Piezoelectric transducer design via multiobjective optimization

The design of piezoelectric transducers is usually based on single-objective optimization only. In most practical applications of piezoelectric transducers, however, there exist multiple design objectives that often are contradictory to each other by their very nature. It is impossible to find a solution at which each objective function gets its optimal value simultaneously. Our design approach is to first find a set of Pareto-optimal solutions, which can be considered to be best compromises among multiple design objectives. Among these Pareto-optimal solutions, the designer can then select the one solution which he considers to be the best one. In this paper we investigate the optimal design of a Langevin transducer. The design problem is formulated mathematically as a constrained multiobjective optimization problem. The maximum vibration amplitude and the minimum electrical input power are considered as optimization objectives. Design variables involve continuous variables (dimensions of the transducer) and discrete variables (the number of piezoelectric rings and material types). In order to formulate the optimization problem, the behavior of piezoelectric transducers is modeled using the transfer matrix method based on analytical models. Multiobjective evolutionary algorithms are applied in the optimization process and a set of Pareto-optimal designs is calculated. The optimized results are analyzed and the preferred design is determined.     

压电陶瓷复合换能器固有频率的有限差分法*

为丰富换能器固有频率的研究理论，以及提供一种新的计算方法供工程人员选择，提出了计算其固有频率的有限差分法。以由径向极化的压电陶瓷圆管与金属预应力管沿径向复合而成的二元压电陶瓷复合换能器为例，建立并推导了其向振动的数学模型及其有限差分形式，给出了换能器径向振动的特征方程。利用MTALAB对计算实例的径向振动的固有频率进行编程计算，理论计算结果与已有实验结果符合很好，验证了有限差分法计算压电陶瓷复合换能器固有频率的可行性及准确性。通过仿真计算，给出了换能器径向振动固有频率与其结构尺寸的影响关系：换能器径向振动的固有频率随压电陶瓷圆管内径的增大而降低，随换能器壁厚比的增大而降低。该文所建立的换能器径向振动固有频率的有限差分法同样适用于结构形式相近的换能器及其他元器件。     

Broadband multimode baffled piezoelectric cylindrical shell transducers

Hollow piezoelectric cylindrical shell transducers may be made directional for underwater acoustic applications by the use of suitable acoustical baffles and the operational bandwidth may be extended by using multiple resonant modes. A theoretical and experimental investigation was performed for circumferentially baffled piezoelectric cylindrical shell transducers operating in the zero and one modes of extensional vibration. The frequency responses and directivity patterns were analyzed under various conditions of energizing separate halves of electrodes. It was found that the broadest frequency response with nearly constant beamwidth can be obtained when the two halves of the piezoelectric ring are electromechanically excited 90 deg out-of-phase. The experimental results obtained with a proof-of-concept transducer were in good agreement with the theoretical predictions.     

Hybrid linear and matrix acoustic arrays

This work describes a new technique for constructing both linear and matrix array transducers. It used completely separated piezoelectric elements whose vibration modes have been studied experimentally. Each piezoelectric element has a $\text{λ}\text{4}$ matching plate and backing, and so it forms a separate transducer. The array is formed by an assembly of these transducers.The technique shows some interesting features such as the possibility of reducing the dispersion of the electroacoustic characteristics of the single elements to the required value, mechanical strength, and the possibility of periodical maintenance.     

复合圆环弯曲振动四极子模态分析

针对压电圆环弯曲振动机电转换性能较差的问题,提出了一种复合圆环弯曲振动换能器,它由一个径向极化的压电陶瓷内圆环和一个金属外圆环复合而成。基于能量原理推导得到了复合圆环弯曲振动的谐振频率和有效机电耦合系数,探讨了弯曲振动四极子模态特性与其结构尺寸间的关系。当压电圆环尺寸不变时,随外侧金属圆环壁厚增加,复合圆环弯曲振动四极子模态谐振频率上升,有效机电耦合系数迅速上升到极大值后缓慢下降。最后,设计制作了圆环换能器并对其谐振频率和有效机电耦合系数进行了实验测试,测试结果与解析结果和数值模拟结果吻合得较好。      

Study of the sandwiched piezoelectric ultrasonic torsional transducer

The sandwiched piezoelectric ultrasonic torsional transducer was studied. The transducer consists of front and back metal cylinders, and coaxially segmented, tangentially polarized, piezoelectric ceramic tubes. The torsional vibration of the tangentially polarized piezoelectric ceramic slender tube was studied first and its electromechanical equivalent circuit was derived. Based on the network theory and the electromechanical equivalent circuit, the torsional vibration of the piezoelectric ceramic cylinder, formed by stacking a number of identical short piezoelectric ceramic rings, was analysed and the electromechanical equivalent circuit of the piezoelectric ceramic stack in torsional vibration was developed. Finally, the sandwiched ultrasonic torsional transducer was studied and resonance frequency equations were derived which can be used to design and calculate the torsional transducers for different applications.     

