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.     

环形ZnO薄膜谐振器的横模抑制与测试分析

采用Tiersten方程研究了环形ZnO薄膜谐振器中横模寄生问题, 获得了环(圆)形薄膜谐振器的横模振动方程, 求得横模位移场解和频率色散方程; 然后采用电磁学模式合成理论进行分析, 发现环形薄膜谐振器横模频率与环形电极的内外径之比a/b有关, 振动模式可由圆形薄膜谐振器横模模式合成得到, 通过控制a/b能够抑制横模模式数和调控基膜频率. 采用外差激光干涉仪和网络矢量分析仪测量并比较了同批次的圆形和环形薄膜谐振器的上电极横模振动图样和电阻抗曲线. 振动图样显示环形薄膜谐振器振动模式可由半径为a和半径为b的圆形薄膜谐振器振动模式合成, 仅存在节圆数大于0的横模振动, 等于0的横模模式被抑制; 电阻抗曲线显示当a/b为0.436时, 环形薄膜谐振器的基频(约1217 MHz)和圆形的(0, 1)模式频率相等. 测量数据验证了模式合成理论的分析结果正确性, 为薄膜谐振器的横模抑制研究提供了理论基础和新方法.     

Elastic guided wave propagation in a periodic array of multi-layered piezoelectric plates with finite cross-sections

In this study, we present a model study of guided wave dispersion and resonance behavior of an array of piezoelectric plates with arbitrary cross-sections. The objective of this work is to analyze the influence of the geometry of an element of a 1D-array ultrasound transducer on generating multi-resonance frequency so as to increase the frequency bandwidth of the transducers. A semi-analytical finite-element (SAFE) method is used to model guided wave propagation in multi-layered 1D-array ultrasound transducers. Each element of the array is composed of LiNbO₃ piezoelectric material with rectangular or subdiced cross-section. Four-node bilinear finite-elements have been used to discretize the cross-section of the transducer. Dispersion curves showing the dependence of phase and group velocities on the frequency, and mode shapes of propagating modes were obtained for different geometry consurations. A parametric analysis was carried out to determine the effect of the aspect ratio, subdicing, inversion layer and matching layers on the vibrational behavior of 1D-array ultrasound transducers. It was found that the geometry with subdiced cross-section causes more vibration modes compared with the rectangular section. Modal analysis showed that the additional modes correspond to lateral modes of the piezoelectric subdiced section. In addition, some modes have strong normal displacements, which may influence the bandwidth and the pressure field in front of the transducer. In addition, the dispersion curves reveal strong coupling between waveguide modes due to the anisotropy of the piezoelectric crystal. The effect of the matching layers was to cluster extensional and flexural modes within a certain frequency range. Finally, inversion layer is found to have a minor effect on the dispersion curves. This analysis may provide a means to analyze and understand the dynamic response of 1D-array ultrasound transducers.     

Coupled whispering gallery modes in a multilayer-coated microsphere

Whispering gallery modes in a microsphere coated with three layers of high, low, and high refractive indices (RIs) are considered. Coastal modes and inland modes, centered on the outer and inner high-RI layers, exist as different radial modes. At right values of RI and thickness of the three layers, an inland mode and a coastal mode couple to produce a radial distribution of the photonic field that resembles bonding and antibonding orbitals. The coupling occurs across a layer of the middle low-RI layer, much thicker than the wavelength of light. The coupling is analyzed in a quantum-mechanical analog of a one-dimensional particle in a double-well potential.     

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。      

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。      

Thermoelastic damping in thin microrings with two-dimensional heat conduction

Accurate determination of thermoelastic damping (TED) is very challenging in the design of micro-resonators. Microrings are widely used in many micro-resonators. In the past, to model the TED effect on the microrings, some analytical models have been developed. However, in the previous works, the heat conduction within the microring is modeled by using the one-dimensional approach. The governing equation for heat conduction is solved only for the one-dimensional heat conduction along the radial thickness of the microring. This paper presents a simple analytical model for TED in microrings. The two-dimensional heat conduction over the thermoelastic temperature gradients along the radial thickness and the circumferential direction are considered in the present model. A two-dimensional heat conduction equation is developed. The solution of the equation is represented by the product of an assumed sine series along the radial thickness and an assumed trigonometric series along the circumferential direction. The analytical results obtained by the present 2-D model show a good agreement with the numerical (FEM) results. The limitations of the previous 1-D model are assessed.     

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。     

夹心式径向复合压电超声换能器

对夹心式径向复合压电换能器径向振动特性进行了研究。该换能器由弹性内芯、预应力金属管及柱面压电陶瓷晶堆径向复合而成.利用机电类比法,得到了换能器的径向振动等效电路及频率方程。探讨了换能器第1、2阶径向共振频率及有效机电耦合系数与其几何尺寸的关系。研究表明,换能器第1阶径向共振频率随其内芯内径及预应力管壁厚度增大而降低;第2阶共振频率随内芯内径增大存在极小值,但随预应力管壁厚度增大单调下降。此外,采用第2阶径向共振模式能获得较高的有效机电耦合系数,并且压电陶瓷处于位移节线时,换能器有效机电耦合系数达极大值。对换能器共振频率的测试与有限元仿真表明。理论与实验及仿真结果符合较好。      

Further studies on thickness vibrations of piezoelectric plate excited by parallel field

