Multi-field coupling and free vibration of a sandwiched functionally-graded piezoelectric semiconductor plate

Sandwiched functionally-graded piezoelectric semiconductor(FGPS)plates possess high strength and excellent piezoelectric and semiconductor properties,and have significant potential applications in micro-electro-mechanical systems.The multi-field coupling and free vibration of a sandwiched FGPS plate are studied,and the governing equation and natural frequency are derived with the consideration of electron movement.The material properties in the functionally-graded layers are assumed to vary smoothly,and the first-order shear deformation theory is introduced to derive the multi-field coupling in the plate.The total strain energy of the plate is obtained,and the governing equations are presented by using Hamilton’s principle.By introducing the boundary conditions,the coupling physical fields are solved.In numerical examples,the natural frequencies of sandwiched FGPS plates under different geometrical and physical parameters are discussed.It is found that the initial electron density can be used to modulate the natural frequencies and vibrational displacement of sandwiched FGPS plates in the case of nano-size.The effects of the material properties of FGPS layers on the natural frequencies are also examined in detail.

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals(PCs),a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper.This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform.Firstly,the vibration of the model is analyzed theoretically,the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established,and the resonance frequency equation is derived.The effects of the length,width,and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method,the effective electromechanical coupling coefficient is also analyzed.The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate.The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method.The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated.The results show that the theoretical results are in good agreement with the simulation results.When the resonance frequency is in the band gap,the decoupling phenomenon occurs,and then the vibration mode in the thickness direction is purer.

Temperature dependence of mode coupling effect in piezoelectric vibrator made of[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT ternary single crystals with high electromechanical coupling factor

The influence of temperature on mode coupling effect in piezoelectric vibrators remains unclear.In this work,we discuss the influence of temperature on two-dimensional(2D)mode coupling effect and electromechanical coupling coefficient of cylindrical[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT piezoelectric single-crystal vibrator with an arbitrary configuration ratio.The electromechanical coupling coefficient kt decreases with temperature increasing,whereas k33 is largely invariant in a temperature range of 25℃-55℃.With the increase of temperature,the shift in the‘mode dividing point’increases the scale of the poling direction of the piezoelectric vibrator.The temperature has little effect on coupling constantΓ.At a given temperature,the coupling constantΓof the cylindrical vibrator is slightly greater than that of the rectangular vibrator.When the temperature changes,the applicability index(M)values of the two piezoelectric vibrators are close to 1,indicating that the coupling theory can be applied to piezoelectric vibrators made of late-model piezoelectric single crystals.

雪花形二维耦合振动夹心式压电超声换能器的设计

为了实现单个换能器的多方向超声辐射,提出了一种新型的雪花形二维耦合振动夹心式压电超声换能器,它由正六棱柱形金属块、6组压电陶瓷晶堆和6个金属盖板组成。基于耦合振动理论和力电类比原理建立了换能器等效电路模型,推导了其共振与反共振频率方程。通过等效电路法、有限元法和试验研究了换能器的二维耦合振动特性。结果表明:当压电陶瓷晶堆越靠近正六棱柱形金属块时,换能器的有效机电偶合系数越高;随着换能器轴向尺寸的增加纵向耦合共振频率降低;在纵向耦合共振模式下,换能器的6个输出端均可输出一致的纵向位移振幅;等效电路法、有限元仿真和试验测试取得了较为一致的结果。该研究结果为该类换能器的工程应用提供了简明设计理论,研究成果有望应用于多维超声加工、多向超声辐射等领域。

Further studies on thickness vibrations of piezoelectric plate excited by parallel field

In this paper, the thickness vibrations of the piezoclectric plate excited by a parallel field are further analysed. The new formula of resonant frequency equation and electromechanical coupling factor of the coupling modes are obtained. The characteristics of piezoelectrically-tunable frequency for the pure and coupling modes are investigated and ap plied to two examples.