The use of distributed pressure receivers based on elastic piezoelectric composite materials for measuring the hydrodynamic noise produced by a near-wall turbulence

Receiving electroacoustic transducers with sensing elements made of an elastic piezoelectric composite material are described. The parameters of a composite material that exhibits a bulk piezoelectric effect are presented. Results obtained by measuring the turbulent noise in a hydrodynamic channel with the use of piezoelectric composite receivers are reported. The results are compared with those of the noise measurements by a miniature piezoceramic receiver and are considered in the light of the known models of near-wall turbulence.     

Modeling of lamb waves generated by integrated transducers in composite plates using a coupled finite element-normal modes expansion method

Thin piezoelectric transducers attached to or embedded within composite structures could be used for in situ structural health monitoring. For plate-shaped structures, the useful ultrasonic vibration modes are Lamb waves. Preliminary testing has already demonstrated the suitability and practical feasibility of such integrated transducers, but better control of the generation of Lamb modes seems to be necessary. Therefore, an original modeling approach has been developed, which can be used to design and optimize these "sensitive materials." This modeling technique allows the determination of the amplitude of each Lamb mode excited in a composite plate with surface-bonded or bulk-embedded piezoelectric elements. The method consists of a coupling of the finite element method (FEM) and the normal modes expansion method. The limited finite element mesh of the transducer and its vicinity enables the computation of the mechanical field created by the transducer, which is then introduced as a forcing function into the normal modes equations. The adequacy and accuracy of this modeling method have been numerically and experimentally verified.     

Optical detection of amplitude and phase of mechanical displacements in the Åstrom range

Light reflected from a periodically vibrating surface is frequency modulated. After appropriate frequency mixing the modulation index, and consequently the amplitude of the displacement, can be determined absolutely. Vibration displacements down to 0.03 Å have been measured in the frequency range from 45 kHz to 45 MHz. Using a frequency-modulated auxiliary light beam for the mixing, it is also possible to determine the phase of the displacement. This allows an accurate analysis to determine, for example, the vibration modes of transducers, resonators or vibrating targets, and also whether or not a certain material has a complex piezoelectric constant.     

Modal analysis of the electromechanical conversion in piezoelectric ceramic spherical shells

The current study considers piezoelectric ceramic electromechanical transducers utilizing axisymmetric vibrations of complete and incomplete spherical shells. Analysis is focused on generating the modes of vibration that can be employed in the design of multimode unidirectional electroacoustic transducers for underwater applications and on determining the electrode configurations that achieve optimal electromechanical coupling for the different modes of vibration considered. Analytical expressions are presented for the modal and intermodal equivalent parameters characterizing the energy state of the shell vibration. Results of calculation and experimental verification of the resonance frequencies and effective coupling coefficients for different modes of vibration of the complete and incomplete spherical shells are in good agreement.     

The directivity pattern of an interferometer for measuring thermal acoustic radiation

The directivity patterns of a pair of piezoelectric transducers for measuring the spatial correlation function of sound pressures produced by sources of thermal acoustic radiation in the megahertz frequency range are calculated. Sources in the form of a heated plane or strip are considered. The signal detection by two circular or rectangular piezoelectric transducers and by focusing transducers is studied. It is demonstrated that, for measuring the correlation function, the piezoelectric transducers must partially overlap. To determine the directivity pattern with a strong dependence on the distance between the heated object and the pair of piezoelectric transducers, focusing piezoelectric transducers should be used. The results obtained offer possibilities for a noninvasive measurement of the absorption coefficient of a medium and also for the realization of the previously proposed [20] passive acoustic thermotomograph, which does not use a priori information on the absorption coefficient of the medium.     

