Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system’s vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode(TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro–mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro–mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element(FE) analyses. Finally, a prototype of the coupling electro–mechanical resonator is fabricated with two shear-mode PZT5 A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5 A.     

小型超导电源系统退磁保护回路建模与仿真

计算了采用二极管等效电压源模型和等效电阻模型的退磁回路电流响应和二极管功耗,分析了两个模型的特点和差异,在此基础上,为了进一步提高精度,充分考虑了二极管的非线性特性,以实际二极管伏安特性进行曲线拟合建立函数关系式得到二极管非线性模型,代入回路方程并求解。综合对比各模型的仿真结果后,得出采用二极管非线性模型和等效电压源模型能更好地模拟退磁保护响应。     

Sound absorption characteristics of a thin plate with PZT and shunt circuitⅠ.Theoretical analysis

The feasibility of sound absorbing by a vibrating plate with piezoelectric material and shunt circuits is theoretically investigated.Based on an equivalent compliance of a piezoelectric wafer shunted with RL circuits,the governing equations for the flexural vibration of the plate with the piezoelectric wafer are derived using Lagrange's approach.The equations take into account not only the mass,stiffness and structural damping of the plate and the wafer,but also the electrical resistance and electrical i...     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.     

Optimization of the piezoelectric transducer response by means of electrical correcting circuits

A method of shortening the transient response of a piezoelectric transducer is described. It can be applied to thickness mode piezoelectric transducers of arbitrary electromechanical coupling. The system incorporates electrical correcting circuits and can produce a transient response with a duration much shorter than the transit time of an ultrasonic wave travelling through the piezoelectric plate.     

非线性系统的一种图解分析方法及其在隧道二极管线路分析中的应用

本文提出了一个分析非线性系统瞬变过程的新计算方法。这个方法首先把非线性系统用非线性及线性的R,L,C线路元件等效。从等效线路选择适当变量,用线路分析法则写成特定形式的非线性微分方程组。然后在相平面上用我们提出的图解方法进行积分来求解方程。这方法具有下列优点:(1)可以从非线性元件的实验曲线直接求微分方程的解,不必先求出非线性函数的解析表示式;(2)计算方便,工具简单,分析过程的物理图象清楚;(3)有一定的精确度。应用这个方法分析了隧道二极管的几种基本运用线路。得出的计算结果与实验和用电子计算机计算的结果符     

Thermoelastic equivalent circuit for laser ultrasound

I.IntroductionItiswe11knownthatultrasonicwavecanbegenerated'bytherma1expansionwhenalaserbeamisincidentonsamples.Accordingto1incarthcory,laserultrasonicsignalcanbcderivedfromtheso1utionofthermoe1asticdifferentialcquationinwho1espacc.Asanimportantparameter,theamp1itudeofsoundwavehasbeenappliedtoquantitutivemeas.rements['-3l.Recentpapersbegintofocusonanotherconsiderablecharactcr-thctempora1profileofultrasonicsignalwhoscfrequencyandphasespectruminvolvemoreinfOrmationofmaterialproperhesl~8l.And,c…     

SET-MOS混合结构的细胞神经网络及其应用

基于细胞神经网络（CNN）细胞单元的等效电路及其电学特性模型,利用SET-MOS混合结构反相器实现了模型中的激活函数电路,用耦合电容单元实现CNN细胞的系统模板,构建了SET-MOS CNN细胞硬件电路,并将其应用在图像处理中.仿真结果表明,所设计的CNN硬件电路具有结构简单、功耗低、响应速度快等特点,可用于构成各种规模的CNN电路,进一步满足大规模信号处理的需求及提高集成电路的集成度. 关键词： 单电子晶体管 MOS管 细胞神经网络 图像处理     

压电陶瓷非线性对大功率换能器结构参数匹配 影响的计算分析

在Guyomar非线性模型基础上,通过机电等效法将晶堆前向负载作为等效质量和阻尼加入振动方程的质量项和阻尼项,推导了换能器振速、辐射声压级和谐振频率偏移率等表达式,计算分析了压电陶瓷非线性参数和结构参数对换能器声辐射性能的影响,研究了压电陶瓷的非线性对换能器结构参数匹配的影响。结果表明,换能器节面靠前,前盖板厚度越小,前盖板大径越小,都可以减少压电陶瓷非线性引起的换能器频率偏移。当设计频率确定时,压电陶瓷处于非线性工作域的换能器的结构参数有所减小。换能器加入辐射端匹配后,可以改善压电晶堆前向负载匹配,降低换能器的谐振频率偏移率。换能器激励电流也会出现频率偏移现象。在提高换能器激励电压时,换能器的结构参数应适当减小。得到的结论可为换能器设计提供理论依据和帮助。     

