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.     

基于2-2型压电复合材料的新型宽频带径向振动超声换能器

本文提出了一种基于2-2型压电复合材料的新型宽频带径向振动超声换能器,它主要由内金属圆环和外压电陶瓷复合材料圆环组成.首先利用Newnham串并联理论和均匀场理论推导了2-2型压电复合材料的等效参数;其次利用解析法得到了金属圆环和径向极化压电复合陶瓷圆环径向振动的机电等效电路;最后得到了换能器的六端机电等效电路,从而得到了换能器的频率方程.接着分析了换能器共振频率和反共振频率以及有效机电耦合系数与几何尺寸、两相体积占比的关系,采用仿真软件对新型换能器的径向振动进行了数值模拟.结果表明,利用解析法得到的共振频率和反共振频率与数值模拟结果吻合较好.此外,对换能器在水下的辐射声场进行了仿真研究,结果表明新型复合材料径向换能器相比传统纯陶瓷径向换能器,发射电压响应幅值更大,工作带宽提高接近一倍,声匹配更佳.     

Effect of surface acoustic waves on the catalytic decomposition of ethanol employing a comb transducer for ultrasonic generation

The effect of surface acoustic waves, generated on a silver catalyst using a comb transducer, on the catalytic decomposition of ethanol is examined. The comb transducer employs purely mechanical means for surface acoustic wave (SAW) transduction. Unlike interdigital SAW transducers on piezoelectric substrates, the complicating effects of heat generation due to electromechanical coupling, high electric fields between adjacent electrodes, and acoustoelectric currents are avoided. The ethanol decomposition reactions are carried out at 473 K. The rates of acetaldehyde and ethylene production are retarded when acoustic waves are applied. The rates recover to varying degrees when acoustic excitation ceases.     

Theoretical analysis and experimental validation of radial cascaded composite ultrasonic transducer

A radial cascaded composite ultrasonic transducer is analyzed.The transducer consists of three short metal tubes and two radially polarized piezoelectric ceramic short tubes arranged alternately along the radial direction.The short metal tubes and the piezoelectric ceramic short tubes are connected in parallel electrically and in series mechanically,which can multiply the input sound power and sound intensity.Based on the theory of plane stress,the electro-mechanical equivalent circuit of radial vibration of the transducer is derived firstly.The resonance/anti-resonance frequency equation and the expression of the effective electromechanical coupling coefficient are obtained.Excellent electromechanical characteristics are determined by changing the radial geometric dimensions.Two prototypes of the transducers are designed and manufactured to support the analytical theory.It is concluded that the theoretical resonance/anti-resonance frequencies are consistent with the numerical and experimental results.When R_2 is at certain values,both the anti-resonance frequency and effective electromechanical coupling coefficient corresponding to the second mode have maximal values.The radial cascaded composite ultrasonic transducer is expected to be used in the fields of ultrasonic water treatment and underwater acoustics.     

Study on the multifrequency Langevin ultrasonic transducer

Langevin ultrasonic transducers are widely used in high-power ultrasonics and underwater sound. In ultrasonic cleaning, a matching metal horn rather than a metal cylinder is used as the radiator in order to enhance the radiating surface and improve the acoustic matching between the transducer and the processed medium. To raise the effect of ultrasonic cleaning, the standing wave in the cleaning tank should be eliminated. One method to eliminate the standing wave in the tank is to use the multifrequency ultrasonic transducer. In this paper, the Langevin ultrasonic horn transducer, with two resonance frequencies, is studied. The transducer consists of two groups of piezoelectric ceramic elements: the back metal cylinder, the middle metal cylinder and the front matching metal horn. The vibrational modes of the transducer are analysed, and resonance frequency equations of the transducer in the half-wave and the all-wave vibrational modes are derived. According to the resonance frequency equations, transducers with two resonance frequencies are designed and made. The resonance frequencies, the effective electromechanical coupling coefficients and the equivalent electric impedances of the transducers are measured. It is shown that the measured resonance frequencies are in good agreement with the computed results, and the transducer can be excited to vibrate at two resonance frequencies, which correspond to the half-wave and the all-wave vibrational modes of the transducer.     

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。      

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.     

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.     

钹型换能器的优化设计*

本文研究的钹型换能器,是由一个压电陶瓷圆环和一个金属浅球壳组成。为了得到这种钹型换能器的解析解和它在不同介质中的机电性能。首先,根据前人得出的压电陶瓷圆环和金属浅球壳的理论模型,用等效电路法从理论上计算出了该换能器的共振频率并与仿真结果做了对比,发现二者近似吻合,验证了理论计算的可靠性,为这种钹型换能器的优化设计提供了理论指导。然后利用COMSOL Multiphysics分别模拟了压电陶瓷为圆盘和圆环的钹型换能器的共振频率,仿真结果表明：同等条件下,当圆环的外径和圆盘的半径相等时,压电陶瓷为圆环的钹型换能器共振频率更低,使其具有频率低、体积小的特点更加明显。利用数值方法,分析了钹型换能器的几何尺寸对其共振频率、反共振频率及有效机电耦合系数的影响。最后模拟了钹型换能器在水中的机电特性及声压分布。     

Mode analysis of trilaminar bender bar transducers using an approximation method

Based on the vibration theory of a thin plate, an analytical treatment of the trilaminar bender bar with piezoelectric elements and inert substrate of various lengths is presented for mode analysis. Resonance frequency and effective electromechanical coupling coefficient are calculated by this method. The impacts of the geometries of the bender bar on the performance of its fundamental and third-order flexural mode are investigated in detail under rigid boundary conditions. It is shown that resonance frequency is extremely sensitive to the thickness of inert substrate. Moreover, the effective electromechanical coupling coefficient has peaks as the length of piezoelectric elements varies. The peaks are achieved when the length of piezoelectric elements equals the length between two nodes having zero strains in the x-direction. The trilaminar bender bar will be effectively excited when the strains on the piezoelectric element are in the same phase, which is important to disclose the vibration mechanisms of this kind of transducer. Also, analytical results are compared with the ones of numerical simulation. The results suggest that effective electromechanical coupling coefficient shares similar patterns with electrical conductance, which can be used to characterize transducer performance to a certain extent. It also demonstrates that the analytical treatment provides an efficient alternative way for optimizing the bender bar transducer design.     