压电功能梯度层合梁的力-电-热耦合梁单元及最优振动控制

给出了一个压电功能梯度层合梁振动分析的两节点力-电-热耦合梁单元,并将其用于功能梯度层合梁的振动最优控制。在这个多场耦合梁单元中,功能梯度材料的等效力学性能用Voigt或Mori-Tanaka模型表征;梁的位移场用Shi改进的三阶剪切变形板理论描述;压电层的电势场用Layer-wise理论分层表征,且呈高阶非线性电势场的压电层可离散成数个子层。用Hamilton原理推导了压电功能梯度梁的力-电-热耦合单元列式,用拟协调元法给出了多场耦合梁单元的高计算效率的显式单元刚度矩阵,以及采用线性二次型(LQR)最优控制算法进行压电功能梯度层合梁的最优振动控制。使用所得力-电-热耦合梁单元进行了压电功能梯度层合梁的静力和动力分析。数值算例表明,所得力-电-热耦合梁单元可靠、准确和高效,LQR最优控制算法得到最优控制电压可有效抑制功能梯度梁的振动且实现控制系统能量的优化。

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.

风力机叶片压电抑振效应与能量耗散机制研究

压电智能叶片是随着风力机向大型化发展而被提出的自适应减振概念叶片,本文探索了叶片压电抑振效应和能量耗散机制,提出了适用于变截面三维叶片的等效梁截面气弹模型设计方法,并基于同步测振测力气弹风洞试验对比研究了15 MW风力机叶片压电抑振效应;再基于二次开发的机电耦合叶片动力学模型,分析了机电气弹耦合模态的转速演变规律与能量分布形式,揭示了压电叶片的能量耗散机制。研究表明:提出的气弹风洞试验方法可有效反映压电叶片风振抑制效果;压电材料可缩小风力机叶片的敏感风向角区间,提高大幅锁频振动临界风速,延长气弹失稳的能量积累时间;压电材料导致叶片风振能量在模态空间均分转移,削弱了负阻尼模态的能量集聚,增强了正阻尼模态的能量耗散。

基于扩张状态观测器的压电结构复合滑模振动控制

针对压电固支板振动系统的模型不确定、高次谐波和外部激励等干扰问题,设计出一种基于线性扩张状态观测器与滑模控制的复合振动主动控制策略。首先,基于辅助变量法建立压电固支板结构的数学模型,进而设计线性扩张状态观测器对系统状态变量与总干扰进行实时估计,再通过前馈通道补偿的方式,抵消模型误差、外界激励等干扰对系统的影响;然后,基于估计值设计滑模控制器,利用较小的切换项增益抑制观测器的估计误差,从而降低滑模控制的抖振,并利用李雅普诺夫稳定判据准则分析所提振动控制系统的全局稳定性。最后,基于NI-PCIe6343采集系统,搭建振动控制实验平台,并对设计的复合振动主动控制策略进行实验。实验验证结果表明,所提振动控制策略对压电固支板的振动幅值降低87.5%,具有较强的抗干扰能力且对压电固支板的振动抑制性能良好。

四激励二维正交复合夹心式压电超声换能器的设计

提出了一种四激励二维正交复合夹心式压电超声换能器,换能器由四组纵向极化压电陶瓷晶堆、一个中心耦合金属块和四个外部金属圆锥组成。基于二维耦合振动机理和机电类比原理,建立了换能器的等效电路模型并推导了其谐振频率方程。利用有限元软件仿真分析了四激励正交复合换能器的频响特性和振动特性,并与其单独一个方向振子的振动特性进行了对比。加工了反相和同相模态的换能器,利用阻抗分析仪和激光测振仪测试了其频率响应和二维四向纵振动输出特性,并进行了大功率二维四向超声乳化实验测试。理论、仿真和实验结果表明:换能器具有反相和同相两个纵向正交共振模态,在这两种共振模态下均可实现二维四向纵振动输出,且换能器两个正交方向振子的纵向振动具有相互耦合加强的作用;等效电路法和有限元法所得换能器的共振频率和有效机电耦合系数与实验测试结果吻合,通过与单激励正交复合夹心式压电超声换能器的有效机电耦合系数对比,发现该换能器具有更高的有效机电耦合系数。