A Nonlinear Electric Model of the Transient Photoelectric Current in an Organic Photodiode

One of the possible causes of the degradation of organic photodiodes is explained in terms of a nonlinear resistance–capacitance model. Electronic switches for switching photodiode parameters when light is turned on and off are used as nonlinear elements in the equivalent circuit. The model treats the photodiode as a spatially localized photovoltage generator loaded on a passive four-terminal device connected with the electrodes through passive interface layers. The presence of passive layers that have areas with oppositely directed built-in pulling electric fields is the main cause of the degradation of photodiode characteristics. The proposed equivalent circuit well reproduces the experimental transient and steady-state processes in organic photodiodes and can be useful both for measuring the electrical parameters of photodiodes and for studying the processes leading to their degradation.     

Nonlinear optimization of acoustic energy harvesting using piezoelectric devices

In the first part of the paper, a single degree-of-freedom model of a vibrating membrane with piezoelectric inserts is introduced and is initially applied to the case when a plane wave is incident with frequency close to one of the resonance frequencies. The model is a prototype of a device which converts ambient acoustical energy to electrical energy with the use of piezoelectric devices. The paper then proposes an enhancement of the energy harvesting process using a nonlinear processing of the output voltage of piezoelectric actuators, and suggests that this improves the energy conversion and reduces the sensitivity to frequency drifts. A theoretical discussion is given for the electrical power that can be expected making use of various models. This and supporting experimental results suggest that a nonlinear optimization approach allows a gain of up to 10 in harvested energy and a doubling of the bandwidth. A model is introduced in the latter part of the paper for predicting the behavior of the energy-harvesting device with changes in acoustic frequency, this model taking into account the damping effect and the frequency changes introduced by the nonlinear processes in the device.     

A theoretical model of acoustoelectric transducer with a nonuniform distribution of piezoelectric coefficient: application to transducer optimization

A general equation is derived that describes the behavior of a piezoelectric transducer with a nonuniform distribution of piezoelectric coefficient within its bulk, when submitted to an arbitrary distribution of acoustic pressure. Based on this equation, an expression for the receiving transfer function of the transducer is calculated. The results demonstrate the dependence of the transfer function on the distribution of piezoelectric coefficient, and that it is possible to benefit from a nonuniform distribution to optimize the transfer function. The general equation also describes the influence of the external electric circuit loading the transducer, which leads to another independent means of optimizing the transfer function. The proposed model combines effects of piezoelectric material characteristics, acoustic backing, and electric loading, without resorting to Mason or other equivalent circuits for the transducer.     

Electro-acoustical characterization procedure for cMUTs

A procedure for the electro-acoustical characterization in air of cMUTs is reported. First, the measured input electrical impedance of the transducer is used to calculate the transducer parameters at different bias voltages by fitting it with the Mason model. Then, the single membrane equivalent circuit can be calculated. Second, the cMUT impulse response is obtained through a send-and-receive experiment to be compared with the one predicted by the Mason model. In order to minimize the influence of the emitter in the obtained impulse response an ad hoc broadband piezoelectric transducer centered at the resonant frequency of the cMUT was fabricated. Using this transducer, no deconvolution of the impulse response of the emitter in the cMUT reception pulse is necessary. The procedure is tested for two cMUTs with silicon-rich nitride as structural layer and different membrane diameters (60 and 70 microm).     

