狭缝式环形超声聚能器的径向振动特性

对一种狭缝式环形超声聚能器的径向振动特性进行了研究。基于机电类比原理,通过引入面积比系数,推出了聚能器的径向振动机电等效电路及频率方程;得出了其径向位移振幅放大系数表达式。通过数值计算,探讨了聚能器第1、2阶径向共振频率及振幅放大系数与其半径比的关系;分析了狭缝长度、角度及数目对聚能器振幅放大系数及共振频率的影响,并进行了有限元仿真。研究表明,聚能器的振幅放大系数随其半径比的变化存在极大值,并随狭缝数量、长度及宽度增加而增大;而其径向共振频率则随三者的增加而减小,理论与有限元仿真及实验结果符合较好。      

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。      

Study on the step-type circular ring ultrasonic concentrator in radial vibration

In this paper, the plane radial vibration of an isotropic metal thin circular rings is studied and its equivalent circuit model is obtained. Based on the equivalent circuit model, the step-type circular ring concentrator consisting of two metal thin circular rings in radial vibration is analyzed. Its compound equivalent circuit is derived and the resonance frequency equation is obtained. The relationship between the resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions is analyzed. The resonance frequency of the step-type radial concentrator is calculated based on the resonance frequency equation. For comparison, the resonance frequency of the step-type radial concentrator is also obtained by using numerical method. It is illustrated that the resonance frequencies from these two methods are in a good agreement with each other.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

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。     

Existence of axisymmetric modes of thin cylindrical shells with axial displacement restraint

A necessary and sufficient condition is derived for the existence of the axisymmetric mode of cylindrical shells with a radial displacement having one half wave along the axis and axial displacement restrained at both ends. The condition is purely geometric and consists of an upper bound on the mean radius to thickness ratio for a given fixed value of the length to mean radius ratio, above which the mode with one half wave in radial displacement along the axis ceases to exist. The proof is based on enforcing two basic lemmas concerned with the simplicity of the eigenvalues of the shell and the uniform ordering of these eigenvalues with the number of nodes of their corresponding radial displacement eigenfunctions.     

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.     

Observation of long-distance radial correlation in toroidal plasma turbulence

This Letter presents the discovery of macroscale electron temperature fluctuations with a long radial correlation length comparable to the plasma minor radius in a toroidal plasma. Their spatiotemporal structure is characterized by a low frequency of ～1-3 kHz, ballistic radial propagation, a poloidal or toroidal mode number of m/n=1/1 (or 2/1), and an amplitude of ～2% at maximum. Nonlinear coupling between the long-range fluctuations and the microscopic fluctuations is identified. A change of the amplitude of the long-range fluctuation is transmitted across the plasma radius at the velocity which is of the order of the drift velocity.     

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。      

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。      

光声池径向共振模式耦合系数理论分析

光声光谱法是基于红外吸收光谱原理的一种高灵敏度的微量气体探测技术。它使用声共振腔来实现微弱声信号的共振放大。通过调节激光的调制频率,当它等于腔的某个共振频率时,在腔内形成声驻波,而腔本身的作用相当于一声放大器。共振腔的放大作用取决于当前被激活的共振模式、腔的品质因素、声传感器的状态以及电磁辐射与腔共振模式的耦合作用。值得关注的是,红外激光相对于声共振腔的入射方位不同则激励产生的光声信号幅值也不同。采用理论推导与数值计算相结合的方法,以圆柱形光声池为例,研究了径向共振模式下耦合系数受激光入射方位的影响。研究表明,激光入射角在0～π/2范围变化时耦合系数存在2个零点和2个极大值：入射角为0或tan-1(0.859 2×2R/L)时,耦合系数为零而径向共振失效;入射角为tan-1(0.556 8×2R/L)或tan-1(2R/L)时,耦合系数极大而径向共振最强。此处R为池径而L为池长。结果可用于指导光声池结构优化设计与安装调试,增强光声法检测微量气体的信号幅值,提高检测灵敏度。     

Radial vibration and ultrasonic field of a long tubular ultrasonic radiator

The radial vibration of a metal long circular tube is studied analytically and its electro-mechanical equivalent circuit is obtained. Based on the equivalent circuit, the radial resonance frequency equation is derived. The theoretical relationship between the radial resonance frequency and the geometrical dimensions is studied. Finite element method is used to simulate the radial vibration and the radiated ultrasonic field and the results are compared with those from the analytical method. It is concluded that the radial resonance frequency for a solid metal rod is larger than that for a metal tube with the same outer radius. The radial resonance frequencies from the analytical method are in good agreement with those from the numerical method. Based on the acoustic field analysis, it is concluded that the long metal tube with small wall thickness is superior to that with large wall thickness in producing radial vibration and ultrasonic radiation. Therefore, it is expected to be used as an effective radial ultrasonic radiator in ultrasonic sewage treatment, ultrasonic antiscale and descaling and other ultrasonic liquid handling applications.     