基于ZnO压电薄膜的弯曲振动硅微压电超声换能器的研究

对所研制的硅微压电超声换能器（PMUT）的振动特性进行了研究分析。对硅微压电超声换能的振动膜薄板的厚度相对于薄板的尺度（边长）而言较薄的情况,理论分析与实验结果均表明残余应力对换能器的谐振频率影响较大:不考虑残余应力的理论分析得出的换能器谐振频率与器件的实验测量的结果相差较大,而考虑残余应力的分析给出的谐振频率结果与实验结果是符合的。本文还对所制作的硅微压电超声换能器的谐振频率及导纳进行测量,并给出其等效电路参数。其中振动膜边长为1mm的换能器的谐振频率为71.25 kHz。最后对其进行了简单接收发射实验,测得谐振频率处的接收灵敏度为-201.6 dB（ref 1 V/μPa）,发射电压响应约为137 dB（ref 1 μPa·m/V）。      

Radial vibration characteristics of spherical piezoelectric transducers

This paper presents the vibration characteristics of the radial mode in spherical piezoelectric transducers. The differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential. Applying mechanical and electrical boundary conditions yielded a characteristic equation for radial vibration. Theoretical calculations of the fundamental natural frequency have been compared with numerical and experimental results for transducers of several sizes, and have shown a good agreement. This paper discusses the dependence of natural frequencies on the radius and thickness of the piezoelectric spheres and the difference between piezoelectric and elastic resonances. From the results it has been concluded that the natural frequency was not affected for the first radial mode but was reduced by the piezoelectric phenomenon. It has also been concluded that the natural frequency of the first radial mode depended mostly on the radius rather than on the thickness of the sphere whereas the natural frequency of the second radial mode depended mostly on the thickness rather than the radius.     

径向复合圆柱压电超声换能器

提出一种三元径向复合圆柱压电超声换能器,并对其径向振动特性进行了研究。基于弹性力学理论及机电类比原理,导出了柱坐标系中分割处理径向极化压电陶瓷管准厚度模振动及薄壁短圆管径向振动的机电等效电路;利用径向力和振速连续的边界条件,得出了径向复合圆柱压电换能器系统的径向振动机电等效电路及其共振频率方程。探讨了换能器径向共振频率及有效机电耦合系数随其几何尺寸的变化关系。研究表明,换能器的径向共振频率及有效机电耦合系数随其内芯半径和预应力管壁厚度增大而降低。研制了一些径向复合圆柱压电换能器,并对其径向共振频率进行了测试。结果表明,理论与实验结果基本一致。      

Finite element reduced order model for noise and vibration reduction of double sandwich panels using shunted piezoelectric patches

This work concerns the control of sound transmission through double laminated panels with viscoelastic core using semi-passive piezoelectric shunt technique. More specifically, the system consists of two laminated walls, each one composed of three layers and called sandwich panel with an air cavity in between. The external sandwich panel has a surface-mounted piezoelectric patches. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of some specific resonance frequencies of the coupled system. Firstly, a finite element formulation of the fully coupled visco-electro-mechanical-acoustic system is presented. This formulation takes into account the frequency dependence of the viscoelastic material. A modal reduction approach is then proposed to solve the problem at a lower cost. In the proposed technique, the coupled system is solved by projecting the mechanical displacement unknown on a truncated basis composed by the first real short-circuit structural normal modes and the pressure unknown on a truncated basis composed by the first acoustic modes with rigid boundaries conditions. The few initial electrical unknowns are kept in the reduced system. A static correction is also introduced in order to take into account the effect of higher modes. Various results are presented in order to validate and illustrate the efficiency of the proposed finite element reduced order formulation.     

Modeling of functionally graded piezoelectric ultrasonic transducers

The application of functionally graded material (FGM) concept to piezoelectric transducers allows the design of composite transducers without interfaces, due to the continuous change of property values. Thus, large improvements can be achieved, as reduction of stress concentration, increasing of bonding strength, and bandwidth. This work proposes to design and to model FGM piezoelectric transducers and to compare their performance with non-FGM ones. Analytical and finite element (FE) modeling of FGM piezoelectric transducers radiating a plane pressure wave in fluid medium are developed and their results are compared. The ANSYS software is used for the FE modeling. The analytical model is based on FGM-equivalent acoustic transmission-line model, which is implemented using MATLAB software. Two cases are considered: (i) the transducer emits a pressure wave in water and it is composed of a graded piezoceramic disk, and backing and matching layers made of homogeneous materials; (ii) the transducer has no backing and matching layer; in this case, no external load is simulated. Time and frequency pressure responses are obtained through a transient analysis. The material properties are graded along thickness direction. Linear and exponential gradation functions are implemented to illustrate the influence of gradation on the transducer pressure response, electrical impedance, and resonance frequencies.     