Traveling wave ultrasonic motor: coupling effects in free stator

Generally a stator of traveling wave ultrasonic motor (TWUM) consists of piezoelectric transducers (annular plate or rods) coupled by the way of a metallic ring. These transducers divided into halves are excited independently by two electrical signals with different phases of about 90 degrees. So an elastic traveling wave propagates along the circumference of the ring and a rotor pressed on this vibrating surface is then driven by the stator via contact forces. Many difficulties appear in developing TWUM because the contact between the stator and the rotor via a frictional material is very important. However that may be, the first stage consists in obtaining a vibrating stator with optimum characteristics with two symmetrical phases. The aim of this paper is to discuss some coupling effects in a free stator through an enhanced equivalent circuit model. A simple experimental method based on impedance measurements is performed to estimate the coupling characteristics at a low driving voltage. This paper reports results obtained with the free stator of the well known piezoelectric ultrasonic motor "USR60" by Shinsei Co. Ltd. Since the stator behaves as an elastic body, interactions between the two electrical inputs might be described by the introduction of a coupling oscillator. The comparison of experimental and theoretical results leads to validate the new equivalent circuit of the free stator. The presence of coupling impedance could imply a change of electrical supply condition to optimize the TWUM efficiency. The effects of unbalanced features for each electrical input and the applicability of the proposed model to actual operating condition are discussed in the paper.     

On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage

In this article, a comprehensive nonlinear analysis for a piezoelectric laminated micro system around its static deflection is presented. This static deflection is created by an electrostatic DC control voltage through an electrode plate. The micro system beam is assumed as an elastic Euler-Bernoulli beam with clamped-free end conditions. The dynamic equations of this model have been derived by using the Hamilton method and considering the nonlinear inertia, curvature, piezoelectric and electrostatic terms. The static and dynamic solutions have been achieved by using the Galerkin method and the multiple-scales perturbation approach, respectively. The results are compared with numerical and other existing experimental results. By studying the primary resonance excitation, the effects of different parameters such as geometry, material and excitations voltage on the system?s softening and hardening behaviors are evaluated. In a piezoelectrically actuated micro system it was showed that because of existence of curvature and inertia nonlinear terms a small change in excitation amplitude can lead to the formation and expansion of nonlinear response. In this paper, it is demonstrated that by applying an electrostatic DC control voltage, these nonlinearities can be controlled and altered to a linear domain. This model can be used to design a nano or micro-scale smart device.     

Simulation and optimization of dynamic characteristics of piezoelectric smart structures

The paper deals with optimization of dynamic characteristics of smart structures based on piezoelectric materials with external electric circuits comprising resistance, capacitance and inductance. The dynamic parameters to be optimized are resonance frequencies and damping properties. For numerical estimation of the dynamic characteristics of the model system, a natural vibration problem of an electroviscoelastic solid with differing external electric circuits is proposed. Model examples are given to demonstrate the efficiency of the natural vibration problem in finding dynamically optimum piezoelectric smart structures with external electric circuits.     

Measurement of resonance frequency and loss factor of a microphone diaphragm using a laser vibrometer

The pressure sensitivity of a laboratory standard microphone is determined using a reciprocity technique that measures the electrical transfer impedance of two microphones connected acoustically by a coupler. The electrical transfer impedance is a function of the coupler volume and the equivalent volumes of the microphones. The equivalent volume given as a function of the frequency can be determined in experiments or can be calculated if the equivalent volume at a low frequency as well as the resonance frequency and loss factor of the microphone diaphragm are known. Therefore, it is necessary to determine the resonance frequency and the loss factor accurately to obtain an accurate reading of the pressure sensitivity.In this paper, a new method to determine the resonance frequency and loss factor of a microphone diaphragm is proposed. The frequency response of the diaphragm displacement is measured by a laser vibrometer and the part of the response near the resonance frequency is used to determine the microphone parameters via least square fitting with the equation of a vibration model with one degree-of-freedom. Since the values measured by this method are close to the nominal values and the repeatability is highly feasible, the proposed method will be useful to determine the resonance frequency and loss factor of a microphone diaphragm.     

Modeling NDT piezoelectric ultrasonic transmitters

Ultrasonic NDT applications are frequently based on the spike excitation of piezoelectric transducers by means of efficient pulsers which usually include a power switching device (e.g. SCR or MOS-FET) and some rectifier components. In this paper we present an approximate frequency domain electro-acoustic model for pulsed piezoelectric ultrasonic transmitters which, by integrating partial models of the different stages (driving electronics, tuning/matching networks and broadband piezoelectric transducer), allows the computation of the emission transfer function and output force temporal waveform. An approximate frequency domain model is used for the evaluation of the electrical driving pulse from the spike generator. Tuning circuits, interconnecting cable and mechanical impedance matching layers are modeled by means of transmission lines and the classical quadripole approach. The KLM model is used for the piezoelectric transducer. In addition, a PSPICE scheme is used for an alternative simulation of the broadband driving spike, including the accurate evaluation of non-linear driving effects. Several examples illustrate the capabilities of the specifically developed software.