基于传输矩阵法的任意变厚度环型压电超声换能器

变厚度环型径向振动压电超声换能器可以实现阻抗变换、能量集中,具有辐射面积大、全指向性等优点,在功率超声、水声等领域被广泛应用.由于求解复杂变厚度金属圆环径向振动的波动方程比较困难,本文使用传输矩阵法将变厚度金属圆环的径向振动转化为N个等厚度金属圆环径向振动的叠加,得到了任意变厚度金属薄圆环径向振动的等效电路图、共振频率方程和位移放大系数表达式,分析了锥型、幂函数型、指数型、悬链线型金属圆环的位移放大系数与几何尺寸的关系.在此基础上,推导了由任意变厚度金属圆环和等厚度压电圆环复合而成的压电超声换能器径向振动的等效电路和共振频率方程.为了验证理论结果的正确性,使用有限元软件进行仿真,所得一阶、二阶的共振频率和位移放大系数的数值解与理论解符合较好.本研究给出了任意变厚度金属圆环径向振动的普适解,为设计和优化径向压电超声换能器提供了理论指导.     

大尺寸夹心式压电超声换能器的设计

现有的夹心式压电超声换能器的设计方法多从一维理论出发，它对横向尺寸较大的换能器并不适用．本文研究了大尺寸夹心换能错的铝合振动，通过引人振动体的等效弹性系数，推出了换能器的耦合振动频率方程，并给出了换能器纵向共振频率的设计准则．与数值法相比，本方法计算非常简单．与一维理论的计算结果相比，利用本文理论得出的换能器的纵向共报频率与实测值更加符合．     

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。     

夹心式压电换能器频率方程的矩阵表示

本文从夹心式压电换能器的等效线路出发,得出了整体频率方程的矩阵表示式,为夹心式压电换能器的优化设计提供了一定的理论基础及研究途径。     

四激励二维正交复合夹心式压电超声换能器的设计

提出了一种四激励二维正交复合夹心式压电超声换能器,换能器由四组纵向极化压电陶瓷晶堆、一个中心耦合金属块和四个外部金属圆锥组成。基于二维耦合振动机理和机电类比原理,建立了换能器的等效电路模型并推导了其谐振频率方程。利用有限元软件仿真分析了四激励正交复合换能器的频响特性和振动特性,并与其单独一个方向振子的振动特性进行了对比。加工了反相和同相模态的换能器,利用阻抗分析仪和激光测振仪测试了其频率响应和二维四向纵振动输出特性,并进行了大功率二维四向超声乳化实验测试。理论、仿真和实验结果表明:换能器具有反相和同相两个纵向正交共振模态,在这两种共振模态下均可实现二维四向纵振动输出,且换能器两个正交方向振子的纵向振动具有相互耦合加强的作用;等效电路法和有限元法所得换能器的共振频率和有效机电耦合系数与实验测试结果吻合,通过与单激励正交复合夹心式压电超声换能器的有效机电耦合系数对比,发现该换能器具有更高的有效机电耦合系数。     

压电换能器数字模型软件包

最近美国NTR系统公司(NTR System Inc.,1902 North 34th Street,Seattle,WA 98103,USA)推出了一个压电换能器数字模型软件包,PiezoCAD。这个软件包用传输矩阵法计算换能器的整体特性。用户可以从软件包里的数据库选择压电材料的参数。这个数据库里有陶瓷、晶体、聚合物和复合材料的板、条、棒的大量参数。用户可以规定多层匹配层、多层背衬层和负载的特性。在电端可以规定各种电匹配网络,包括电阻、电容、电感、变压器和同轴电缆的串联、并联及各种组合。用T型网络表示的非理想变压器也包括在     

夹心式纵-扭复合模式压电超声换能器的共振频率

本文对夹心式纵－扭复合振动模式压电超声换能进行了研究，从换能器的等效电路出发，在无耦合时，得出换热能器纵向振动模式及扭转振动模式的各自共振频率方程，实验表明，换能器各自共振频率的测试值与理论计算值基本符合。     

夹心式纵-扭复合模式压电超声换能器的共振频率

本文对夹心式纵-扭复合振动模式压电超声换能器进行了研究．从换能器的等效电路出发，在无耦合时，得出了换能器中纵向振动模式及扭转振动模式的各自共振频率方程．实验表明，换能器各自共振频率的测试值与理论计算值基本符合．     

夹心式压电换能器的谐振频率跟踪方案设计

分析了夹心式压电换能器的阻抗特性,讨论了基于相位方式的现有跟踪方案的不足,提出了一种新的频率跟踪方案,介绍了实现该方案的电路系统。该方案的特点是:采用先扫频后跟踪的策略,解决了频率范围设定难的问题;增加解锁控制,使得系统在死锁或误跟踪时自动回到频率搜索状态;采用直接数字合成器(DDS)作为频率调整和信号产生的器件,实现了全数字系统,调整方便,精度高;采用复杂可编程逻辑器件(CPLD)做相位比较和DDS控制,使频率跟踪速度快,并且跟踪精度和速度均可控制。     

