示为被控压电悬臂梁在自由振动、吸能抑振、SSDI控制和注能控振技术下的压电电压与结构位移的时域波形图，其中吸能抑振和注能控振可通过控制系统进行切换。可以看出，三种压电分流技术对结构振动均有控制效果。自由振动条件下，振动幅值为2.26 mm；在外接负载为1 MΩ的吸能抑振阶段，位移幅值为1.50 mm，与自由振动时的幅值相比下降了33.3%；通过SSDI技术控制后的位移幅值为0.91 mm，下降了59.6%。注能控振技术相较于其他两种技术，压电元件两端电压更大，对振动控制效果也更好，在开关时间系数τ=4.66（闭合时间0.38 ms）时，位移幅值为0.54 mm，下降了75.9%，此时仍可调节开关时间系数以获得更好的控制效果。
如图7所示为在外界激振力FM相同的情况下，吸能抑振和注能控振两个阶段的位移振幅对比。图中实线为理论计算结果，带标记符号的实线为实验测试结果，两者变化趋势基本一致，存在误差的主要原因在于变压器原、副边转换损耗，压电元件电压高频振荡等影响了振动衰减效果，导致实际振动幅值整体偏大。
由图7可知随着外接负载的增大和开关时间系数的增大，结构振幅均在减小，注能控振阶段的振幅抑制效果优于纯粹吸能阶段。当负载无穷大或开关时间系数为0时，结构振幅抑制效果与SSDI支路一致。需要说明的是，虽然吸能抑振阶段的振动衰减率要小，但该功能无需外界提供结构振动抑制的能量，反而还能收集一定的振动能量，起到自取能发电的效果。
图8为半个振动周期（单次动作）内，两种控制模式下，能量操控和结构振幅在相应控制技术下的变化关系。其中注能控振主要通过调节支路中注能开关的闭合时间实现，吸能抑振则通过改变支路中负载电阻的值进行调节，两种控制模式的选择通过支路中的开关状态进行切换。
在注能控振功能下，注入的能量随开关时间系数τ的增大而增大，当τ=8.45时，注入的能量为7.1×10−5 J，结构振幅基本被抑制住。在吸能抑振功能下，压电分流支路吸收的能量随着外接负载的阻值先增大再减小，在1 MΩ左右获得的能量最大。虽然随着电阻值的增大，对结构振动的控制效果会更好，但此时回收到的能量却急剧减少。对比两种控制模式，虽然注能控振的结构振动控制效果更好，但注能操控中的能量要高一个数量级，并且属于纯粹的能量消耗；吸能抑振中，振幅抑制效果虽然较差，但从能量的角度来说，控制系统能获得正收益，即不仅不需要提供电能，还能从被控结构中获得电能。
3　结论
收起
本文在开关型压电分流支路和反激变压器的基础上，提出了一种能量操控式压电分流支路，并研究了不同能量操控模式对被控结构振幅的影响。该压电分流支路通过控制相应的电子开关进行切换，可自适应地根据结构振动需求和被控系统能耗进行控制模式切换。例如，当外界激励源变小且结构自由振动幅值变小时，可自适应地切换至吸能抑振模式，防止因控制系统注入过多电能而导致振动发散，引发控制失稳问题。仿真和试验结果验证了上述能量操控方法的可行性。下一步工作将根据实际应用场景，如考虑外界激励加速度随机变化，系统功耗约束等条件，设计基于微处理器的结构振动控制系统，力争用更小的能耗获得更优的结构振幅抑制效果，并且保证控制系统始终稳定、可靠。
基金
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  • 国家自然科学基金资助项目(52022039)
  • 南京航空航天大学前瞻布局科研专项资金资助项目
文献
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2025年第38卷第1期
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doi: 10.16385/j.cnki.issn.1004-4523.2025.01.001
  • 接收时间：2022-12-14
  • 首发时间：2026-02-11
  • 出版时间：2025-01-10
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  • 收稿日期：2022-12-14
  • 修回日期：2023-03-09
基金
国家自然科学基金资助项目(52022039)
南京航空航天大学前瞻布局科研专项资金资助项目
作者信息
    1.南京航空航天大学航空航天结构力学及控制全国重点实验室，江苏 南京 210016
    2.航空工业成都飞机工业（集团）有限责任公司，四川 成都 610073

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吴义鹏（1986—），男，博士，副教授。E-mail：
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2种不同金属材料的力学参数
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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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