One-dimensional pressure transfer models for acoustic–electric transmission channels_第1页
One-dimensional pressure transfer models for acoustic–electric transmission channels_第2页
One-dimensional pressure transfer models for acoustic–electric transmission channels_第3页
One-dimensional pressure transfer models for acoustic–electric transmission channels_第4页
One-dimensional pressure transfer models for acoustic–electric transmission channels_第5页
已阅读5页,还剩11页未读 继续免费阅读

下载本文档

版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领

文档简介

Article history:Received 30 April 2014Received in revised form2 February 2015Accepted 26 April 2015Handling Editor: Y. AureganAvailable online 23 May 2015, has requiredthrough. In manyprovidedwall. Establishedelectromagneticcellent. In takingadvantage of this fact, acousticelectric transmission systems have been of high interest; used for both power and dataContents lists available at ScienceDirectjournal homepage: /locate/jsviJournal of Sound and VibrationJournal of Sound and Vibration 352 (2015) 1581730022-460X/& 2015 Elsevier Ltd. All rights reserved./10.1016/j.jsv.2015.04.031nCorresponding author.E-mail addresses: (K.R. Wilt), (T.J. Lawry), (H.A. Scarton), (G.J. Saulnier).transmission solutions.1. IntroductionTraditionally, the transmission of electrical signals across a solid barrier, e.g., the wall of a pressure vesselthe addition of mechanical penetrations through the obstacle in order to pass physical electric connectionscases, these feedthroughs are undesirable as they may reduce the structural integrity and environmental isolationby the barrier. Therefore, it would be beneficial to have an alternate means of transmission through theradio frequency (RF) techniques are ineffective in these situations as conductive media greatly attenuatesignals. Despite this limitation, the propagation of ultrasonic energy within the barrier is generally exis also shown that the piezoelectric models electrical interface is compatible withA method for modeling piezoelectric-based ultrasonic acousticelectric power and datatransmission channels is presented. These channels employ piezoelectric disk transducersto convey signals across a series of physical layers using ultrasonic waves. This modeldecomposes the mechanical pathway of the signal into individual ultrasonic propagationlayers which are generally independent of the layers adjacent domains. Each layer isrepresented by a two-by-two traveling pressure wave transfer matrix which relates theforward and reverse pressure waves on one side of the layer to the pressure waves on theopposite face, where each face is assumed to be in contact with a domain of arbitraryreference acoustic impedance. A rigorous implementation of ultrasonic beam spreading isintroduced and implemented within applicable domains. Compatible pressure-wavemodels for piezoelectric transducers are given, which relate the electric voltage andcurrent interface of the transducer to the pressure waves on one mechanical interfacewhile also allowing for passive acoustic loading of the secondary mechanical interface. Ittransmission line parameters (ABCD-parameters), allowing for connection of electroniccomponents and networks. The model is shown to be capable of reproducing the behaviorof realistic physical channels.& 2015 Elsevier Ltd. All rights reserved.article info abstractOne-dimensional pressure transfer modelsfor acousticelectric transmission channelsK.R. Wilta,n, T.J. Lawryb, H.A. Scartona, G.J. SaulnieraaRensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, United StatesbApplied Physical Sciences Corp., Groton, CT 06340, United StatesK.R. Wilt et al. / Journal of Sound and Vibration 352 (2015) 158173 159The generation and reception of the ultrasonic waves may be accomplished through multiple means, thoughpiezoelectric transducers are primarily employed. Physical demonstrations of such systems, or channels, have beendiscussed from multiple sources which show these types of systems capable of both high-power and high data-rateoperation. In considering data transmission, several systems 13 have been shown to successfully transmit data at ratessubstantially less than 1 Mbps while simultaneously transmitting power in the opposite direction using the samemechanical channel. This type of system is useful in low-rate telemetry applications. Dedicated data implementations ofthese systems 46 have been shown to be capable of high data-rate communications, with both implementationsemploying multicarrier transmission techniques to achieve over 15 Mbps data-rates, with predictions of much higher ratesbeing