Analysis of the sandwich piezoelectric ultrasonic transducer in coupled vibration

The coupled vibration of the sandwich piezoelectric transducer with a large cross-section is analyzed using an approximate analytic method. The resonance frequency equations of the transducer are derived and the effect of the geometrical dimensions on the resonance frequency is studied. It is illustrated that when the radial vibration in the transducer is considered, the vibration of the sandwich transducer becomes more complex. Apart from the longitudinal resonance frequency, the radial resonance frequency can also be obtained. For comparison, numerical methods are also used to simulate the coupled vibration; the resonance frequency and the vibrational displacement distribution are computed. Compared with one-dimensional longitudinal theory, the radial dimensions of the transducer are no longer limited because the coupled vibration is considered. Compared with numerical methods, the physical meaning of the analytic method is concise. It is illustrated that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with those from numerical methods, and they are in better agreement with the measured results than those from one-dimensional theory. Since the radial and the coupled vibration are considered in the analysis, more resonance frequencies can be obtained. Therefore, using the coupled resonance frequency equations, the sandwich transducer with multifrequency or wide frequency bandwidth can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry and other applications.     

矩形辐射器压电多频超声换能器的研究

研究了一种具有多个共振频率的矩形辐射器夹心式超声换能器,换能器由圆柱形后盖板、压电陶瓷晶堆及矩形六面体辐射器前盖板组合而成。利用表观弹性法和一维近似理论给出了多频换能器横向及纵向理论共振频率方程。对一种特殊情况下的此类换能器进行了有限元及实验分析,给出了各自的频率输入导纳曲线。对理论和实验结果进行分析后表明,此类矩形辐射器夹心式超声换能器可以在不同的振动模态上工作,具有多个共振频率.     

Investigations of the barbell ultrasonic transducer operated in the full-wave vibrational mode

In this paper, the resonance frequency equation and expression of displacement amplitude magnifications of a full-wave barber ultrasonic horn are obtained. By discussing the relationships between the displacement amplitude magnifications and the geometrical dimensions, the optimized design of the horn for the largest magnification is proposed, which is helpful to improve the radiation power and the transfer efficiency of the acoustic energy of the ultrasonic oscillatory system. Based on the optimized design of the horn, we introduced a barbell ultrasonic transducer operated in the longitudinal full-wave vibrational model and obtained the resonance frequency equations. For comparison, the resonance frequencies of the full-wave barbell horn and the full-wave barbell transducer are also analyzed by finite element method (FEM). It is shown that the values obtained by theoretical analysis and FEM are in good agreement with experimental observations. We hope that the research of this paper is helpful for the use of the barbell horn and transducer in the applications such as ultrasonic liquid processing.     

阶梯圆环压电超声换能器径向振动性能的理论研究*

提出了一种阶梯圆环径向振动压电超声换能器,根据力电类比原理建立了阶梯圆环及阶梯圆环换能器的径向振动等效电路,推导了阶梯圆环的径向共振频率方程和位移放大系数,在此基础上进一步推导了换能器的径向共振和反共振频率方程。通过理论推导和有限元仿真模拟分析了阶梯圆环压电超声换能器的径向振动性能。结果表明,增大阶梯圆环中内外环的径向厚度之比K1或减小轴向厚度之比K2,阶梯圆环的一阶径向共振频率减小,二阶径向共振频率增大;在二阶径向共振模式下,K1、K2值在一定范围内阶梯圆环可实现由内向外的径向位移振幅放大;随着压电陶瓷圆环的内半径增大,阶梯圆环压电超声换能器的一阶、二阶径向共振和反共振频率减小,二阶径向共振下的有效机电转换系数趋于零;增大阶梯圆环内环的外半径,换能器的一阶径向共振和反共振频率减小,二阶径向共振和反共振频率先增大后减小,理论推导与仿真模拟结果符合良好。本文研究结果为阶梯圆环压电超声换能器的工程应用提供理论参考。     

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.     

Study on the compound multifrequency ultrasonic transducer in flexural vibration

A new type of compound multifrequency ultrasonic transducer is analyzed in this paper. The compound multifrequency ultrasonic transducer consists of two sandwiched ultrasonic transducers and a rectangular radiator. In virtue of the coupling between longitudinal vibration of the sandwiched ultrasonic transducers and flexural vibration of the rectangular radiator, the compound multifrequency ultrasonic transducer can produce several resonance frequencies. Some compound multifrequency ultrasonic transducers are designed and simulated by finite element method (ANSYS), and modal shapes and harmonic response are analyzed. The compound multifrequency ultrasonic transducers are designed and manufactured. The resonance frequencies are measured and compared with the numerical results. The effect of the geometrical dimensions of the compound multifrequency ultrasonic transducer and the location of two sandwiched ultrasonic transducers on the compound multifrequency ultrasonic transducer is discussed. It is shown experimentally and numerically that the compound multifrequency ultrasonic transducer has several resonance frequencies.     

