A scale mixer model for sis waveguide receivers

We report results from measurements of a scale mixer model, built to investigate the embedding impedance presented to a superconductor-insulator-superconductor (SIS) tunnel junction detector in a full height waveguide with two tuning elements. The embedding impedance is measured as a function of junction position across the waveguide channel. The results are compared to i) computer simulations of the embedding impedance using waveguide theory, ii) a lumped element circuit derived from the theory, iii) an SIS receiver operating between 200 and 280 GHz.     

Hand-arm vibration part III: A distributed parameter dynamic model of the human hand-arm system

An anatomically analogous distributed parameter dynamic model of the human arm is proposed and quantitatively validated. Distributed mass and stiffness parameters have been obtained by representing each long bone of the arm as a flexural beam. A distributed damping parameter was introduced by allowing the beam stiffness to be a complex quantity. Hand properties were modelled as a lumped parameter damped spring-mass system. Mechanical driving point impedance techniques were used to verify the model. A dual beam model of the forearm was first proposed, and its frequency response was compared with impedance data collected on the forearm. After having established the validity of the forearm model, it was then extended to include the upper arm. The frequency response of the whole-arm model was then compared with impedance data on the whole arm collected by a previous investigator. It is concluded that the beam model of the human arm adequately represented its dynamic behavior as measured by mechanical driving point impedance techniques. The amount of information concerning the dynamic behavior of the arm yielded by the distributed parameter model is found to be vastly greater than that yielded by lumped parameter models.     

Improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme

New approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments. Specifically, the exact eigendata, i.e., the exact natural frequencies and mode shapes, of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration. This is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions. Once the updated matrices for the linear structure are found, the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. Numerical experiments show that for the same number of elements, the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model. Alternatively, the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model.     

基于集总元件的低频宽带超材料吸波体设计与实验研究

提出一种基于集总元件的超材料吸波体结构设计, 并进行了理论分析和实验验证. 仿真结果表明, 该吸波体在2.5 GHz到4.46 GHz的低频带内具有吸收率超过95%、半高宽达到70.4%的良好吸收特性. 反演计算得到的等效输入阻抗表明集总元件的加入可以使该结构在较宽的频率范围内有较好的阻抗匹配特性, 介质表面能量损耗分布的模拟计算结果说明能量主要损耗在了集总电阻中, 从而实现低频宽带的吸收特性. 制备了实验样品并用自由空间法进行测试, 测试结果与模拟结果符合得较好. 进一步的实验测试结果表明FR4基板的厚度对该吸波体的吸收特性有明显的调控作用, 且对于固定参数的结构存在最佳匹配厚度. 关键词： 集总元件 超材料吸波体 低频 宽带     

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.     

弯曲振动薄圆盘的共振频率和等效电路参数研究

机电等效电路是分析复合换能器常用的一种解析方法, 但对薄圆盘而言, 由于弯曲振动的复杂性, 其等效集中参数很难获得, 该方法很少被应用. 本文从分布参数系统与集中参数系统等效角度, 根据动能相等原则和势能相等原则, 给出了弯曲振动薄圆盘的集中参数: 等效质量和等效弹性系数, 得到了共振频率方程, 并用ATILA软件模拟了其振动分布情况, 可以看出解析结果与数值结果趋于一致. 最后给出了分析复合振动系统时薄圆盘集中参数模型的等效电路. 本文的结果对弯曲振动复合换能器的设计提供了理论参考.     

Middle-ear circuit model parameters based on a population of human ears

Middle-ear circuit model parameters are selected to produce overall magnitude and phase agreement with pressure to stapes velocity transfer function measurements made on 16 human temporal bones, up to approximately 12 kHz. The circuit model, which was previously used for the cat, represents the tympanic membrane (TM) as a distributed parameter acoustic transmission line, and ossicular chain and cochlea as a network of lumped circuit elements. For some ears the TM transmission line primarily affects the magnitude of the response, while for others it primarily affects the phase. Model responses also compare favorably with velocity ratio data between the umbo and stapes footplate as well as between the umbo and incus, and exhibit similar characteristics to three previous input impedance measurements, including two from living ears. Similarities are also shown between the model magnitude and adjusted pressure to stapes velocity measurements from living ears, suggesting that the model may suitably approximate the behavior of living ears. In addition to fitting individual measurements, a set of parameters is selected to produce agreement with the mean of the 16 measurements up to 10 kHz, to allow the main features of the ensemble to be reproduced from a single parameter set.     

Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone

This paper presents the nonlinear identification of a capacitive dual-backplate microelectromechanical systems (MEMS) microphone. First, a nonlinear lumped element model of the coupled electromechanical microphone dynamics is developed. Nonlinear finite element analyses are performed to verify the accuracy of the lumped linear and cubic stiffnesses of the diaphragm. In order to experimentally extract the system parameters, an approximate solution using the second-order multiple scales method is synthesized for a nonlinear microphone model, subject to an electrical step input. A nonlinear least-squares technique is then implemented to extract system parameters from laser vibrometry data of the diaphragm motion. The results indicate that the theoretical fundamental resonant frequency, damping ratio and nonlinear stiffness parameter agree with the corresponding extracted experimental parameters with 95% confidence interval estimates.     

Influence of nonparallelism of the surfaces of a piezoelectric layer on the frequency band of an electroacoustic piezoelectric transducer

The influence of nonparallelism of the surfaces of a piezoelectric transducer on its impedance and frequency band is analyzed theoretically. The model of a wedge-shaped piezoelectric layer taken for the analysis consists of a set of n plane-parallel elements arranged in succession along the length of the transducer with a gradual increase in the thickness of the piezoelectric layer. The analysis performed demonstrates the possibility of significantly expanding the band of working frequencies of a piezoelectric transducer when its electroacoustic conversion efficiency is reduced. In some cases, however, a decrease in conversion efficiency can be employed to optimize an acoustic device, for example, in creating a filter-type piezoelectric transducer, where electromagnetic energy is converted into acoustic energy successively from one cell of the filter to another. The proposed method for expanding the frequency band can be useful, for example, in creating high-frequency acousto-optic Bragg cells. Zh. Tekh. Fiz. 69, 72–73 (March 1999)     

Numerical and experimental modal analysis of the reed and pipe of a clarinet

A modal computation of a complete clarinet is presented by the association of finite-element models of the reed and of part of the pipe with a lumped-element model of the rest of the pipe. In the first part, we compare modal computations of the reed and the air inside the mouthpiece and barrel with measurements performed by holographic interferometry. In the second part, the complete clarinet is modeled by adjoining a series of lumped elements for the remaining part of the pipe. The parameters of the lumped-resonator model are determined from acoustic impedance measurements. Computed eigenmodes of the whole system show that modal patterns of the reed differ significantly whether it is alone or coupled to air. Some modes exhibit mostly reed motion and a small contribution of the acoustic pressure inside the pipe. Resonance frequencies measured on a clarinet with the mouthpiece replaced by the cylinder of equal volume differ significantly from the computed eigenfrequencies of the clarinet taking the actual shape of the mouthpiece into account and from those including the (linear) dynamics of the reed. This suggests revisiting the customary quality index based on the alignment of the peaks of the input acoustical impedance curve.     

Hybrid holographic-numerical method for modal analysis of complex structures

This paper presents a hybrid holographic-numerical method for modal analysis of complex structures. A continuous structure is first lumped into a number of discrete elements to form an elastically connected lumped linear system. The matrix of influence coefficients of the lumped linear system are then determined by exerting a static load to the element centers and measuring the corresponding whole-field displacement using digital holographic interferometry. The eigenvalues and eigenvectors of the influence coefficients, which in a physical sense represent the natural frequencies and mode shapes of the structure, are then calculated using the numerical method. A major advantage of the proposed hybrid method is that it is not necessary to know the Young's modulus, the Poisson's ratio of the material and the boundary conditions, as the displacement field measured by the optical method has automatically reflected the real boundary conditions and the material properties, which makes this method particularly useful for studying objects made from anisotropic materials such as composites. Another advantage of the proposed method is that structures of any complex and irregular shape will not increase the complexity of the characterization process. The proposed is also suitable for experimentally validating the modal analysis results from finite element method models.     

Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems

The objective of this paper is to present a coupled magneto-electro-mechanical (MEM) lumped parameter model for the response of the proposed magneto-electro-elastic (MEE) energy harvesting systems under base excitation. The proposed model can be used to create self-powering systems, which are not limited to a finite battery energy. As a novel approach, the MEE composites are used instead of the conventional piezoelectric materials in order to enhance the harvested electrical power. The considered structure consists of a MEE layer deposited on a layer of non-MEE material, in the framework of unimorph cantilever bars (longitudinal displacement) and beams (transverse displacement). To use the generated electrical potential, two electrodes are connected to the top and bottom surfaces of the MEE layer. Additionally, a stationary external coil is wrapped around the vibrating structure to induce a voltage in the coil by the magnetic field generated in the MEE layer. In order to simplify the design procedure of the proposed energy harvester and obtain closed form solutions, a lumped parameter model is prepared. As a first step in modeling process, the governing constitutive equations, Gauss's and Faraday's laws, are used to derive the coupled MEM differential equations. The derived equations are then solved analytically to obtain the dynamic behavior and the harvested voltages and powers of the proposed energy harvesting systems. Finally, the influences of the parameters that affect the performance of the MEE energy harvesters such as excitation frequency, external resistive loads and number of coil turns are discussed in detail. The results clearly show the benefit of the coil circuit implementation, whereby significant increases in the total useful harvested power as much as 38% and 36% are obtained for the beam and bar systems, respectively.     

Law-of-the-wall in a boundary-layer over regularly distributed roughness elements

As opposed to the log-region, the roughness sublayer present above rough surfaces is still poorly understood due to the complex interaction between wakes developing behind roughness elements. To investigate the spatially averaged flow velocity in this region, a data-set has been collected from several direct numerical simulations and wind-tunnel experiments available in the literature. A generalised law-of-the-wall has been derived, applicable to a roughness sublayer present over regularly distributed roughness elements. The key roughness parameter of this new law is the effective height ?, which characterises the interaction between the roughness and the outer flow in a temporally and spatially averaged sense. A morphometric study reveals that ? is closely related to a new roughness density parameter, λ₂, that accounts for the roughness element shape and the inter-element spacing. This allows ? to be a universal parameter on roughness characterisation. The derived values of the classical roughness length z₀ of the log-law compare well with previous experimental data and geometrical model predictions. Finally, the main properties of the roughness sublayer such as its height are discussed using the geometrical and the roughness parameters proposed in the study.     

Lumped parameter models of acoustic filters using normal modes and bond graphs

The low-frequency behavior of shell and tube reactive filters can be predicted fairly well by representing the tubes as inertia elements and the volumes as capacitive elements. At higher frequencies, the wave length may become comparable to some tube or shell dimensions and the simple lumped parameter model is no longer valid. A simple method, based on dual formulations and normal modes, is presented for extending the frequency range of lumped parameter models. Bond graph representations are given for the models so that computer formulation of the equations by using the ENPORT program is possible. Experimental and computational results are shown for an example case.     

Lumped modeling with circuit elements for nonreciprocal magnetoelectric tunable band-pass filter

This paper presents a lumped equivalent circuit model of the nonreciprocal magnetoelectric tunable microwave bandpass filter.The reciprocal coupled-line circuit is based on the converse magnetoelectric effect of magnetoelectric composites,includes the electrical tunable equivalent factor of the piezoelectric layer,and is established by the introduced lumped elements,such as radiation capacitance,radiation inductance,and coupling inductance,according to the transmission characteristics of the electromagnetic wave and magnetostatic wave in an inverted-L-shaped microstrip line and ferrite slab.The nonreciprocal transmission property of the filter is described by the introduced T-shaped circuit containing controlled sources.Finally,the lumped equivalent circuit of a nonreciprocal magnetoelectric tunable microwave band-pass filter is given and the lumped parameters are also expressed.When the deviation angles of the ferrite slab are respectively 0° and45°,the corresponding magnetoelectric devices are respectively a reciprocal device and a nonreciprocal device.The curves of S parameter obtained by the lumped equivalent circuit model and electromagnetic simulation are in good agreement with the experimental results.When the deviation angle is between 0° and 45°,the maximum value of the S parameter predicted by the lumped equivalent circuit model is in good agreement with the experimental result.The comparison results of the paper show that the lumped equivalent circuit model is valid.Further,the effect of some key material parameters on the performance of devices is predicted by the lumped equivalent circuit model.The research can provide the theoretical basis for the design and application of nonreciprocal magnetoelectric tunable devices.     