possible. Conversely, for strictly power transmission, a system 7 composed of disk transducers across a thickstainless steel barrier was shown to be capable of delivering at least 140 W with an approximate efficiency of 67 percent at1.25 MHz; whereas Bao et al. 8 demonstrated delivery of over 1 kW at 24.5 kHz with an efficiency of 84 percent whileusing highly specialized piezoelectric transducer stacks operating on a thin titanium barrier.Modeling of these types of systems has been performed using a variety of methods. A significant amount of modeling ofsuch systems has been done using a coupled continuum equation approach. Both planar 9 and cylindrical 10,11Fig. 1. Generic construction of an acousticelectric channel.configurations of channels were considered, as well as nonlinear effects 12. While these models are well developed, theyare inherently coupled and therefore channels with many layers are bulky to construct and evaluate. Alternative to fullycoupled modeling, equivalent circuit modeling techniques have been implemented which have been shown to be equally asvalid 13 and easily assessed using time domain analysis 14,15. Finite element analysis of such channels has been done8,16,17 which is capable of a more comprehensive system model, allowing for complex geometries to be represented.While the finite element method is capable of producing a more complete model, it is severely hampered by the requiredevaluation time and computer resources, which becomes unacceptable for large degrees of freedom models (e.g., high-frequency and/or large geometry models).A pressure-wave based layer model of generic layered acousticelectric transmission channels is constructed in thiswork, where individual layers are represented by 2C22 matrices multiplied together to form a complete model of thestructure. Specifically, the scientific objectives for the construction of this model were to design a simulation method whichavoids the time and computational requirements of finite element models. Additionally, it was required to maintain themodularity provided by finite element software, where addition or subtraction of layers within a system model is relativelytrivial as compared to the fully coupled mathematical models, which require a complete rederivation to achieve. This trait isshared by equivalent circuit models, where most layers may be implemented with transmission line elements; however,unlike the equivalent circuit models, this model resides completely within the mechanical domain, allowing for easierinterpretation of elements within the full model.A similar type of model has been described by Lawry et al. 18, which approached modeling of the channels individuallayers by isolating each layer and then modeling them using forcevoltage mechanical analog ABCD-parameters, commonlyknown as acoustic transfer matrices, which map the pressure and particle velocities to adjacent interfaces. The modelingpresented within this paper considers the independently traveling forward and reverse pressure waves as the mappedvariables, which allows for a more intuitive understanding of the power flow characteristics of such systems. This paperexpands on the means for modeling and reduction of the axisymmetric two-dimensional effects due to acoustic beamK.R. Wilt et al. / Journal of Sound and Vibration 352 (2015) 158173160divergence into a usable one-dimensional approximation proposed by Lawry. For simplicity, only longitudinal wavepropagation traveling inline with the transducers axes is considered.2. The acousticelectric channelThe target acousticelectric channel, or simply the channel, of interest in this model is constructed using twopiezoelectric disk transducers coupled on opposite sides of a barrier and aligned coaxially. This arrangement is illustratedin Fig. 1. Either fluid or hardening couplants may be used to enable the efficient transmission of ultrasonic energy betweenthe transducers and barrier. Epoxies are commonly used to rigidly couple and bond the transducers to the wall, howevertemporary agents, such as oils or gels, are usable as well. For this application, it is assumed that each component of thechannel (e.g., transducers, wall, epoxy) has effectively parallel interfacial surfaces.Excitation of the channel is accomplished by the application of a sinusoidal voltage (power transmission) or morecomplex time varying signals (data communication) to the transmit transducer. The transducer converts the electric signalinto an ultrasonic wave, which propagates across the barrier to interact with the receive transducer. A portion of the