A new type of high power composite ultrasonic transducer

A new type of high power composite ultrasonic transducer was proposed and studied. The composite transducer consists of a sandwich longitudinal piezoelectric transducer, an isotropic metal hollow cylinder with large radial dimension, and the front and back metal radiation mass. By means of its special structure and Poisson’s effect, the composite transducer can produce vibrations both in its longitudinal and radial directions, and therefore, it can radiate sound waves in three-dimensional space. The electro-mechanical equivalent circuit of the composite transducer was derived and the resonance frequency equation was obtained analytically. Numerical methods were used to simulate the vibration of the composite transducer, and the vibrational displacement distribution, the resonance frequency and the radiation sound field are given. Some composite transducers are designed and manufactured; their resonance frequencies and the radiation acoustic field are measured and compared with the analytical and numerical results. It can be seen that the measured frequencies and acoustic field contour are in good agreement with the analytical and numerical results. It is expected that this kind of composite ultrasonic transducer can be used in more and more power ultrasonic applications, such as ultrasonic cleaning, ultrasonic extraction, ultrasonic sonochemistry and other ultrasonic liquid processing, where high ultrasonic power and large ultrasonic processing space are needed increasingly.     

幂函数型环形聚能器径向振动的等效电路

基于机电类比原理和变厚度薄圆环的平面应力方程,推导了幂函数型环形聚能器径向振动的等效电路、共振频率方程和位移放大系数。讨论了第一、二阶径向共振频率及相应的位移放大系数随圆环半径比的变化关系。结果表明,幂函数型环形聚能器径向振动的等效电路是一种非互易二端口等效网络;一阶和二阶共振频率随圆环内外半径比的增大而增大;一阶径向共振模式下位移放大系数随圆环半径比的增大先降低后升高,二阶径向共振模式下位移放大系数随圆环半径比的增大而降低,但二阶时的位移放大系数整体大于一阶,因此二阶径向共振模式具有更好的径向振动性能。用COMSOL有限元软件对解析理论分析结果进行了验证,仿真模拟结果与解析理论符合良好。根据幂函数型环形聚能器的等效电路模型,进一步设计了一种压电环形换能器,计算了第一、二阶径向共振频率、反共振频率及有效机电耦合系数,通过与COMSOL有限元软件模拟结果对比,符合良好。本文研究结果为幂函数型环形聚能器及压电环形换能器的工程应用提供了简明设计理论,文中研究结论可作为一种径向超声切割刀在超声工程中获得重要应用。      

Measurement of velocity variations along a wave path in the through-thickness direction in a plate

In this paper there is given a method to predict ultrasonic wave velocity variations along a wave path in the through-thickness direction in a plate from thickness resonance spectra. Thickness resonance spectra are numerically calculated and two simple rules used to predict the entire ultrasonic wave velocity variation are derived. In the calculation, the wave path is assumed to be straight along the thickness direction and the velocity variation is assumed to be either as a parabolic curve dependence or a linear dependence with respect to the distance from the surface and to be symmetric with respect to the plate center. To see if the numerical calculation method is reliable, thickness resonance frequencies of a sample with three-layers were measured by EMAT (electromagnetic acoustic transducer) with a good agreement between the measured and the calculated frequencies. This method can be applied to the ultrasonic measurement of material characteristics, internal stress or various other properties of plate materials.     

Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by finite displacements of its boundary

A method of describing oscillations in resonators on the basis of evolution equations is proposed. The latter are obtained by simplifying the functional equations under the assumption that the distortions of travelling waves within the resonator length are small, that the Mach number for the moving boundary oscillations is small, and that the frequency is close to one of the natural frequencies of the resonator. The problems of nonstationary oscillations of a layer with a moving boundary are solved. The law that should govern the wall oscillations to provide the development of steady-state linear resonance oscillations is determined. The shape of the resonance curve formed in the presence of a boundary nonlinearity is calculated. The method of matching of asymptotics is applied to the singularly perturbed problem with small dissipation. It is shown that a boundary nonlinearity leads to a distortion of the temporal profile of the standing wave and to the generation of higher harmonics in the process of the development of steady-state oscillations. In contrast to the classical linear problems where the resonance occurs at the coincidence of the external force frequency with one of the natural frequencies, in the case under study the resonance behavior is observed in frequency bands, which are wider the higher the amplitude of the boundary oscillations is.     

锥形剖面径向复合超声换能器的机电等效电路

研究了一种锥形剖面径向复合超声换能器.该换能器由一个等截面内金属圆环、一个轴向极化的压电陶瓷圆环和一个锥形剖面外金属圆环沿径向复合而成,且换能器的径向尺寸远大于高度.锥形剖面外金属圆环满足关系式h= h0r,ho为厚度变化常数.基于平面应力径向振动理论,推导了换能器的机电等效电路,得到了共振频率方程和反共振频率方程,进...     

