Finite element simulation of non-linear acoustic generation in a horn loudspeaker

The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.     

Acoustic coupling between the loudspeaker and the resonator in a standing-wave thermoacoustic device

Thermoacoustic refrigerators work with high amplitude sound waves, which are often created using an acoustic source coupled to a resonator. This coupling can be calculated analytically using linear acoustic equations and a linear model of the loudspeaker. This paper makes a comparison between such a coupling and measurements obtained in a large-scale thermoacoustic resonator constructed at the University of Manchester. The resonator was driven from low to large pressure amplitudes, with drive ratios up to 10%. It is shown that a good agreement is obtained for small amplitudes and this progressively worsens as the amplitude is increased. In the absence of wave harmonics and loudspeaker nonlinearities, the increasing discrepancy is attributed to the presence of minor losses.     

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied.A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation.Because of the nonlinear wave distortion and reflected sound waves at the mouth,broadband time-domain impedance boundary conditions are employed.The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions,which can be calculated by fast and efficient recursive convolution.The numerical results agree very well with experimental data in the situations of weak nonlinear wave propagation in an exponential horn,it is shown that the model can describe the broadband characteristics caused by nonlinear distortion.Moreover,finite-amplitude acoustic propagation in types of horns is simulated,including hyperbolic,conical,exponential and sinusoidal horns.It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles,the driving velocity and frequency of the piston.The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.     

有限长号筒中非线性声传播的数值模拟研究

研究了大振幅活塞声源经有限长号筒向外辐射声波的非线性声学问题。采用具有频散保持特性的高精度计算格式求解了适用于变截面管道的一维非线性声场模型,并考虑到声波的非线性畸变及管口处的声反射,加入了宽频时域声阻抗边界条件。宽频阻抗模型的共轭复数系数采用优化拟合方法近似求解,并采用递推卷积算法快速求解出时域声阻抗。在弱非线性条件下模拟指数形号筒中的声传播取得了与已有实验相一致的结果,表明模型能够描述声波非线性畸变带来的宽频特性。进而采用本模型数值模拟了大振幅活塞声源在双曲形、锥形、指数形和正弦形号筒中的非线性声传播问题,结果表明号筒出口声压级受活塞振动速度、频率以及号筒形状的影响,并分析讨论了波形畸变与号筒几何形状之间的关系。      

电动声源热声致冷机声学和计算实例

我们将各种热声致机简化为一包括声学终端在内的声管道系统，并通过实例讨论了致冷机的声学特性，该管道系统与一般声管道不同：１．在热声堆中热波和粘滞波不可不计。２．在热声堆与声管连接时，必需考虑合成波的体积流；而热声堆内只需考虑传播波的体积流。本文对此提出了阻抗连接条件的修正。实例使用电动扬声器为声源，给出了热声行波和驻波致冷的声学计算方法以及它们的声学特性，所用扬声器的标称伏安为１００ＶＡ，可为热声致     

PVDF-driven flexible and transparent loudspeaker

A flexible and transparent loudspeaker driven by piezoelectric polymer was proposed. The core structure was an assemblage of a flexible plastic film with piezoelectric polymer pasted over the whole surface. We fabricated a prototype loudspeaker using polyethersulfone (PES) and polyvinylidenefluoride (PVDF), and it had flexibility and transparency. Its acoustic characteristics and surface vibration mode were investigated. The investigation yielded low distortion characteristics in comparison with those of a loudspeaker made only of PVDF, and its advantages originated from the use of the plastic film as a diaphragm.     

Finite element modelling of dense and porous piezoceramic disc hydrophones

The acoustic characteristics of dense and porous piezoceramic disc hydrophones have been studied by finite element modelling (FEM). The FEM results are validated initially by an analytical model for a simple disc of dense piezoceramic material and then it is extended to a porous piezoceramic disc replicating a foam-reticulated sample. Axisymmetric model was used for dense piezoceramic hydrophone due its regular geometric shape. 3-dimensional model was used for the porous piezoceramics, since the unit cell model is inadequate to fully represent transducers of finite lateral dimensions. The porous PZT discs have been synthesised by foam-reticulation technique. The electrical impedance and the receiving sensitivity of the hydrophones in water are evaluated in the frequency range 10-100 kHz. The model results are compared with the experimental data. The receiving sensitivity of piezocomposite hydrophones is found to be reasonably constant over the frequency range studied. The sharp resonance peaks observed for the dense piezoceramic hydrophone has broadened to a large extent for porous piezoceramic hydrophones, indicating higher losses. The flat frequency response suggests that the 3-3 piezocomposites are useful for wide-band hydrophone applications.     

