Analysis of Natural Vibrations of Round Bimorph Piezoelectric Ceramic Plates of Arbitrary Dimensions. I. Simply Supported Piezoelectric Plate

The problem of natural vibrations of a round bimorph simply supported piezoelectric ceramic plate (piezoplate) of an arbitrary thickness with arbitrary axisymmetric electrodes is solved in the exact formulation using the method of finite elements. The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distribution over the piezoplate surfaces (vibration modes) is also analyzed and the dynamic electromechanical coupling coefficient (DCC) is investigated as a function of the relative plate thickness for various piezoelectric ceramic compositions. Round bimorph piezoplates with partial electrodes have been also considered. The results obtained make it possible to estimate the limits of applicability of an approximate one-dimensional theory and choose the optimum geometric dimensions of the plate and electrodes that ensure the maximum DCC.     

Analysis of Natural Vibrations of Round Bimorph Piezoelectric Ceramic Plates of Arbitrary Dimensions. II. Rigidly Fixed Piezoelectric Plate

The problem of natural vibrations of a round bimorph rigidly fixed supported piezoelectric ceramic plate (piezoplate) of an arbitrary thickness with arbitrary axisymmetric electrodes is solved using the method of finite elements. The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the piezoplate surfaces (vibration modes) are also analyzed and the dynamic electromechanical coupling coefficient (DCC) is investigated as a function of the relative plate thickness for various piezoelectric ceramic compositions. Round bimorph piezoplates with partial electrodes are considered; it is shown that the DCC can be significantly (by tens times) raised using partial electrodes. The results obtained make it possible to estimate the limits of applicability of the approximate one-dimensional theory and choose the optimum geometric dimensions of the plate and electrodes that ensure the maximum DCC.     

复合管功率超声压电换能器的径向振动特性

在纵向复合压电超声换能器基础上,提出并研究带预应力外壳的径向复合管压电超声换能器的径向振动特性。换能器由径向极化薄壁压电陶瓷圆管与预应力金属圆管外壳径向复合而成。依据机电类比原理,建立起复合系统的径向振动等效电路,并给出其径向振动共振频率方程。结合数值计算例,探讨换能器的共振和反共振频率以及有效机电耦合系数与预应力圆管半径比之间的关系。设计制作4个径向复合管压电超声换能器样品,通过试验测量换能器径向振动共振和反共振频率。结果表明,换能器径向共振频率的理论值与测量结果符合较好,误差小于5%。     

Analysis of acoustic radiation of circular piezoelectric plates enclosed in a flat rigid shield

Acoustic radiation of circular piezoelectric plates encased in a flat rigid shield is analyzed on the basis of a combined numerical-analytical method. It is shown that a plate made of piezoelectric ceramics of the second type with a higher dynamic coefficient of electromechanical coupling ensures a higher sensitivity in the transmission mode and a wider band of radiated frequencies. In addition, a plate of this type of piezoceramics has a lower level of side lobes of the directivity characteristic because of the more uniform normal-displacement distribution on its flat surface.     

Analysis of Inherent Oscillations in Round Piezoceramic Plates of Variable Thicknesses

The method of finite elements has been used in solving the problem of inherent oscillations in round piezoceramic plates of variable thicknesses. The paper considers two symmetric versions of piezoelectric plates with linearly changing thicknesses: biconvex and biconcave ones. Spectra of inherent frequencies have been analyzed under conditions of resonance and antiresonance. The dynamic coefficient of electromechanical coupling and displacement distributions on driving surfaces of plates have been calculated. The paper considers improvements in characteristics of thickness oscillations in plates (specifically, increasing the dynamic coefficient of electromechanical coupling and smoothing the distribution of the normal displacement component on driving surfaces) owing to their variable-thickness shapes. Such improvement can be obtained only in biconvex piezoelectric plates, whereas characteristics of thickness oscillations are worse in biconcave plates. Feature! s of thickness oscillation characteristics in piezoelectric plates from various materials are discussed.     

Correcting natural oscillations of a round piezoceramic plate by changing its shape

Characteristics of thickness vibrations of a round piezoceramic plate can be improved (the distribution of the normal displacement component on the plate surface can be smoothed, and the dynamic coefficient of electromechanical coupling can be increased) by changing the shape of its side surface. With this end in view, the paper suggests replacing conventional plates of constant radii, which are commonly used, with plates whose radii are variable. Acoustic modes of two types of symmetric piezoelectric plates have been investigated. The paper considers correction of thickness vibrations in round piezoelectric plates with variable radii from piezoceramics of different compositions.     