Optimization design of high power ultrasonic circular ring radiator in coupled vibration

This paper presents a new high power ultrasonic (HPU) radiator, which consists of a transducer, an ultrasonic horn, and a metal circular ring. Both the transducer and horn in longitudinal vibrations are used to drive a metal circular ring in a radial-axial coupled vibration. This coupled vibration cannot only generate ultrasound in both the radial and axial directions, but also focus the ultrasound inside the circular ring. Except for the radial-axial coupled vibration mode, the third longitudinal harmonic vibration mode with relative large vibration amplitude is also detected, which can be used as another operation mode. Overall, the HPU with these two vibration modes should have good potential to be applied in liquid processing, such as sonochemistry, ultrasonic cleaning, and Chinese herbal medicine extraction.     

超声换能器表面的振动状态

从超声波在波密介质和波疏介质之间的传播以及诱发共振发射超声波的角度,讨论了空气中超声声速测量实验所用超声换能器的表面振动状态.理论分析及实验测量结果表明:超声换能器表面振动状态与其结构有关,超声接收器表面位移振幅一般不为零.     

超声波作用下泡群的共振声响应

从球状泡群气泡动力学方程出发, 考虑泡群间次级声辐射的影响, 得到了声场中两泡群共同存在时气泡振动的动力学方程, 并以此为基础探讨声波驱动下双泡群振动系统的共振响应特征. 由于泡群间气泡间的相互作用, 系统存在低频共振和高频共振现象, 两不同共振频率的数值与泡群内气泡的本征频率相关. 泡群内气泡的本征频率又受到初始半径、泡群大小和泡群内气泡数量的影响. 气泡自由振动和驱动声波的耦合激起泡群内气泡的受迫振动, 气泡初始半径、气泡数密度和驱动声波频率等都会影响泡群内气泡的振动幅值和初相位. 关键词： 气泡群 共振 声响应 超声空化     

模式转换型超声塑焊振动系统的设计

基于弯曲振动理论和耦合振动理论,设计了一种新型大尺寸筒形超声塑焊振动系统。该振动系统由纵向振动换能器及变幅杆、弯曲振动金属圆盘和耦合振动圆筒四部分组成。换能器和变幅杆的纵向振动驱动圆盘的二次弯曲模式振动,圆盘的二次弯曲模式振动激励圆筒的纵向模式振动,实现了工具头在较高频率下谐振。实验结果表明,振动系统的测试频率与计算频率比较符合,在大信号下测试的纵-弯-纵振动模式转换效果很好。研究结果为高频大尺寸超声焊接系统的设计提供了思路。      

Study on the Langevin piezoelectric ceramic ultrasonic transducer of longitudinal-flexural composite vibrational mode

In this paper, the Langevin longitudinal-flexural composite mode piezoelectric ultrasonic transducer is studied. This type of transducers consists of slender metal rods and longitudinally polarized piezoelectric ceramic rings. The resonance frequency equations for the longitudinal and flexural vibrations in the transducer are derived. By correcting the length of the metal slender rods, the simultaneous resonance of the longitudinal and flexural vibrations in the transducer is acquired. The experimental results show that the measured resonance frequencies of the transducers are in good agreement with the computed ones, and the measured resonance frequencies of the longitudinal and the flexural vibrations in the composite transducers are also in good agreement with each other.     

Equivalent circuits and directivity patterns of air-coupled ultrasonic transducers

Air-coupled transducers for producing ultrasonic radiation in gases are studied. The transducer consists of a circular thin plate in flexural vibration and a sandwich longitudinal electromechanical vibrator that is attached to the center of the plate. The lowest-order axially symmetric flexural vibrational mode of a circular thin plate is analyzed. The equivalent circuits of the circular plate in flexural vibration and the compound transducer are presented and the frequency equation is derived. The radiated ultrasonic field of the circular thin plate in flexural vibration is calculated and the directivity pattern is obtained theoretically. Some transducers of this type are designed according to the frequency equation, and their resonance frequencies are measured. The measured resonance frequencies are in good agreement with the theoretical results, and the calculated radiation ultrasonic field is also in good agreement with the measured results of a previous work.     

Standing Friedel waves: a quantum probe of electronic states in nanoscale devices

We report a theoretical study of the dynamic response of electrons in a metallic nanowire or a two-dimensional electron gas under a capacitively coupled "spot gate" driven by an ac voltage. A dynamic standing Friedel wave (SFW) is formed near the spot gate and near edges and boundaries, analogous to the static Friedel oscillations near defects. The SFW wavelength is controlled by the ac voltage frequency and the device's Fermi velocity, whereby the latter can be measured. In addition, the SFW amplitude exhibits resonant behavior at driving frequencies that are related to eigenenergy spacings in the device, allowing their direct measurement.     

双泡模型共振频率的超声空化动力学研究

该研究旨在研究双泡模型的自然共振频率对超声空化的影响,通过理论计算研究了自然共振频率的影响因素,以及单频超声和双频超声与自然共振频率的关系。研究结果表明：气泡初始半径是影响自然共振频率的主要因素;低频驱动下的非线性波动程度会比高频的更加剧烈,当驱动频率等于气泡自然共振频率时,超声空化的效果更好;双频超声取气泡自然共振频率时超声空化效果远远优于单频超声驱动。该研究在超声医学和理解超声空化特性方面有着重要的意义。