超声扭振系统的四端网络设计法

本文将组成超声扭振系统的每一部件都等效为一机械四端网络，将所得的各网络矩阵相乘。得到系统的等效网络矩阵．由此求出该系统的谐振频率或指定频率的某一设计尺寸以及角位移放大系数，方便了设计和计算．文中给出了计算实例，其结果与实际情况吻合得较好．     

用传递矩阵法预测单层或多层微孔板的吸声性能

提出用实验测得含不同孔径孔的微孔板声阻抗率来预测由其形成的单层或多层微孔板的吸声特性，并用传递矩阵法来预测该微孔板的各种组合结构的整体吸声性能。采用该方法获得的微孔板吸声性能曲线与实测结果相当接近，能较好地预测各种组合微孔板的吸声性能。表明传递矩阵法是预测较复杂形式微孔板结构吸声性能的一种有效的方法。     

The transfer matrix: A geometrical perspective

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical resonators. In all these cases, the transfer matrix has the same algebraic properties as the Lorentz group in a (2+1)-dimensional spacetime, as well as the group of unimodular real matrices underlying the structure of the abcd$abcd$ law, which explains many subtle details. We elaborate on the geometrical interpretation of the transfer-matrix action as a mapping on the unit disk and apply a simple trace criterion to classify the systems into three types with very different geometrical and physical properties. This approach is applied to some practical examples and, in particular, an alternative framework to deal with periodic (and quasiperiodic) systems is proposed.     

Coupling transfer matrix method to finite element method for analyzing the acoustics of complex hollow body networks

This paper exposes a procedure to couple multiport transfer matrices to finite elements for analyzing the acoustics of automotive hollow body networks with a minimum of memory requirements and computational time. Generally, hollow body networks are made up from a series of elongated fluid partitions similar to ducts or waveguides. These fluid partitions generally contain complex elements: junctions, noise control elements, and cavities. The location and type of these elements in the network, mainly the noise control elements (e.g., sealing parts), may impact the noise inside a car. In the proposed hybrid method, the elongated fluid partitions are modeled with fluid finite elements. All complexities are modeled with two-port or multiport transfer matrices. The coupling of these matrices to finite elements is naturally done at the weak integral formulation stage of the acoustical problem. The coupling does not add any degrees of freedom to, nor modify, the original finite element matrix system. Consequently, changing locations and types of noise control elements in the hollow body network is fast and does not require rebuilding the finite element system. This enables optimizing the acoustics of a complex network on a desktop computer. The hybrid method is compared to experimental results on a tee-shaped hollow body networks. Good correlations are obtained.     

Sound transmission in multilayered structures – Introducing finite structural connections in the transfer matrix method

The transfer matrix technique is an efficient tool for calculating sound transmission through multilayered structures. Recent developments, as to the calculation of the sound reduction index, have given better fit to measurement data, e.g. due to the simulation of finite size samples by the spatial windowing technique. In practice, however, finite size structural connections (points or lines) normally do exist between leaves in wall constructions and these are not “natural” elements in the transfer matrix method. The paper describes a simple method to account for the effect of point- and line-connections in double-leaf constructions in a transfer matrix setup. To cover the frequency range above the critical frequency of the constituent plates, some new developments as to the forced radiation from plates were needed. Predicted results compare favorably with measurement results for a number of different cases, also including a heavy wall.     

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

多层介质的转移矩阵及其在声子晶体中的应用

引入四维波矢的概念,推导出弹性波斜入射到多层介质系统时的转移矩阵以及透射系数和反射系数。利用这些公式计算了纵波和横波正入射到一维掺杂声子晶体时纵波和横波的透射系数。得出:当纵波正入射时,透射波中纵波在一定频率范围内出现了禁带,并且在禁带的中心频率处出现了缺陷模。当横波正入射时也有相同的结果。     

Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.     

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech$^{2}$ barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 \wx{Quantum Mechanics (Non-relativistic Theory)}{} (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.     

Preproduction prediction of the optical normalized reflectance transient of MOVPE-grown AlGaAs films using transfer matrix method

This paper reported on the prediction and analysis of the optical normalized reflectance (NR) transient of AlGaAs multi layers and Distributed Bragg Reflector (DBR) using transfer matrix method (TMM). The simulation result correlated well with the measured NR transient of grown samples. Deviations of Al_xGa_1?xAs composition between the expected and real grown sample were predicted successfully. Smaller optical oscillation amplitude in the first DBR layer was predicted and could be used as an indication of Al composition. Special characteristics of NR transient within the first three pairs of DBR were also clarified using the calculated transmissivity changing with the growth thickness. TMM simulation of NR transient was thus shown to be a convenient and reliable pre-production technique, also not restricted to the AlGaAs material.