Diffraction aperture non-ideal behaviour of air coupled transducers array elements designed for NDT

Air coupled piezoelectric ultrasonic array transducers are a novel tool that could lead to interesting advances in the area of non-contact laminar material testing using Lamb wave's propagation techniques. A key issue on the development of such transducers is their efficient coupling to air media (impedance mismatch between the piezoelectric material and air is 90 dB or more). Adaptation layers are used in order to attain good matching and avoid possible serious signal degradation. However, the introduction of these matching layers modify the transducer surface behaviour and, consequently, radiation characteristics are altered, making the usual idealization criteria (of uniform surface movement) adopted for field simulation purposes inaccurate. In our system, we have a concave linear-array transducer of 64 elements (electrically coupled by pairs) working at 0.8 MHz made of PZ27 rectangular piezoceramics (15 mm x 0.3 mm) with two matching layers made of polyurethane and porous cellulose bonded on them. Experimental measurements of the acoustic aperture of single excited array elements have shown an increment on the geometrical dimensions of its active surface. A sub-millimeter vibrometer laser scan has revealed an extension of the aperture beyond the supposed physical single array element dimensions. Non-uniform symmetric apodized velocity surface vibration amplitude profile with a concave delay contour indicates the presumed existence of travelling wave phenomena over the surface of the outer array matching layer. Also, asymptotic propagation velocities around 2500 m/s and attenuation coefficient between 15 and 20 dB/mm has been determined for the travelling waves showing clear tendencies. Further comparisons between the experimental measurements of single array element field radiation diagram and simulated equivalent aperture counterpart reveal good agreement versus the ideal (uniform displaced) rectangular aperture. For this purpose an Impulse Response Method (IRM) has been used.     

功率型压电陶瓷的分类及研究进展综述

功率型压电材料是大功率换能器及压电变压器等的核心功能材料,广泛应用于声纳系统、超声检测、振动控制及其它机电设备等。尽管其组成和制备方法与其他压电材料类似,但特定的使用目的对功率型压电材料提出了特殊的综合性能要求。本文基于对功率型压电陶瓷材料组成的分类归纳,综述了该材料的性能特点、国内外研究进展,并对现存问题和应用前景进行了论述。     

The analysis of adhesive bonds using electromagnetic acoustic transducers

The paper presented here outlines a technique for examining aerospace adhesive bonds using electromagnetic acoustic transducers (EMAT). The main restriction on the use of bonded structures is the lack of a reliable, applicable non-destructive test. Simple acoustic theory shows that a shear wave at normal incidence to an interface should be a more sensitive probe of interfacing coupling than a longitudinal wave. Conventional piezoelectric shear transducers require a very viscous couplant which makes scanning problematic. The EMAT described here consists of a pancake coil, and a permanent magnet behind the coil provides a static magnetic field normal to the surface of the sample and the plane of the coil. The EMATs used have the advantage of generating broadband radially polarized shear waves, while requiring no acoustic couplant. They are also comparable in size to typical piezoelectric transducers. The broadband nature of the transducer gives it a high spatial resolution in the direction of wave propagation. Experiments performed on plate-like samples have successfully detected deliberately constructed defects, while monitoring the adhesive thickness. Defects have been identified using a C-scan technique using a single EMAT in send-receive mode from either side of the bond.     

Dynamic Modeling and Analysis of Wind Turbine Blade of Piezoelectric Plate Shell

This paper presents a theoretical analysis of vibration control technology of wind turbine blades made of piezoelectric intelligent structures. The design of the blade structure, which is made from piezoelectric material, is approximately equivalent to a flat shell structure. The differential equations of piezoelectric shallow shells for vibration control are derived based on piezoelectric laminated shell theory. On this basis, wind turbine blades are simplified as elastic piezoelectric laminated shells. We establish the electromechanical coupling system dynamic model of intelligent structures and the dynamic equation of composite piezoelectric flat shell structures by analyzing simulations of active vibration control. Simulation results show that, under wind load, blade vibration is reduced upon applying the control voltage.