Influence of the Nonlinearity of Loudspeakers on the Performance of Thermoacoustic Refrigerators Driven by Current and Voltage

The influence of the nonlinearity of electrodynamic loudspeakers on the performance of thermoacoustic refrigerators with the loudspeakers as acoustic sources is studied by nonlinear equivalent circuit models of electrodynamic loudspeakers driven by current and voltage. The simulated results demonstrate that there are different nonlinear effects between current-drive and voltage-drive refrigerators, and the differences are mainly induced by the motional electromotive force caused by the coil moving in the magnetic field. With voltage driving, the influence of the nonlinearity of the loudspeaker on the diaphragm displacement and acoustic output power is much smaller than that with current driving. Therefore, considering the nonlinearity of the loudspeakers, a proper driving method must be chosen according to the practical applications although little difference is found with the linear models.     

An electro-acoustics impedance error criterion and its application to active noise control

Characteristics of radiation impedance and its inducing variation of electrical impedance for a controllable source have been investigated. An impedance-based error criterion has been proposed and its application to active noise control is demonstrated through a coil driven loudspeaker. A general formula of radiation impedance is derived for two control strategies, according to the criterion of total acoustic power output. The radiation impedances of some commonly used sound sources are calculated. We discuss in detail the relation between variation of the input electrical impedance and radiation impedance for the two control strategies. An AC-bridge circuit is designed to measure the weak variation of electrical impedance resulted from radiation impedance. The input electrical impedance of a loudspeaker was measured and the experimental result is consistent with that of theoretical analysis. An impedance-based error criterion is proposed since the AC-bridge relative output is unique for a certain control strategy. The implementation of this criterion applied to an active control system is analyzed by simulations. An analogue control system is set up and experiments are carried out in a semi-anechoic chamber to verify the new control approach.     

Experimental and finite element modelling studies on single-layer and multi-layer 1-3 piezocomposite transducers

Finite element modelling (FEM) using ATILA code and experimental studies have been carried out on 1-3 piezocomposite transducers. FEM study was initially carried out on a piezocomposite infinite plate and then extended to transducers of finite size. The infinite-plate model results agree well with that of a simple analytical model and experiments. The acoustic performance of multi-layer finite-size piezocomposite transducers was also studied. Transducer stacks were fabricated with different number of layers. The transducer characteristics such as the electrical impedance, the transmitting voltage response (TVR) and the receiving sensitivity (RS) of the 1-3 piezocomposite transducers were evaluated as functions of frequency, ceramic volume fractions and the number of layers. TVR increases and RS decreases with increase in ceramic volume fractions. The model results are found to agree with the experimental data, especially when the number of layers is less.     

A finite element approach to a coupled structural-acoustic radiation system with application to loudspeaker characteristic calculation

The finite element method is applied to an elastic shell which is vibrating to generate acoustic radiation. A vibrating shell of revolution backed by an enclosure in its rear side is to radiate sound waves into a semi-infinite space in front. As a numerical example, some characteristics of a direct radiator type loudspeaker model are calculated and discussed. The driving point impedance and the far field sound pressure frequency characteristics are shown, together with the effects of the radiation and the enclosure.     

气流扬声器振动系统的设计原理

本文用等效电路方法分析了电动气流扬声器振动系统的特性,求得了气流扬声器的输入阻抗和位移振幅的频率特性,并把结果用于典型扬声器,说明用等效电路分析指导气流扬声器设计的作用。气流扬声器振动系统所需的电功率与其机械共振频率的四次方成正比,其声辐射主要限于共振频率以下,因而高频特性较差。求得了在共振频率以下,频率响应平直的最佳条件,实验表明,在最佳条件下,气流扬声器的高频特性随着磁隙中的磁感应强度的增加仍稍有提高。实验结果符合理论分析,测得气流扬声器喇叭喉部的声压级在不同情况下达181分贝或184.8分贝(零分贝等于2×10^-5牛顿/米²)。     

Weak nonlinear propagation of sound in a finite exponential horn.

