活塞驱动的指数形谐振管内的非线性振荡

本文通过理论分析和推导得到了活塞驱动的指数形谐振管内气体的压力和压比的近似表达式。对指数形谐振管的各种驱动幅值,计算了管端压比随形状参数m的变化曲线,获得最大压比时的谐振管形状参数。本文的研究结果可用于活塞驱动的指数形谐振管内非线性振荡的分析和大声幅谐振管的设计。     

Toward an adjustable nonlinear low frequency acoustic absorber

A study of the targeted energy transfer (TET) phenomenon between an acoustic resonator and a thin viscoelastic membrane has recently been presented in the paper [R. Bellet et al., Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber, Journal of Sound and Vibration 329 (2010) 2768-2791], providing a new path to passive sound control in the low frequency domain where no efficient dissipative device exists. This paper presents experimental results showing that a loudspeaker used as a suspended piston working outside its range of linearity can also be used as a nonlinear acoustic absorber. The main advantage of this technology of absorber is the perspective to adjust independently the device parameters (mass, nonlinear stiffness and damping) according to the operational conditions. To achieve this purpose, quasi-static and dynamic tests have been performed on three types of commercial devices (one with structural modi?cations), in order to de?ne the constructive characteristics that it should present. An experimental setup has been developed using a one-dimensional acoustic linear system coupled through a box (acting as a weak spring) to a loudspeaker used as a suspended piston acting as an essentially nonlinear oscillator. The tests carried out on the whole vibro-acoustic system have showed the occurrence of the acoustic TET from the acoustic media to the suspended piston and demonstrated the efficiency of this new kind of absorber at low frequencies over a wide frequency range. Moreover, the experimental analyses conducted with different NES masses have con?rmed that it is possible to optimize the noise absorption with respect to the excitation level of the acoustic resonator.     

激发圆形管道内多阶声模态的扬声器阵列控制方法

声模态发生器是通过控制扬声器阵列在管道内激发声模态波的一种装置。为了解决在管道内同时激发多个声模态的问题,研究了激发圆形管道内多阶声模态的扬声器阵列控制方法。采用轴向多圈布置的声源阵列,并调节各个声源的幅值和相位,实现同时激发包括径向声模态在内的多个声模态。同时考虑声源的周向位置和轴向位置信息,建立各个声源与多个目标模态系数之间的线性关系,运用最小二乘法求解得到激发目标多模态所需各个声源的复强度（包括幅值和相位）,所研制的高阶模态发生器以计算的声源复强度为输入量,采用数字信号系统控制扬声器输出的幅值和相位,用于实现管道内声源激发,该模态激发过程无需针对特定模态优化声源的位置。实验结果表明,所研制的模态发生器可精确激发单个或多个声模态,且目标模态系数信噪比几乎都大于10 dB。      

Generation of subharmonics in acoustic resonators containing bubbly liquids: A numerical study of the excitation threshold and hysteretic behavior

In this paper we study the generation and behavior of subharmonics in a bubbly liquid confined in an acoustic resonator, through numerical simulations carried out at finite-amplitude acoustic pressure. Several configurations in terms of resonator length and driving frequency are considered here. Our results show that these frequency components, created from a higher-frequency signal at the source (ultrasound), are due to the nonlinearity of the medium at high acoustic-pressure amplitude and to the configuration of the resonator (geometry and boundaries). We also show that they have an amplitude-threshold dependence, which is in concordance with the literature. The response of these subharmonics to different sequences of pressure amplitudes also reveals the hysteretic nature of the bubbly liquid.     