incidentultrasonic energy is converted back into a voltage by the receive transducer, which may then be used as a power source ordecoded to obtain transmitted data. Any reflected energy returns towards the transmit transducer and with successivereflections a reverberant field is established. Energy is removed from the field through three dominant methods: conversionback to the electrical domain via either transducer, material absorption and subsequent conversion to heat, and acousticbeam divergence within the barrier, where energy propagates away from the channel laterally.3. Pressure transfer matricesThe basis for this modeling is that the acousticelectric channel may be decomposed into independent layers andinterfaces. These components are modeled as 2C22 matrices which relate the inward and outward pressure waves on eachface of the layer or interface. These matrix models are referred to as pressure transfer matrices. The interface model is aconstruct to apply the acoustic reflection condition between two layers without the need for inclusion into the layer models.There are three general layers types discussed here: basic, spreading, and piezoelectric. The basic type is intended to modellayers whose behavior essentially allows for plane harmonic waves to propagate through whereas the spreading typeconsiders effects of ultrasonic beam diffraction. The basic type is usable for most non-piezoelectric layers (e.g., epoxy,electrode) which are either (a) cylindrical with a radius comparable to the transducers or (b) thinner than one wavelengthwith very large lateral dimensions. For cases where the layer thickness and radial proportions are large, the spreading type isapplicable. The piezoelectric type layer model is self-explanatory: the model attempts to reproduce the behavior of apiezoelectric material. Given that a piezoelectric disk transducer has three effective interfaces (two mechanical faces and theelectrical port), to construct a 2C22 model matrix, one of the interfaces, or ports, needs to be constrained with passiveloading.To form a complete channel model, the appropriate layer and interface matrices are simply cascaded together in theorder of the channels construction. This requires that the inward and outward pressure wave definitions of the modelFig. 2. Interfacial acoustic pressure flow diagram.matrices to be compatible; that is, the input of one model matrix, i.e., one faces inward and outward pressure waves, equalsthe output of the adjacent model matrix.3.1. Interface modelThe interface model matrix is meant to represent the pressure wave transmission and reflection properties ofconstitutive layer interfaces. The formulation of this component requires only the acoustic reflection coefficient, , betweenthe two layer materials as described in Fig. 2. The acoustic reflection coefficient is defined via the acoustic impedances, Zland Zr, of the adjacent materials asZrC0ZlZrZl: (1)K.R. Wilt et al. / Journal of Sound and Vibration 352 (2015) 158173 161From Fig. 2, the outward pressure waves, or the waves traveling away from the interface, are easily discerned aspr 1plC0pC0r; (2a)pC0lpl1C0pC0r; (2b)where pland pC0rare the incident pressure waves from the left and right, respectively. With slight manipulation of theseequations, the interface model matrix becomesplpC0l#111 1C20C21prpC0r#lTrprpC0r#; (3)where the notationlTrdescribes the interface model matrix generated between materials l and r.3.2. Basic layerAs stated, the basic layer model is intended for intra-layer pressure wave propagation where the pressure waves may beassumed to be longitudinal and planar. Since the interfacial reflections are separately considered, a linear homogeneousacoustic layer will present only propagation delays (phase changes) and amplitude degradation (attenuation). This impliesthat there is no cross-coupling between the forward and reverse pressure waves, resulting in a diagonal model matrix.Considering the description of the harmonic plane waves as complex phasorspzAeC0jz; (4)where initial phase information is contained within the complex amplitude coefficient A, is the acoustic wavenumber, andthe time dimension is neglected, then the pressures at each end of the layer may be described as in Fig. 3, where p7land p7rare the complex pressure wave amplitudes at z0 and zh, respectively. From this figure, derivation of the model matrix istrivial:plpC0l#ejh00eC0jh#prpC0r#LxprpC0r#: (5)where the notation Lxdescribes a basic layer model matrix constructed of material x.3.3. Spreading layerWhile the basic layer is useful for representing most acoustic