I.IntroductionThcthickncssvibrationsofahomogeneous-anisotropicpiezoclectriccrystalplatewithanexcitingficldparallcltothemajorsurfacesofthep1ate,andalsototheplanewavefront(calledasthepara11e1fic1dcxcitatloninbricO,havebccnana1yzedI'1.Theprimarybehaviourofthick-nessvibrationshasbecnobtaincdasthepIatewitharbitraryorientationisexcitedbythepara11elfield.Inthispapcr,wcwillgofurthcrtogivcancwformu1aofthemechanicalresonantfrequen-cyequation.ILqformisthesameasthercsonantequationofthepuremodeandiseasyt…     

Free localized vibrations of a semi-infinite cylindrical shell

Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff-Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Radial vibrations of eccentric rings

The radial extensional and inextensional modes of vibration of an eccentric circular ring with a rectangular cross section have been studied by perturbation calculations and by measurements on five rings with various eccentricities. In agreement with the theory, only the k = 1 extensional mode was markedly non-degenerate. Formulae for calculating the frequencies are given.     

爆磁压缩发生器的爆炸管动力学效应

 对爆磁压缩发生器中爆炸管2维动力学简化模型进行了模拟计算,分析表明：径向膨胀速度会随径向位置（或者时间）的变化而变化,因此膨胀角也会随径向位置（或者时间）发生变化。对各时间点（或位置点）处的膨胀速度进行了平均,求得理论上的平均膨胀速度,再将该平均膨胀速度与实验测量值进行了比较。模拟结果给出了径向膨胀速度受到端头效应影响的情况,这可为改进实验结果提供参考。由于径向速度与轴向速度的比值一般在5以上,用作爆炸管的物质质量越大,这一比值就越大,因此选择密度较大的金属材料作为爆炸管,可减少滑移。应用2D简化模型计算出的膨胀角数值,与Gurney模型以及1D模型进行了比较,它们之间的差别可能主要来自2D效应。     

The coupling between the radial and thickness vibration of the circular resonator

The paper studies the resonant frequency dependence of radial vibration on the ratio of resonator dimensions. It was found that Rayleigh's correction does not explain the decrease of resonant frequency. This phenomenon was explained quite successfully by coupling between the radial and thickness vibrations of the plate. The calculated curves correspond very well with the measured results. Ceramic resonators manufactured from ceramics based on PbZrO₃-PbTiO₃ were used for these measurements.     

Suppression of radiative losses of surface polaritons on nanostructured thin metal films

The strong electromagnetic coupling between surface plasmon polariton modes on opposite interfaces of a finite thickness periodically nanostructured metal film has been studied. Surface polariton dispersion and associated electromagnetic field distributions have been analyzed. It was shown that at a frequency that corresponds to the crossing of film Bloch modes of different symmetries, the radiative losses of surface polaritons that are related to the polaritons' coupling to light during propagation on the structured surface are suppressed.     

Frequency separation of surface acoustic waves in layered structures with acoustic metamaterials

We show theoretically that in elastic layered structures containing an upper layer of smoothly varied thickness and a substrate of a highly dispersive metametarial it is possible to significantly enhance spatial frequency separation of surface acoustic waves. Theory of Love surface acoustic waves propagation in waveguides with varied thickness, taking into account mutual modes coupling, is built. Appropriate structure of metamatererial with resonant frequency dependence of material parameters, making frequency separation effective, is provided. Efficiency of spatial frequency separation and modes coupling is calculated for various metamaterial parameters and wave frequencies.     

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.     

COINCIDENCE OF THERMOELASTIC AND THERMOVISCOUS ACOUSTIC WAVES IN FLUID-FILLED ELASTIC TUBES

Thermoelastic and thermoviscous acoustic wave propagation in fluid-filled steel tubes is studied using the exact three-dimensional (3-D) fluid-elastic coupled system equations for the vibration in the n=0 and 1 circumferential modes. Water- and air-filled tubes are examined. The water-filled steel tube shows a strong fluid-elastic coupling effect in the lower frequency range and the air-filled tube shows a strong thermal effect for all frequencies. An 88·9 mm outer diameter tube with 3·05 mm wall thickness is used for the study. Due to the fluid-elastic coupling introduced for air having a specific heat ratio of 1·4 (the solution uncouples when the ratio is 1·0), thermal effects are seen to be very important with the modal attenuation rate being at least 32% underestimated if the thermal effect is not included in the air-steel system. A coincidence phenomenon is accurately found directly from the coupled modes in the fluid-elastic coupled system. When coincidence occurs, the axial modal attenuation rate drops sharply, allowing the exact determination of the coincidence frequency by locating the local minimum of the modal spatial attenuation rate with increasing frequency. In the water-steel system, the coincidence frequency is seen to be 8% in error if methods are employed using the uncoupled theory for the separate fluid and elastic wall.     

Numerical studies of surface and bulk modes in attenuated total reflection spectra

The dispersion relations of normal modes in the layered constructions are studied. In the frequency region with negative permittivity, we investigate the normal modes near the air--metal and the air--matematerial interfaces and compare them. An extra bulk mode appearing in a pass band of two media is found near the air--matematerial interface, which is different from the air--metal case. Moreover, the bulk mode will be further proved by the attenuated total reflection (ATR) technique, in which the coupling between the incident electromagnetic waves and the normal modes is studied. For p-polarized incident waves, the ATR spectra based on the Otto and the Kretschmann configurations are obtained numerically, where the dips present the excitations of the surface and bulk modes. Furthermore, we also discuss the influences of the middle layer thickness, the incident angle and the damping term on the reflection in detail. It is found that the coupling frequencies and the maximum strength are strongly dependent on the above media parameters.