镶拼式复合压电超声换能器的径向振动特性

对一种镶拼式复合压电超声换能器的径向振动特性进行分析。该镶拼式复合压电超声换能器由弹性内芯、矩形压电陶瓷晶堆环组及金属预应力管径向复合而成。采用压电陶瓷晶堆,可大幅提高换能器的功率容量及有效机电耦合系数。依据机电类比原理,得出换能器的机电等效电路和共振频率方程;探讨换能器的第1、2阶共振和反共振频率及机电耦合系数与其几何尺寸之间的关系,并进行有限元仿真分析和试验测试。研究表明,换能器第1阶径向共振及反共振频率随其内芯内径及预应力管外径增大而降低;第2阶共振频率随内芯内径增大存在极小值,但随预应力管外径增大而下降,并且第2阶共振模式的有效机电耦合系数较高。对换能器共振频率的测试和仿真表明,理论与试验及仿真结果相符合。     

压电振动电阻尼与能量转换特性研究

根据压电构造方程和振动原理,建立压电振动能量收集的耦合场动力学模型。详细推导电阻尼与外接电阻和机电耦合系数之间的数学关系,并揭示外接电阻对系统固有弹性的作用效果。通过数值模拟研究电阻尼特性对谐振频率、振动幅值和功率的影响关系,并从能量转换效率的角度分析优化电阻与最大输出功率的关系。分别对多种外接电阻条件下压电梁的输出电压及功率进行实验测试,实验结果表明,电阻尼导致压电梁的谐振频率发生偏移,其大小与外接电阻值成正比,而且在外接优化电阻时输出功率最大。     

基于能量法的双晶压电悬臂梁发电装置机电耦合系数分析

针对双晶压电悬臂梁发电装置机电两类能量通过压电效应耦合强弱的问题,将能量法应用到双晶压电悬臂梁发电装置机电耦合系数的分析中。开展了双晶压电悬臂梁发电装置机电耦合系数的理论分析,并建立了其与双晶压电悬臂梁发电装置尺寸参数和材料特性之间的关系,对双晶压电悬臂梁发电装置机电耦合系数与其尺寸参数和材料特性的关系模型进行了实验验证和数值模拟。研究结果表明,实验值与理论解有较好的一致性,且都在压电片厚度为0.25 mm时开路电压最大,验证了该理论模型的可靠性。此外,随着压电梁厚度比的不断增大,其机电耦合系数单调递增;同时,较大的弹性模量比有利于压电梁机电耦合系数的提高,且相对于钢弹性基片,铍青铜弹性基片更有利于压电梁机电耦合系数的提高。     

Topology optimum design of unimorph piezoelectric cantilevered Mindlin plates as a vibrating electric harvester

An FEM-based topology optimization approach is proposed to calculate the topologies of a substrate plate and a piezoelectric layer used for vibrating unimorph cantilevered plate-like electricity generators (energy harvesters). The Mindlin plate theory was combined with a topology optimization algorithm to consider the shear effect. Each optimum topology for a plate and a piezoelectric layer is computed and combined by reflecting the natural frequencies of the substrate plate, electromechanical couplings of piezoelectric materials, tip masses and method of moving asymptotes. The piezoelectric coefficients such as elasticity, piezoelectric coupling and capacitance are interpolated by element density variables. The cantilevered plate generators with optimal topologies were designed for three piezoelectric materials such as PZT, PMN-PT and PMN-PT single crystal fiber MFC, and their voltage outputs were compared using a developed FEM-based optimization code to investigate the suitable material for harvesters.     

Characteristic Vibrational Modes of Piezoceramic Plates with Variable Thicknesses

The paper considers characteristic oscillations of finite round piezoceramic plates of variable thicknesses, with convex and concave surfaces. Characteristic oscillation spectra of these plates were studied in the regimes of resonance and antiresonance, and the dynamic coefficient of electro-mechanical coupling was calculated as a function of plate dimensions and displacement distribution over the surface. Improvements in the characteristics of thickness oscillations in the plates (the possibility of increasing the coefficient of electro-mechanical coupling and smoothing the distribution of the normal displacement component over the plate surface) owing to variable thicknesses of piezoceramic plates have been analyzed. This can be achieved only in plates with convex conical surfaces, whereas concave conical surfaces of plates lead to inferior characteristics of thickness oscillations. Improvements in characteristics of thickness oscillations in piezoelectric plates fabricated from ceramics with various compositions will be discussed.     

压电谐波电机驱动系统非线性主共振分析

为了探索压电谐波电机的机械-压电系统的非线性共振特性,设计了一种集压电驱动、谐波传动和活齿传动为一体的机电集成压电谐波电机。在非线性压电和非线性弹性效应的基础上,建立了驱动系统非线性机电耦合动力学方程。利用Linz Ted-Poincaré法推导了驱动系统非线性主共振响应方程,得出了主共振幅频响应曲线,分析了不同非线性效应对主共振响应的影响,最后通过四阶Runge-Kutta数值法验证了解析解的正确性。结果表明:在两种非线性效应中,非线性压电效应对主共振响应的影响是主要的;压电堆主共振出现在偏离固有频率较远处,且随着频率改变响应值出现跳跃现象;数值解与解析解响应曲线吻合较好。     

Performance analysis of piezoelectric bimorph generator

In this paper, the theoretical model and simulation of the performance of a piezoelectric (PZT) bimorph generator is introduced. The generator consists of two piezoelectric plates bonded on a substrate metal plate. For an effective electromechanical coupling coefficient (EECC) and the generated energy, the analytical formulae are established with the thickness ratio and the Young’s modulus ratio as variables. After giving correlative material parameters, the EECC and generated energy can be computed. The results show that there is a optimal thickness ratio for a piezoelectric bimorph generator to achieve the maximum EECC and electrical energy. The EECC and generated energy decrease with an increase of the Young’s modulus ratio. In addition, the influence of mechanical source on electrical energy generation and power output is also considered.     