transmission layers and is reasonable for use in first-passfull-channel calculations, effects due to acoustic beam diffraction must be considered for most situations in order toaccurately predict the channels lossy characteristics. Considered within this model is the diffraction loss generated by arigid circular acoustic piston radiating into a fluid, a common construct in ultrasonic literature (e.g., 19). While this work isconcerned with the transmission of the ultrasonic energy through solids, it has been shown that the beam diffraction modelfor fluids is an acceptable approximation for use in solids 20. This spreading layer model is concerned with the relativeeffective pressure loss experienced through the layer by calculating the effective, or average, spatial pressure experienced bya circular region of radius a2situated at distance h away from the acoustic piston source of radius a1.The complex pressure pr; produced by the source at point r; is known via the (fluid) beam diffraction model 21:C0C1v0Z1 0Fig. 3. Intra-layer acoustic pressure flow diagram.pr; jcA1r0eC0jrdA1; (6)where r is the straight line distance from the center of the piston source to the point in question, is the angular separationof r and the piston axis, v0is the source particle velocity, A1is the area of the source piston, r0is the distance from adifferential area element on the source, dA1,tor;, and , c, and are the propagation materials density, speed of sound,and wavelength, respectively. Finding the effective (average) pressure, pAvz, on a separate circular region, A2, requires theintegration of pr; about the second region:pAvhZA2pr;C0C1dA2jcv0a22ZA2ZA11r0eC0jr0dA1dA2; (7)K.R. Wilt et al. / Journal of Sound and Vibration 352 (2015) 158173162where h is the axial separation of regions A1and A2. Unfortunately, analytical solutions to Eq. (6) are difficult to produce andare more-so for Eq. (7); therefore, numerical integration is required in many situations. The geometry for calculating theeffective pressure loss for the general case where a1and a2are not equal (but the axes are aligned) is given in Fig. 4. Thisfigure describes the integration geometries with symmetries included: the surface integral over A2may be reduced to asignal line integral of the variable 2and the surface integral over A1may be represented as a double integral over thecoordinates 1and .These symmetries result in the calculation of the differential area elements asdA11d1d (8a)dA222d2: (8b)Substitution of these elements into Eq. (7) results in the triple integral:pAvhjc4v0a22Za20Z0Za1012r0eC0jr0d1d d2; (9)where r0, the distance from dA1to dA2, is calculated asr0 2122C0212cosh2C16C171=2: (10)It is desired to calculate the relative pressure at h and not the absolute pressure (pAvh); therefore, the rigid piston inputpressure (plane wave pressure), cv0, is divided into pAvh to obtain the relationshipFig. 4. Geometry used to find the effective pressure loss in layers with beam diffraction or spreading.ph2ja22Za20Z0Za1012r0eC0jr0d1d d2; (11)where ph is the normalized pressure of the field at distance h.For the special case where a1a2a, Williams 19 has derived a single integral which is capable of calculating theabsolute pressure loss for any h. The relative pressure using this integral ispheC0jhC04Z=20eC0jh24a2cos2psin2 d: (12)Finally, for special cases where the separation h is sufficiently large such that the receiving area may be considered to bewithin the acoustic beams far field, Bass 22 has simplified Williamss integral to an approximate equation which reducesthe numerical integration to Bessel functions:phC25eC0jh1C0 1C0222a2!J0jJ1C2C3eC0jC0j22a2J1eC0j#; (13)where the variable is calculated as2h24a2qC0hC20C21: (14)K.R. Wilt et al. / Journal of Sound and Vibration 352 (2015) 158173 163A simple implementation of the spreading layer may be done by substituting the desired diffraction loss equation (Eqs.(11)(13) into the model for the basic layer, resulting in the diagonal matrix model:plpC0l#phC0100 ph#prpC0r#: (15)This instance of beam spreading considers that diffraction occurs equally among the first beam traversal of the layer andthe subsequent reflections. A more

温馨提示

  • 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
  • 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
  • 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
  • 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
  • 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
  • 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
  • 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。

评论

0/150

提交评论