Shear waves in a resonator with cubic nonlinearity

Shear waves with finite amplitude in a one-dimensional resonator in the form of a layer of a rubber-like medium with a rigid plate of finite mass at the upper surface of the layer are investigated. The lower boundary of the layer oscillates according to a harmonic law with a preset acceleration. The equation of motion for particles in a resonator is determined using a model of a medium with a single relaxation time and cubical dependence of the shear modulus on deformation. The amplitude and form of shear waves in a resonator are calculated numerically by the finite difference method at shifted grids. Resonance curves are obtained at different acceleration amplitudes at the lower boundary of a layer. It is demonstrated that, as the oscillation amplitude in the resonator grows, the value of the resonance frequency increases and the shape of the resonance curve becomes asymmetrical. At sufficiently large amplitudes, a bistability region is observed. Measurements were conducted with a resonator, where a layer with the thickness of 15 mm was manufactured of a rubber-like polymer called plastisol. The shear modulus of the polymer at small deformations and the nonlinearity coefficient were determined according to the experimental dependence of mechanical stress on shear deformation. Oscillation amplitudes in the resonator attained values when the maximum shear deformations in the layer were 0.4–0.6, which provided an opportunity to observe nonlinear effects. Measured dependences of the resonance frequency on the oscillation amplitude corresponded to the calculated ones that were obtained at a smaller value of the nonlinear coefficient.     

Bistability of a compliant cavity induced by acoustic radiation pressure

We report on the first observation of multiple-order bistability due to acoustic radiation pressure in a compliant acoustic cavity formed between a spherical ultrasonic transducer immersed in water and the free liquid surface located at its focus. The hysteretic behavior of the cavity length, observed both with amplitude ramps and frequency sweeps, is accurately described using a one-dimensional model of a compliant Fabry-Pérot resonator assuming the acoustic radiation pressure to be the only coupling between the cavity and the acoustic field.     

Model and estimation method for predicting the sound radiated by a horn loudspeaker - With application to a car horn

This paper deals with a new car horn device made of a sound synthesizer and an electrodynamic horn loudspeaker. It presents an one-dimensional model allowing to predict the loudspeaker efficiency and a specific method to estimate experimentally the model parameters. First, this model aims at reducing the time spent in the design process. Second it aims at correcting the sound emitted by the sound synthesizer in order that the listener hears the sound designed for creating the warning message. The study gives a survey of the vast loudspeaker literature. It is based on the conventional electroacoustic approach used for electrodynamic loudspeakers and on wave propagation models used for characterizing acoustic horns. The estimation of the model parameter values is performed using measurements of the electrical impedance of the loudspeaker and of the acoustic impedance of the horn. The model is assessed by comparing the calculated and measured electrical impedances and horn efficiencies. Results show that the model predicts well the horn efficiency up to 2500 Hz, the limitation being due to the horn radiation impedance modelization.     

Toward broadband electroacoustic resonators through optimized feedback control strategies

This paper presents a methodology for the design of broadband electroacoustic resonators for low-frequency room equalization. An electroacoustic resonator denotes a loudspeaker used as a membrane resonator, the acoustic impedance of which can be modified through proportional feedback control, to match a target impedance. However, such impedance matching only occurs over a limited bandwidth around resonance, which can limit its use for the low-frequency equalization of rooms, requiring an effective control at least up to the Schroeder frequency. Previous experiments have shown that impedance matching can be achieved over a range of a few octaves using a simple proportional control law. But there is still a limit to the feedback gain, beyond which the feedback-controlled loudspeaker becomes non-dissipative. This paper evaluates the benefits of using PID control and phase compensation techniques to improve the overall performance of the electroacoustic resonator. More specifically, it is shown that some adverse effects due to high-order dynamics in the moving-coil transducer can be mitigated. The corresponding control settings are also identified with equivalent electroacoustic resonator parameters, allowing a straightforward design of the controller. Experimental results using PID control and phase compensation are finally compared in terms of sound absorption performances. As a conclusion the overall performances of electroacoustic resonators for damping the modal resonances inside a duct are presented, along with general discussions on practical implementation and the extension to actual room modes damping.     

Acoustic radiation force analysis using finite difference time domain method

Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.     