基于涡致振动的剪切模式压电俘能结构的数值模拟

提出了一种基于水下涡致振动的夹心式剪切模式压电俘能结构。将压电片夹在两金属板中间,金属板上端连接阻流圆管,金属板在振动过程会产生相对位移,使夹在中间的压电片产生切变,进而将机械能转换为电能。分别对前置阻流体的单个压电俘能结构和前置阻流体的2个串列压电俘能结构,进行了流固耦合与压电耦合数值模拟,分析对比2种情况下的涡致振动能量收集性能。研究结果表明:2种情况下,压电俘能结构的振幅响应和电压均随着流速的增大而增大,在流速为1.2 m·s^(-1),中心距为5D时,产生的振幅和电压最大,单俘能结构情况下为6.743 2×10^(-4)m,两个俘能结构串列情况下,上游为7.241 5×10^(-4)m, 13.347 V,下游为1.942 6×10^(-4)m, 3.551 2 V。

声波测井压电振子的有限元分析

压电振子是新一代方位声波测井仪器中相控圆弧阵声波辐射器的重要组成部分。利用有限元法对构成圆弧阵的压电振子进行了设计分析,结果显示了压电振子存在多阶弯曲振动模态,且长度方向一阶弯曲振动能够满足方位声波测井的工作频率要求。针对长度方向一阶弯曲振动模式,数值模拟了几何尺寸对压电振子性能参数的影响。压电振子的谐振频率随着陶瓷片长度、基片或陶瓷片厚度的减小而降低;压电振子的辐射声功率随着陶瓷片长度或压电振子宽度的增加、基片或陶瓷片厚度的减小而增大;合理地选取长度和厚度可使压电振子具有较高的机电耦合系数。数值模拟结果可以对圆弧阵结构优化设计起到良好的指导作用。

径扭复合模式盘形压电超声换能器

提出一种新型的斜缝式结构径扭复合模式振动盘形压电超声换能器,并对其径扭复合模式振动进行了理论和试验研究。通过对斜槽处应力的分解,引入两个机械转换系数,依据机电类比原理,建立起换能器的径扭复合模式振动耦合机电等效电路模型,从等效电路得到换能器的径扭复合振动频率方程,探讨狭缝的斜角对换能器共振频率的影响,数值计算表明换能器共振频率随斜角增大而降低。试验加工三个不同斜度狭缝的换能器,并对其共振频率进行了测试和有限元法模态仿真计算,结果表明,理论与仿真值及试验结果吻合较好。

基于IIR结构的自适应滤波振动主动控制方法

当前自适应滤波前馈控制方法中具有代表性的是滤波-X最小均方(filtered-X least mean square,简称FXLMS)算法,它通常假定干扰源可测且作为前馈控制器的参考输入,但实际振动控制过程中需要考虑控制输出反馈信号对参考信号的影响,因此滤波-X算法面向实际应用具有较大的局限性。针对这一问题,以机敏压电太阳能帆板结构为模拟试验对象,提出一种基于IIR(infinite impulse response,简称IIR)结构的滤波-U最小均方(filtered-U least mean square,简称FULMS)自适应滤波控制方法,着重分析了控制器结构设计、FULMS算法推理过程、试验模型结构设计、试验平台的构建及其试验验证等环节。经过与FXLMS算法对比仿真试验,笔者所设计的控制算法控制效果良好。将其进行试验验证分析,结果表明,所采用的控制器设计方法与控制算法收敛速度快,控制效果好,为自适应振动控制方法向实际工程应用提供了较好的研究基础。