Performance analysis of piezoelectric bimorph generator

In this paper, the theoretical model and simulation of the performance of a piezoelectric (PZT) bimorph generator is introduced. The generator consists of two piezoelectric plates bonded on a substrate metal plate. For an effective electromechanical coupling coefficient (EECC) and the generated energy, the analytical formulae are established with the thickness ratio and the Young’s modulus ratio as variables. After giving correlative material parameters, the EECC and generated energy can be computed. The results show that there is a optimal thickness ratio for a piezoelectric bimorph generator to achieve the maximum EECC and electrical energy. The EECC and generated energy decrease with an increase of the Young’s modulus ratio. In addition, the influence of mechanical source on electrical energy generation and power output is also considered.     

Dynamic response of an anti-plane shear crack in a functionally graded piezoelectric strip

The dynamic response of a cracked functionally graded piezoelectric material (FGPM) under transient anti-plane shear mechanical and in-plane electrical loads is investigated in the present paper. It is assumed that the electroelastic material properties of the FGPM vary smoothly in the form of an exponential function along the thickness of the strip. The analysis is conducted on the basis of the unified (or natural) crack boundary condition which is related to the ellipsoidal crack parameters. By using the Laplace and Fourier transforms, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, the electric field, FGPM gradation, crack length, and electromechanical coupling coefficient.     

四分之一波长夹心式压电超声换能器的设计研究

阐述了四分之一波长夹心式压电超声换能器的结构特点,对其机电振动特性进行了理论分析,得出纵向振动下换能器的机电等效电路图,给出了频率方程,并设计出一个换能器.使用有限元仿真软件ANSYS对换能器进行模态分析,结果显示其纵向振动时的同有频率与理论值十分接近,验证了理论推导的正确性.     

磁铁间距对双稳态压电悬臂梁俘能器输出特性的影响研究

建立了双稳态压电悬臂梁俘能器的机电耦合动力学方程,基于磁偶极子模型进行了 2 个磁铁间磁力的计算,根据静态平衡点分析得到了系统发生双稳态运动时的磁铁间距范围。数值仿真分析了环境激励源振动频率发生变化时磁铁间距变化对系统平均输出功率的影响规律,设计制作了磁铁间距可调的双稳态压电悬臂梁俘能装置,并进行了环境激励频率变化条件下的压电悬臂梁振动能量捕获实验。实验结果与仿真分析具有较好的一致性,为提高双稳态压电悬臂梁俘能器的发电性能提供了一种有效途径。     

压电双晶片的能量传输特性分析

基于压电双晶片的准静态本构方程,详细地分析了准静态情况下悬臂梁式双晶片执行器在常见的三种不同载荷(力、力矩、压力)情况下的机电转换特性,即有效机电耦合系数、最大能量传输系统、最大输出机械能量时效率.分析结果表明:这些特性主要由压电双晶片材料的横向机电耦合系数k31决定;三种载荷中,以力矩形式输出机械能时压电双晶片执行器的效率最高,以力的形式输出时稍低,以压力形式(如用于推动气体或液体)输出时效率最低.这些结论对于设计压电双晶片执行器的结构具有指导意义.     

An electromagnetic model of a piezoelectric transducer

A one-dimensional electromechanical model of a piezoelectric transducer, which reproduces excitation of ultrasonic pulses in a product, reception of echo signals, and calculation of waves in all its elements (damper, protector, piezoelectric element, contact-liquid layer, etc.), is considered. The results of calculations of electric and wave processes in a normal ultrasonic transducer, when it operates jointly with a generator of probing pulses, are presented. Good agreement between the calculation and experimental results is demonstrated.     

轴向预压缩双晶片动力学模型与特性分析

基于欧拉梁的假设,将双晶片简化为3层压电层合梁,由Hamilton原理建立系统的动力学模型,得到描述轴向预压缩压电双晶片的偏微分方程及特定边界条件,通过求解上述微分方程的边值问题得到双晶片在不同轴向力下的输出特性的解析表达式。利用有限元软件对双晶片进行仿真,验证了理论分析的正确性,增加理论分析结果的可信度。最后通过实验的方法研究双晶片的静、动力学特性,证明了施加轴向力可以降低双晶片的弯曲刚度和固有频率,显著增加其机电耦合效率,提高力和位移输出能力。轴向力虽然会影响双晶片启动时的位移峰值,但是对响应时间和带宽影响较小,大轴向力下双晶片仍具有带宽高与响应快的优势。