谐振管形状对热声发动机内非线性声场的影响

研究了谐振管一端受活塞声源激励,另一端刚性封闭条件下,管道形状对热声发动机谐振管内部非线性声场的影响。基于流体力学基本方程建立了渐变截面谐振管内一维非线性声场的模型,考虑了黏性耗散及非线性效应的影响。利用伽辽金法数值求解了该模型的速度势方程,分析了谐振管形状、活塞振动速度及激励频率对管内声场的影响。将双曲形、指数形、锥形、正弦形等四种变截面谐振管内的非线性声场与圆柱形直管的情况进行了比较。结果反映了谐振管内声场的压力波动受活塞振动速度及谐振管形状的影响;显示了当活塞振动幅度较大时,谐振管内出现的波形畸变、频率曲线偏移、共振频率滞后等非线性现象;揭示了变截面谐振管在抑制管内的高阶谐波及提高压比等方面的优越性。      

Wave interaction in acoustic resonators with and without hysteresis

Nonlinear interaction of counterpropagating waves in solids is considered by using a general approach taking into account only the cumulative (resonant) nonlinear perturbations giving a nonzero contribution over the period and, consecutively, potentially able to significantly modify the linear solution. Different stress-strain relations are addressed, including those with hysteresis which serve as basic models for the recent acoustic experiments with rock and metals. An important case of the interaction of counterpropagating waves with close amplitudes in a high-Q resonator (bar) with hysteresis is specially addressed and compared with the case of a ring resonator.     

Influence of resonator shape on nonlinear acoustic field in a thermoacoustic engine

The influence of the resonator shape on nonlinear acoustic field in a thermoacoustic engine is studied.The resonator of themoacoustic engine is boundary driving by a piston at one end,and the other end of it is rigid closed.A one-dimensional wave equation that accounts for gas dynamic nonlinearities and viscous dissipation in the resonator is established based on the governing equations of viscous hydromechanics.The nonlinear wave equation is solved using approximate Galerkin method.The nonlinear acoustic field in four different types of shaped resonators including hyperbolical,exponential,conical and sinusoidal are obtained and compared with that of a cylindrical resonator.It is found that the amplitude and waveform of the pressure are strongly affected by the resonator shape,the driving amplitude and the oscillation frequency of the piston.Waveform distortion,resonance frequency shift and hysteresis are observed,when the piston oscillation amplitude is large enough.The advantages of shaped resonator for thermoacoustic engine lie in inhibition of higher order harmonics and improvement of pressure ratio,etc.     

环形ZnO薄膜谐振器的横模抑制与测试分析

采用Tiersten方程研究了环形ZnO薄膜谐振器中横模寄生问题, 获得了环(圆)形薄膜谐振器的横模振动方程, 求得横模位移场解和频率色散方程; 然后采用电磁学模式合成理论进行分析, 发现环形薄膜谐振器横模频率与环形电极的内外径之比a/b有关, 振动模式可由圆形薄膜谐振器横模模式合成得到, 通过控制a/b能够抑制横模模式数和调控基膜频率. 采用外差激光干涉仪和网络矢量分析仪测量并比较了同批次的圆形和环形薄膜谐振器的上电极横模振动图样和电阻抗曲线. 振动图样显示环形薄膜谐振器振动模式可由半径为a和半径为b的圆形薄膜谐振器振动模式合成, 仅存在节圆数大于0的横模振动, 等于0的横模模式被抑制; 电阻抗曲线显示当a/b为0.436时, 环形薄膜谐振器的基频(约1217 MHz)和圆形的(0, 1)模式频率相等. 测量数据验证了模式合成理论的分析结果正确性, 为薄膜谐振器的横模抑制研究提供了理论基础和新方法.     

Research on coupling between thermoacoustic resonance pipe and piezoelectric acoustic source

Piezoelectric loudspeakers have been used in thermoacoustic refrigerators for operating at the high frequency to miniaturize the system. Then the coupling between the piezoelectric loudspeaker and resonance pipe becomes an important factor for improving the performances of the system. By the equivalent circuit model, the expressions of the acoustic output power and electroacoustic transfer efficiency at a low operating frequency are obtained, and then the structures of the piezoelectric loudspeaker and resonance pipe, as well as the operating frequency, are optimized to achieve a high electroacoustic transfer efficiency and a large acoustic output power. It is also shown that when the total reactance of the system equals zero, the resonance frequency of the resonance pipe is the optimized operating frequency and a high acoustic output power can be achieved. However, the highest transfer efficiency and largest acoustic power cannot be obtained simultaneously, therefore a trade-off condition must be adopted.     