平衡衔铁受话器的非线性特性与失真仿真模型

平衡衔铁受话器(BAR)具有尺寸小、电声转换效率高和灵敏度高等特点。在大振幅振动时, BAR存在显著的非线性,并导致较严重的失真。利用磁路的集总参数模型(LPM)深入研究BAR的非线性,确立可表征其非线性特性的4个非线性参数,采用迭代计算方法研究平衡衔铁磁阻对非线性特性的重要影响。基于所提出的网格移动和旋转等效的有限元模型(FEM),考虑平衡衔铁磁阻的非线性,准确仿真计算得到非线性参数,再将它们代入到非线性LPM模型中,最终建立FEM与LPM相结合的失真仿真模型。实验结果表明,该失真仿真模型可比较准确地预测BAR在不同加载电压时的总谐波失真以及二次和三次谐波失真。     

Modelling the spindle–holder taper joint in machine tools: A tapered zero-thickness finite element method

This study presents a tapered zero-thickness finite element model together with its parameter identification method for modelling the spindle–holder taper joint in machine tools. In the presented model, the spindle and the holder are modelled as solid elements and the taper joint is modelled as a tapered zero-thickness finite element with stiffness and damping but without mass or thickness. The proposed model considers not only the coupling of adjacent degrees of freedom but also the radial, tangential and axial effects of the spindle–holder taper joint. Based on the inverse relationship between the dynamic matrix and frequency response function matrix of a multi-degree-of-freedom system, this study proposes a combined analytical–experimental method to identify the stiffness matrix and damping coefficient of the proposed tapered zero-thickness finite element. The method extracts those parameters from FRFs of an entire specimen that contains only the spindle–holder taper joint. The simulated FRF obtained from the proposed model matches the experimental FRF quite well, which indicates that the presented method provides high accuracy and is easy to implement in modelling the spindle–holder taper joint.     

Modelling metamaterial transmission lines: a review and recent developments

This review paper is devoted to the discussion and comparison of the lumped element equivalent circuit models of the different types of metamaterial transmission lines that have been proposed so far, namely the CL-loaded lines, and those lines based on the resonant type approach. The latter category comprises both artificial lines loaded with split ring resonators (SRRs), or related topologies, and metamaterial transmission lines based on complementary split ring resonators (CSRRs). It will be the main aim of this paper to clearly justify the circuit elements of the models (and link such elements to the line physics and topology), to compare the different lines to the light of these models, and to point out the advantages and drawbacks of the different metamaterial transmission lines. As long as metamaterial transmission lines are exhaustively used for the design of compact microwave and millimeter wave components with improved performance and/or based on new functionalities, and their synthesis is based on the lumped element equivalent circuits, this paper is of actual interest for RF/microwave engineers and in general to those readers involved in metamaterial research and applications.     

A finite element method for modelling dissipative mufflers with a locally reactive lining

The transmission loss of a lined expansion chamber muffler with zero mean flow is studied by using a finite element model of the system. In the cases considered the lining is arranged in small cells so that it is reasonable to assume a locally reacting effect. An existing empirical relationship is used to calculate the lining impedance. The results show that the lining always increases the transmission loss over the unlined chamber valuys; with a thin lining its effect is similar to that of a side branch filter. However, as the thickness increases and the lining impedance approaches the characteristic impedance for the absorption material, the transmission loss develops a single maximum similar to the attenuation produced by a thick lining on the primary mode in a lined duct.     

Electromechanical coupling factor of capacitive micromachined ultrasonic transducers

Recently, a linear, analytical distributed model for capacitive micromachined ultrasonic transducers (CMUTs) was presented, and an electromechanical equivalent circuit based on the theory reported was used to describe the behavior of the transducer [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 159-168 (2002)]. The distributed model is applied here to calculate the dynamic coupling factor k(w) of a lossless CMUT, based on a definition that involves the energies stored in a dynamic vibration cycle, and the results are compared with those obtained with a lumped model. A strong discrepancy is found between the two models as the bias voltage increases. The lumped model predicts an increasing dynamic k factor up to unity, whereas the distributed model predicts a more realistic saturation of this parameter to values substantially lower. It is demonstrated that the maximum value of k(w), corresponding to an operating point close to the diaphragm collapse, is 0.4 for a CMUT single cell with a circular membrane diaphragm and no parasitic capacitance (0.36 for a cell with a circular plate diaphragm). This means that the dynamic coupling factor of a CMUT is comparable to that of a piezoceramic plate oscillating in the thickness mode. Parasitic capacitance decreases the value of k(w), because it does not contribute to the energy conversion. The effective coupling factor k(eff) is also investigated, showing that this parameter coincides with k(w) within the lumped model approximation, but a quite different result is obtained if a computation is made with the more accurate distributed model. As a consequence, k(eff), which can be measured from the transducer electrical impedance, does not give a reliable value of the actual dynamic coupling factor.