This article presents an approximate solution for weak nonlinear standing waves in the interior of an exponential acoustic horn. An analytical approach is chosen assuming one-dimensional plane-wave propagation in a lossless fluid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at the mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressure-density relation in Eulerian coordinates, a perturbation analysis is used to obtain a hierarchy of wave equations with nonlinear source terms. Green's theorem is used to obtain a formal solution of the inhomogeneous equation which takes into account linear reflections at the ends of the horn, and the solution is applied to the nonlinear horn problem to yield the acoustic pressure for each order, first in the frequency and then in the time domain. In order to validate the model, an experimental setup for measuring fundamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained between predicted and measured levels (fundamental and second harmonic) at the mouth of the horn.     

Vibration of piezoelectric elements surrounded by fluid media

In this paper we analyse vibrational characteristics of piezoceramic shells surrounded by acoustic media. Main results are presented for radially polarized piezoceramic PZT5 elements of hollow cylindrical shapes. The coupling in the radial direction between the solid and the acoustic media is accounted for indirectly, via impedance boundary conditions. The model based on such impedance boundary condition approximations offers a robust simplified alternative to a full scale fluid-solid interaction modelling. By using this model, we analyse numerically the influence of the boundary conditions imposed in the axial direction for long, medium, and short (disk-like) piezoceramic elements.     

Time-varying non linear modeling of electrodynamic loudspeakers

This paper deals with the time-varying nonlinear analytical modeling of the electrodynamic loudspeaker. We propose a model which takes into account the variations of Small signal parameters. The six Small signal parameters (R_e, L_e, Bl, R_ms, M_ms, C_ms) depend on both time and input current. The electrodynamic loudspeaker is characterized by the electrical impedance which, precisely measured, allows us to construct polynomial functions for each Small signal parameter. By using this analytical model, we propose to compare two identical electrodynamic loudspeakers. One of them is supposed to be run in and the other one is not. The experimental methodology is based on a precise measurement. In all the paper, the time scale is assumed to be much longer than one period of the harmonic excitation.     

Acoustic characteristics of an electrodynamic planar digital loudspeaker

In this paper, an electrodynamic planar loudspeaker driven by a digital signal is experimentally discussed. The digital loudspeaker consists of 22 voice coils, 11 permanent magnets, a diaphragm with streamlined sections molded in plastic, and a suspension made of handmade Japanese paper between the diaphragm and the frame. First, the acoustic responses are affected by the arrangement of the voice coils, so an asymmetric arrangement is studied. This asymmetric arrangement is designed to obtain as flat a frequency response to an analog signal as possible. This arrangement is compared with a symmetric one and results show that the flatness of the frequency response around 1 kHz and 4 kHz is improved and that the sound reproduction band is from 40 Hz to 10 kHz. Second, to evaluate the acoustic responses to a digital signal, the digital loudspeaker is driven with a pulse code modulation signal. Results show that the digital loudspeaker can reproduce pure sound with a total harmonic distortion of less than 5% from 40 Hz to 10 kHz, exceeding this value only in a narrow frequency band near 4 kHz. This digital loudspeaker was demonstrated to have good linearity over its dynamic range of 84 dB.     

Traveling wave ultrasonic motor: coupling effects in free stator

Generally a stator of traveling wave ultrasonic motor (TWUM) consists of piezoelectric transducers (annular plate or rods) coupled by the way of a metallic ring. These transducers divided into halves are excited independently by two electrical signals with different phases of about 90 degrees. So an elastic traveling wave propagates along the circumference of the ring and a rotor pressed on this vibrating surface is then driven by the stator via contact forces. Many difficulties appear in developing TWUM because the contact between the stator and the rotor via a frictional material is very important. However that may be, the first stage consists in obtaining a vibrating stator with optimum characteristics with two symmetrical phases. The aim of this paper is to discuss some coupling effects in a free stator through an enhanced equivalent circuit model. A simple experimental method based on impedance measurements is performed to estimate the coupling characteristics at a low driving voltage. This paper reports results obtained with the free stator of the well known piezoelectric ultrasonic motor "USR60" by Shinsei Co. Ltd. Since the stator behaves as an elastic body, interactions between the two electrical inputs might be described by the introduction of a coupling oscillator. The comparison of experimental and theoretical results leads to validate the new equivalent circuit of the free stator. The presence of coupling impedance could imply a change of electrical supply condition to optimize the TWUM efficiency. The effects of unbalanced features for each electrical input and the applicability of the proposed model to actual operating condition are discussed in the paper.     