压电耦合板主动控制及稳定性分析

本文研究压电耦合板的主动控制及稳定性。压电耦合板在采用作为传感器和驱动器的压电片之间的速度负反馈时 ,能增大系统的阻尼性能。本文以闭环控制系统方法的特征值分析为基础 ,分析研究了其稳定性。研究表明主动控制在增加系统阻尼性能的同时 ,亦可能导致系统出现不稳定现象。文中指出当仅有对点之间的负反馈时 ,系统是渐近稳定的 ;当负反馈增益矩阵呈非对称或对称但非正定时 ,系统可能出现非稳定。文中以算例进一步给予证实。

压电智能板动力学有限元模型建立及振动控制(Ⅱ)——压电智能板振动控制

在采用有限元法已建立的压电智能板的动力学方程基础上。应用模态控制理论对压电智能板振动控制的原理和策略进行了研究,采用基于二次线性控制(LQR)的独立模态空间控制法来进行板结构的主动控制,采用负速度反馈控制。通过数值仿真,结果表明:有效地控制结构振动。

压电陶瓷矩形薄板振子的弯曲振动研究

在矩形薄板四边自由及简支两种边界条件下，导出了振子共振频率方程的解析表达式，研究了弯曲振动压电陶瓷矩形振子共振频率与其振动模式、几何形状及尺寸之间的相互关系．矩形截面压电陶瓷细长棒的弯曲振动以及细长条矩形振子的条纹模式弯曲振动，可以由本文理论直接导出．实验结果表明。

单相短柱型直线超声电机的设计

提出了一种单相驱动的立式短柱型压电直线超声电机,论述了该电机的动作原理和设计过程。该电机利用纵向振动和横向振动的耦合模态工作。为获得同一驱动频率的一致的双向运动特性,该电机采用对称结构,利用压电陶瓷在短路和开路时弹性模量存在差异的特性,用单相驱动信号实现了纵向和弯曲耦合模态的有效激发。以增大电机弯曲振动模态前后振幅比为目标,利用三自由度集中质量的简化模型,优化了定子的结构。制作了电机的原理样机,对其进行了输出性能测试。实验结果表明,电机的输出性能良好。电机定子长22mm,自重3.3g,0.3N输出推力下最大速度达140mm/s,5N预压力下最大输出推力近1N。

一种新型级联式高强度功率超声压电陶瓷换能器

基于传统夹心式压电陶瓷换能器,提出了一种新型级联式高强度功率超声换能器。该换能器由多个半波长夹心式压电陶瓷换能器通过电端并联及机械端串联而成。基于一维理论,得出了换能器的六端机电等效电路,分析了换能器的电阻抗频率特性,并给出换能器的共振频率方程。研究了不同振动模态下,换能器的共振频率、反共振频率以及有效机电耦合系数与压电陶瓷晶堆间距的依赖关系。实验制造2个级联式功率超声换能器,并对其共振频率和有效机电耦合系数进行了测试,实验结果与理论分析相吻合。此类级联式高强度功率超声换能器可望在超声波液体处理、超声波加工等大功率超声技术中获得应用。

基于压电陶瓷作用的气体主轴抑振研究

针对空气静压主轴气膜刚度不高,在工作中易受自身及外部激励的影响,从而产生不平衡振动的现象,设计了一种基于压电陶瓷的可控空气静压径向轴承,研究了压电陶瓷的相关特性。结合气体主轴建立了轴承-转子-压电陶瓷的耦合模型,并在此基础上建立了基于扩张观测器的滑模控制器,同时将压电陶瓷综合控制器串联其中,在限制条件内利用控制器使压电陶瓷挤压气膜为主轴提供有效的主动控制力,从而抑制空气静压主轴的振动。研究结果表明,利用压电陶瓷对空气静压主轴系统的振动进行抑制取得了良好的效果,对于主要控制点可使其振动位移减小99.17%,对于次要控制点均有不同程度的减振效果,最多可减少94.36%。