径向三腔渡越时间振荡器高频特性分析

 研究了径向三腔渡越时间振荡器的高频特性,提出了一种近似求解方法,获得了各模式的频率以及场分布特性,并进行了数值模拟验证。近似求解所得的谐振模式的频率与数值模拟的结果基本一致,而模式场的振幅有误差。对近似方法进行了误差分析,结果表明:场振幅的误差随谐振腔径向长度与平均半径之比的减小而减小,该比值小于0.3时,场振幅的相对误差小于5.4%,比值大于1时,该方法不适用。     

Dispersion behavior of electromagnetic wave near the resonance in 1D magnetized ferrite photonic crystals

In the present article, we have analyzed the dispersion of electromagnetic wave in the one dimensional magnetized ferrite photonic crystals near the resonance in the permeability of the constituent materials for transverse magnetization in the transverse electric mode. The dispersion relation is obtained by transfer matrix method. It is observed that in the vicinity of resonant frequency, large numbers of oscillations occur in the normalized Bloch wave number. These oscillations in the Bloch wave number are strongly dependent on external magnetic fields, filling factor, and damping constant. The frequency regime of these oscillations is found to be shifted in higher frequency range with increase in the magnitude of the magnetic fields. With increase in the filling factor keeping length of periods fixed, number of oscillations is found to be increased. Near the resonance, effect of incident angle is negligible. It is demonstrated that these nearly equidistant oscillations occurring in the vicinity of resonance may be used for making filter in micro wave frequency range.     

粗细端等长阶梯形变幅杆的有限元分析

本文利用有限元分析软件ANSYS研究了一组粗细端截面积比不同的阶梯形变幅杆，得出了每个变幅杆的第一阶和第三阶谐振频率、粗细端分界面的相对位移和振幅放大系数。结果表明：ANSYS仿真值与实测值的平均偏差仅为0．3％，远小于常用式解析值与实测值的偏差；变幅杆粗细端分界面的运动类似受牵引的薄膜运动；而振幅放大系数与面积比成正比的结论可扩展到粗细端截面积比为100的情况。     

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.     

水平均质表面上液滴聚合过程的可视化实验研究

对水平均匀表面上液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和液滴物性等参数对液滴聚合过程中液滴液桥半径和接触角变化特性的影响规律。实验结果表明:液滴聚合中液桥半径和接触角都呈衰减振荡变化; 聚合前液滴半径越小,液桥半径振荡频率越大,振幅越小,振荡时间越短;液滴的粘度越大,液桥半径的振荡频率越小, 振幅越小,振荡时间越短;液滴聚合前的接触角明显大于聚合液滴静止后的接触角,其差值与固体界面状况和气、固、液物性相关。     

Exact Vibration Solutions of Nonhomogeneous Circular,Annular and Sector Membranes

In this paper, exact vibration frequencies of circular, annular and sector membranes with a radial power law density are presented for the first time. It is found that in general, the sequence of modes may not correspond to increasing azimuthal mode number $n$. The normalized frequency increases with the absolute value of the power index $|ν|$. For a circular membrane, the fundamental frequency occurs at $n = 0$ where $n$ is the number of nodal diameters. For an annular membrane, the frequency increases with respect to the inner radius $b$. When $b$ is close to one, the width $1 − b$ is the dominant factor and the differences in frequencies are small. For a sector membrane, $n − 1$ is the number of internal radial nodes and the fundamental frequency occurs at $n = 1$. Increased opening angle $β$ increases the frequency.     

Vibrated sessile drops: Transition between pinned and mobile contact line oscillations

We study the effects of vertical vibrations on non-wetting large water sessile drops flattened by gravity. The solid substrate is characterized by a finite contact angle hysteresis (10-15 degrees). By varying the frequency and the amplitude of the vertical displacement, we observe two types of oscillations. At low amplitude, the contact line remains pinned and the drop presents eigen modes at different resonance frequencies. At higher amplitude, the contact line moves: it remains circular but its radius oscillates at the excitation frequency. The transition between these two regimes arises when the variations of contact angle exceed the contact angle hysteresis. We interpret different features of these oscillations, such as the decrease of the resonance frequencies at larger vibration amplitudes. The hysteresis acts as solid friction on the contour oscillations, and gives rise to a stick-slip regime at intermediate amplitude.Received: 4 April 2004, Published online: 10 August 2004PACS: 47.55.Dz Drops and bubbles - 68.08.Bc Wetting - 47.35. + i Hydrodynamic waves     

声场作用下两空化泡相互作用的研究

建立了声场作用下两空化泡泡壁的运动方程,得出了双空化泡的共振频率,振动半径及空化噪声声压．由频率方程,振动半径和声压方程可以看出两气泡的运动情况与单气泡的运动情况有着明显的不同．共振频率,共振振幅及声压与两气泡之间的间距有关．在一定的简化条件下,运用MATLAB语言对共振频率,共振振幅及空化噪声声压进行了数值求解,发现共振频率和共振振幅随空泡间距的增大而增大,空化噪声声压随距离增大先增大后减小． 关键词： 超声 空化 频率 声压