Lens-focused transducer modeling using an extended KLM model

The goal of this work was to develop an extended ultrasound transducer model that would optimize the trade-off between accuracy of the calculation and computational time. The derivations are presented for a generalized transducer model, that is center frequency, pulse duration and physical dimensions are all normalized. The paper presents a computationally efficient model for lens-focused, circular (axisymmetric) single element piezoelectric ultrasound transducer. Specifically, the goal of the model is to determine the lens effect on the electro-acoustic response, both on focusing and on matching acoustic properties. The effective focal distance depends on the lens geometry and refraction index, but also on the near field limit, i.e. wavelength and source radius, and on the spectrum bandwidth of the ultrasound source. The broadband (80%) source generated by the transducer was therefore considered in this work. A new model based on a longitudinal-wave assumption is presented and the error introduced by this assumption is discussed in terms of its maximum value (16%) and mean value (5.9%). The simplified model was based on an extension of the classical KLM model for transducer structures and on the related assumptions. The validity of the implemented extended KLM model was evaluated by comparison with finite element modeling, itself previously validated analytically for the one-dimensional planar geometry considered. The pressure field was then propagated using the adequate formulation of the Rayleigh integral for both the extended KLM and finite element results. The simplified approach based on the KLM model delivered the focused response with good accuracy, and hundred-fold lower calculation time in comparison with a mode comprehensive FEM method. The trade-off between precision and time thus becomes compatible with an iterative procedure, used here for the optimization of the acoustic impedance of the lens for the chosen configuration. An experimental comparison was performed and found to be in good agreement with such an extension of the KLM model. The experiments confirm the accuracy of such a model in a validity domain up to −12 dB on the pulse-echo voltage within a relative error of 9% between experiment and modeling. This extended KLM model can advantageously be used for other transducer geometries satisfying the assumption of a predominantly longitudinal vibration or in an optimization procedure involving an adequate criteria for a particular application.     

Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor

Quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors are based on a recent approach to photoacoustic detection which employs a quartz tuning fork as an acoustic transducer. These sensors enable detection of trace gases for air quality monitoring, industrial process control, and medical diagnostics. To detect a trace gas, modulated laser radiation is directed between the tines of a tuning fork. The optical energy absorbed by the gas results in a periodic thermal expansion which gives rise to a weak acoustic pressure wave. This pressure wave excites a resonant vibration of the tuning fork thereby generating an electrical signal via the piezoelectric effect. This paper describes a theoretical model of a QEPAS sensor. By deriving analytical solutions for the partial differential equations in the model, we obtain a formula for the piezoelectric current in terms of the optical, mechanical, and electrical parameters of the system. We use the model to calculate the optimal position of the laser beam with respect to the tuning fork and the phase of the piezoelectric current. We also show that a QEPAS transducer with a particular 32.8 kHz tuning fork is 2–3 times as sensitive as one with a 4.25 kHz tuning fork. These simulation results closely match experimental data.     

An analytical model for a dodecahedron loudspeaker applied to the design of omni-directional loudspeaker arrays

The dodecahedron (12 sided) loudspeaker is used extensively for acoustic measurements as an approximation to an omni-directional sound source, for example in building acoustics and automotive applications. In many instances its use is favoured above other omni-directional source approximations e.g. open pipe because of its greater power. However, analysis by other authors has shown that the radiation deviates from omni-directional above a certain frequency. In this paper an analytical model of the sound pressure field generated by a dodecahedron loudspeaker is constructed. The sound pressure field generated by the model is then compared with measured data and good agreement is demonstrated. Having established and validated the model, it is adapted to form alternative spherical loudspeaker arrays based on Platonic and Archimedean solid geometry and also a number of spherical packing routines. The aim of the analysis is to determine the optimal geometry for an omni-directional source using pistonic loudspeakers.The analysis shows that constructive interference of the pressure field across the spherical baffle surface and not individual loudspeaker pistonic radiation characteristics is the most significant factor with respect to deviations from omni-directional radiation for a complete spherical array. Consequently, loudspeaker elements which physically occupy the spherical baffle surface to their maximum extent provide the most extended frequency range of omni-directional operation. The most optimal spherical array distribution is shown to be the dodecahedron.