Matching a transducer to water at cavitation: acoustic horn design principles

High-power ultrasound for several decades has been an integral part of many industrial processes conducted in aqueous solutions. Maximizing the transfer efficiency of the acoustic energy between electromechanical transducers and water at cavitation is crucial when designing industrial ultrasonic reactors with large active volumes. This can be achieved by matching the acoustic impedances of transducers to water at cavitation using appropriately designed ultrasonic horns. In the present work, a set of criteria characterizing the matching capabilities of ultrasonic horns is developed. It is shown that none of the commonly used tapered-shape horns can achieve the necessary conditions. An analytical method for designing five-element acoustic horns with the desirable matching properties is introduced, and five novel types of such horns, most suitable for practical applications, are proposed. An evaluation of the horns' performance is presented in a set of experiments, demonstrating the validity of the developed theoretical methodology. Power transfer efficiency increase by almost an order of magnitude is shown to be possible with the presented horn designs, as compared to those traditionally utilized.     

Scattering matrix for a junction of two horns

The asymptotic behavior of the scattering matrix for a junction of two horns is studied. Dedicated to the memory of Vladimir Borovikov     

变厚度圆板、环板振动分析的传递矩阵法*

变厚度圆板和环板是在工程设计中经常遇到的一类构件,与等厚度板相比,通过适当的沿径向厚度的变化,这种变厚度板在振动、失稳、弯曲等方面能起到更好的效果。将沿径向任意变厚度圆板、环板划分为一系列等厚度环板单元,基于Mindlin中厚板理论采用逆向推导的方式推导了其传递矩阵,建立起变厚度圆板、环板的频率方程。通过计算线性变厚度环板自由振动时的频率,并与ANSYS模态分析结果相比较,验证了计算模型的精确性。逆向推导法避免了高阶数传递矩阵推导复杂的问题,是对传递矩阵法的很好推广。     

An extension of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area

The transfer matrix method was used to analyze the acoustical properties of stepped acoustic resonator in the previous paper. The present paper extends the application of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area. The transfer matrices and the resonant conditions are derived for acoustic resonators with four different kinds of gradually varying geometric shape: tapered, trigonometric, exponential and hyperbolic. Based on the derived transfer matrices, the acoustic properties of these resonators are derived, including the resonant frequency, phase and radiation impedance. Compared with other analytical methods based on the wave equation and boundary conditions, the transfer matrix method is simple to implement and convenient for computation.     

Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media.

The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness matrix is represented analytically. It is shown that the elements of the stiffness matrix are as simple as those of the transfer matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer matrix method. The stiffness matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness matrix method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.     

TEM喇叭天线脉冲辐射特性

采用时域有限积分法（FIT）对相同几何口径尺寸下不同长度TEM喇叭天线的主轴辐射特性进行了研究,分析了有限长TEM喇叭天线与理想（无限长）TEM喇叭天线主轴辐射场存在差异的原因,导出了有限长TEM喇叭天线主轴辐射场在接近理想TEM喇叭天线辐射场条件下天线长度与激励脉冲宽度（或脉冲上升时间）之间的关系。在此基础上,根据文献中的研究结果,并结合激励脉冲波形,给出了TEM喇叭天线几何参数的优化设计方法。     

圆镜共焦腔激光横模的传输矩阵法模拟和分析

共焦腔是一般稳定腔的特例,由于等价性,共焦腔中自再现模的振幅分布、损耗和光斑尺寸常常被用于讨论一般稳定腔。为了分析具有大菲涅尔数的圆镜共焦腔,本文利用传输矩阵方法对腔模进行计算和讨论。研究结果表明:传输矩阵方法的结果与Fox-Li积分迭代法的结果一致,并且传输矩阵方法实用于大菲涅尔数共焦腔。     

Approximating the vocal tract by conical horns

The transmission-line method is studied systematically as applied to the vocal tract approximated by a sequence of conical horns. The constructed scheme describes the propagation of plane waves in conical horns, with all factors interesting in terms of acoustic theory of speech production, viz., losses, nonrigid vocal tract walls, and potential side-branches, taken into account. The derived equations are tested on a cross-sectional areas of the vocal tract measured by magnetic-resonance tomography on a real speaker.     

夹心式压电超声换能器串并联传输矩阵设计法

将压电环片等效为一有源六端网络,考虑预应力螺栓对系统建模的影响,并将其等效为一机械四端网络,基于串并联传输矩阵法,建立了Langevin换能器的总体网络模型,导出其总传输矩阵,进而推算出换能器的共振频率。结果显示该方法比普遍采用的Langevin换能器传输矩阵设计法有更高的参量计算精度。此方法也为分析换能器其它电学参数提供了方便。     

Raman and surface‐enhanced Raman spectroscopy on horns and their correlation with biomechanical properties

Recently horns are considered as potential candidates for various biomedical applications because of their distinct biomechanical properties. We therefore performed Raman spectral analysis and mechanical test on the horns of buffalo, cattle and sheep to obtain information about the molecular compositions in various parts of the horns and their correlation with biomechanical properties. We also developed a surface enhanced Raman spectroscopy (SERS) to trace their degradation products. We found that various parts of the horns have similar overall molecular compositions, but have differences in the bands of C–C–S–S–C–C conformation, α‐helix and β‐sheet conformation, especially in the bands of 507–515 cm⁻¹ which reflect the relative sulfur content and the structural conformation of the disulfide linkages. The Raman intensities at the region are highly correlated with the Young's modulus and tensile strength of the horns, indicating that the biomechanical properties of the horns are mainly determined by their disulfide bonds. It also suggests that Raman spectroscopy has the potential to perform non‐destructive detection on the mechanical strength of horns. The SERS measurements verified that the main constituents of the degradation products from both the buffalo and sheep horns were amino acids and polypeptides, suggesting that the horns are suitable candidates for biomaterial scaffolds. Copyright © 2016 John Wiley & Sons, Ltd.     

Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method

Branched pipes of arbitrary shapes are prevalent in pipe systems. Considering fluid–structure interaction (FSI), an absorbing transfer matrix method in frequency domain for fluid-filled pipelines with any branched pipes is proposed in this paper. A dominant chain of pipeline would be selected, and the point transfer matrix of each junction on the dominant chain would be determined. Here, the point transfer matrix, representing the influence of branched pipes at the junction on the dominant pipeline, was “absorbed” by the dominant chain. Based on these, with transfer matrixes of other elements, the fluid and structure dynamics problem could be solved following the chain transfer matrix method process.     

The performance and design of ultrasonic vibration system for flexural mode

The matrix method for analyzing flexural vibration system is outlined. The displacement, stress and velocity gain of ultrasonic flexural vibration systems are investigated by transfer matrix method. A design method is given for flexural transducer and vibration system.     

激光模场传递矩阵分析方法的精度控制

讨论激光模场的传递矩阵分析法,并对计算精度进行控制.结果表明,传递矩阵分析方法与传统的积分数值迭代法计算结果一致,只要合理控制计算精度,可以解决积分数值迭代法难于收敛的问题,满足激光谐振腔模场分析的实际要求.     

Solution of the H-plane problem of radiation from a two-dimensional horn with a complex piecewise linear contour

Conclusions The method presented here is highly algorithmic and permits computerizing the calculation of the characteristics of two-dimensional H-phane horns with piecewise linear contours within a broad range of geometrical parameters. The resultant program can be used for analyzing and selecting the optimal geometry of specific radiative assemblies.The data derived in the analysis of the radiation and matching characteristics of thickwalled sectorial horns and of box horns will be useful in the design of antenna assemblies.Zaporozhe Mechanical Engineering Institute. Translated from Izvestiya Vysshikh Uchebnikh Zavedenii, Radiofizika, Vol. 33, No. 5, pp. 604–610, May, 1990.     

Acoustic particle velocity horns

The paper considers receiving acoustic horns designed for particle velocity amplification and suitable for use in vector sensing applications. Unlike conventional horns, designed for acoustic pressure amplification, acoustic velocity horns (AVHs) deliver significant velocity amplification even when the overall size of the horn is much less than an acoustic wavelength. An AVH requires an open-ended configuration, as compared to pressure horns which are terminated at the throat. The appropriate formulation, based on Webster's one-dimensional horn equation, is derived and analyzed for single conical and exponential horns as well as for double-horn configurations. Predicted horn amplification factors (ratio of mouth-to-throat radii) were verified using numerical modeling. It is shown that three independent geometrical parameters principally control a horn's performance: length l, throat radius R(1), and flare rate. Below a predicted resonance region, velocity amplification is practically independent of frequency. Acoustic velocity horns are naturally directional, providing maximum velocity amplification along the boresight.     

Free vibration of non-circular cylindrical shells with longitudinal interior partitions

An analysis is presented for the free vibration of a simply supported non-circular cylindrical shell with longitudinal interior partitions. For this purpose, the governing equations of vibration of a non-circular cylindrical shell including a plate as special case are written in a matrix differential equation by using the transfer matrix in the circumferential direction. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrix of the shell and the point matrix at the joint of the structure matrix. The method is applied to approximately elliptical cylindrical shells with an interior plate, and the natural frequencies and the mode shapes of vibration are calculated numerically, giving the results.     

Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid-structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid-structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.     

光子晶体理论应用于取样光纤光栅的研究

将取样光纤光栅近似为引入多个有规律的大尺寸缺陷的一维二元光子晶体,运用光子晶体传输矩阵理论分析了其长度L、周期LA、折射率调制量δneff和采样率p等参量对其反射谱的影响规律,并将所得结果与用取样光纤光栅传输矩阵法计算所得结果进行了比较,得出了用光子晶体理论分析与用传统的模耦合理论分析相吻合的特性。在分析取样光纤光栅的其它性质以及将其应用于实际时都可借鉴此理论,以达到工程实际应用的最佳效果。     

Calculation of electromechanical coupling coefficient of Lamb waves in multilayered plates

Two methods have been always used to calculate the electromechanical coupling coefficient of a Lamb wave in a multilayered plate: one is an approximate method using the acoustic velocity difference under different electric boundary conditions and the other is the Green's function method. The Green's function method is more accurate but more complicated, because an 8N-order matrix is used for calculating the electromechanical coupling coefficient of the Lamb wave in an N-layered plate, which induces great computation loads and some calculation deviations. In this paper, a transfer matrix method is used for calculating the electromechanical coupling coefficient of Lamb waves in a multilayered plate, in which only an 8-order matrix is needed regardless of the number of layers of the plate. The results show that the transfer matrix method can obtain the same accuracy as those by the Green's function method, but the computation load and deviation are greatly decreased by avoiding the use of a high order matrix used in the Green's function method.     

Free vibration of non-circular cylindrical shells with variable circumferential profile

An analysis is presented of the free vibration of non-circular cylindrical shells with a variable circumferential profile expressed as an arbitrary function. The applicability of thin-shell theory is assumed and the governing equations of vibration of a non-circular cylindrical shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the transfer matrix has been determined by numerical integration of the matrix equation, the natural frequencies and mode shapes of vibration are calculated numerically in terms of the matrix elements. The method is applied to cylindrical shells of three or four-lobed cross-section, and the effects of the length of the shell and the radius at the lobed corners on the vibration are studied.