A tri-modal directional transducer

Acoustic transducers made from piezoelectric ceramic cylinders usually exploit the breathing or omnidirectional (omni) mode of vibration. However, with suitable voltage distribution, higher order extensional modes of the cylinder can be excited which produce directional radiation patterns. These modal radiation patterns can then be combined to synthesize desired beam patterns which may be steered by incrementing the excitation. This paper describes a model for the combined acoustic response of the extensional modes of vibration of a piezoelectric ceramic cylinder, a method of synthesizing a desired radiation pattern, and an experimental implementation of a directional transducer that uses these techniques. This tri-modal transducer is broadband and directional with a frequency independent beam pattern yet simple, small, and lightweight.     

热疗用聚焦超声换能器的研究

本文通过数值计算及实际测量,研究了凹球面声透镜聚焦换能器及凹球面自聚焦换能器产生的声场,证实此两种聚焦方式均可获得理想的聚焦效果,但自聚焦方式更适合高强度聚焦超声(HIFU)加热治疗。     

Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

Application of piezoelectric transient response in transducer acoustic power measurement

To explore a more convenient method for measuring the focused ultrasound power,a piezoelectric ceramic plate was used to receive ultrasonic signal directly.Due to an acoustic force acts on the surface of piezoelectric ceramic plate,the piezoelectric response was obtained by means of electromechanical analogy,which was composed of voltage response caused by forced vibration and high frequency attenuation response caused by natural vibration.The conversion relationship between output signal of piezoelectric ceramic plate and acoustic power of transducer was analyzed.The envelope of output piezoelectric signal was extracted in twice,and a voltage amplitude curve with sinusoidal distribution that could describe the changes of acoustic power was obtained.Under different drive voltage of transducer,the maximum peak voltage of envelope curve was found respectively.Their squared values were made a linear fitting with acoustic power measured by acoustic power meter,and then the proportional coefficient of theoretical relational expression was calibrated.The experimental results are in good agreement with the theory.The relative error between calibrated theoretical acoustic power and that measured by acoustic power meter was less than 8.7%.The paper can provide a guideline for measuring acoustic power of transducer by using piezoelectric signal.     

The performance of thick piezoelectric transducers as wide-band ultrasonic detectors

A Q-switched Nd:YAG laser has been used to generate reproducible acoustic displacements in metallic samples. The acoustic waveforms were initially detected by an absolute displacement-sensitive, capacitance transducer. The capacitance transducer was then replaced in turn by two piezoelectric ceramic transducers of different thickness and diameter. Comparison of waveforms from the two types of detector indicate that thick piezoelectric transducers are useful in the detection of fast rise-time displacement waveforms at metal surfaces. Their performance is optimized by making them as thick as possible, with a small area of contact with the surface.     

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。      

厚度模压电超声换能器无源声学材料研究进展*

厚度模压电超声换能器作为超声波发射、接收以及电信号间转换的载体,是超声成像与检测系统的核心器件,一般由压电层、匹配层和背衬层3部分组成。超声换能器的性能一定程度上决定着整体超声设备的性能,影响了其在工业、医学、军事等领域的应用。该换能器的关键性能指标(带宽、灵敏度)除了受到压电层的影响,还与匹配层、背衬层等无源声学材料的设计密切相关。该文综述了近年来厚度模压电超声换能器无源声学材料(匹配层、背衬层和声透镜)的研究进展,提出了当前该类材料面临的难题和解决途径,并对其未来发展方向进行了展望。     

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.     

Characteristics of backing impacts on the performance of the thickness mode piezoelectric transducer

The impacts of the thickness, the specific acoustic impedance and the mechanical loss factor of the backing on the performance of the thickness mode piezoelectric transducer are systemically studied, which are focused on the effective electromechanical coupling coefficient and the mechanical quality factor near the center frequency. The results show that with contin?uous increasing of the backing thickness, the effective electromechanical coupling coefficient and the mechanical quality factor are found rapidly declined by oscillation way. With the increase of the difference value of the acoustic impedance between the backing material and the piezoelec?tric material, the effective electromechanical coupling coefficient deceases and the mechanical quality factor increases. Under condition that the thickness of the piezoelectric material is fixed, the effective electromechanical coupling coefficient is found declined with the increase of the mechanical loss factor by monotonous way. The mechanical quality factor has minimum value and the electric characteristic curve tends to be smooth in a given frequency range. The equivalent circuit theory result is in good agreement with the ones by finite element method and the experimental results. The work mentioned above provides a theoretical guidance for the design and experimental fabrication of the thickness mode piezoelectric transducer.     

Full-wave modeling of piezoelectric transducers for SAW acousto-optical interactions

In this paper we present an accurate and efficient numerical method for a rigorous full-wave analysis of interdigital transducers (IDT) for the excitation of surface acoustic waves on the piezoelectric substrate of acousto-optical devices. The problem is formulated in terms of an integral equation that is solved by the method of moments. The transducer input admittance and the power coupling factors to both surface and bulk waves are computed. Numerical results for some configurations of X-Y LiNbO₃ IDT for acousto-optic applications are in very good agreement with measured data. It is pointed out that bulk wave excitation may be a serious limitation in the design of efficient, wide band transducers for acousto-optical devices.