Low Mach number analysis of idealized thermoacoustic engines with numerical solution

A model of an idealized thermoacoustic engine is formulated, coupling nonlinear flow and heat exchange in the heat exchangers and stack with a simple linear acoustic model of the resonator and load. Correct coupling results in an asymptotically consistent global model, in the small Mach number approximation. A well-resolved numerical solution is obtained for two-dimensional heat exchangers and stack. The model assumes that the heat exchangers and stack are shorter than the overall length by a factor of the order of a representative Mach number. The model is well-suited for simulation of the entire startup process, whereby as a result of some excitation, an initially specified temperature profile in the stack evolves toward a near-steady profile, eventually reaching stationary operation. A validation analysis is presented, together with results showing the early amplitude growth and approach of a stationary regime. Two types of initial excitation are used: Random noise and a small periodic wave. The set of assumptions made leads to a heat-exchanger section that acts as a source of volume but is transparent to pressure and to a local heat-exchanger model characterized by a dynamically incompressible flow to which a locally spatially uniform acoustic pressure fluctuation is superimposed.     

Evanescent modes and anomalous streaming in a thermoacoustic device

An oil-heated thermoacoustic refrigerator was constructed in order to investigate the use of waste-heat sources to operate a refrigerator. Fluid flows within the resonator in the vicinity of the stack/heat exchanger assemblies were measured through optical means. During the course of the experiment, anomalous centerline steady flows were observed at magnitudes of up to three times the acoustic amplitudes within the resonator of the thermoacoustic device. An evanescent component of the acoustic field was also measured at the same location. An order of magnitude calculation indicates that the body force induced by the evanescent mode is of sufficient magnitude and structure to be the source of the streaming.     

Noise control in enclosures: modeling and experiments with T-shaped acoustic resonators

This paper presents a theoretical and experimental study of noise control in enclosures using a T-shaped acoustic resonator array. A general model with multiple resonators is developed to predict the acoustic performance of small resonators placed in an acoustic enclosure. Analytical solutions for the sound pressure inside the enclosure and the volume velocity source strength out of the resonator aperture are derived when a single resonator is installed, which provides insight into the physics of acoustic interaction between the enclosure and the resonator. Based on the understanding of the coupling between the individual resonators and enclosure modes, both targeted and nontargeted, a sequential design methodology is proposed for noise control in the enclosure using an array of acoustic resonators. Design examples are given to illustrate the control performance at a specific or at several resonance peaks within a frequency band of interest. Experiments are conducted to systematically validate the theory and the design method. The agreement between the theoretical and experimental results shows that, with the help of the presented theory and design methodology, either single or multiple resonance peaks of the enclosure can be successfully controlled using an optimally located acoustic resonator array.     

Tunable bulk acoustic wave resonators with the induced piezoelectric effect in a ferroelectric

An electromechanical model of the piezoelectric effect induced in an acoustic resonator based on a ferroelectric film under the action of a dc or weak ac voltage is developed. The basic equation is obtained by expansion of the free energy in a series with respect to the electric induction and the mechanical deformation. The system of electromechanical equations for variable components of the induction and the mechanical deformation involves all linear terms along with the component of the electrostriction nonlinear with respect to the mechanical deformation. These electromechanical equations made it possible to obtain a one-dimensional approximation for the effective parameters of the material: the piezoelectric modulus and the elastic modulus as a function of the strength of the electric field applied to the acoustic layer. Expressions for the controlled electromechanical coupling coefficient and resonance frequencies of the tunable acoustic resonator are found. It is shown that the most significant parameter responsible for the tuning is the nonlinear electros-triction coefficient M, whose magnitude and sign were evaluated from the available experimental data.     

Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids.

Nonlinear standing waves in a one-dimensional tube are studied numerically by using a finite-difference algorithm. The numerical code models the acoustic field in resonators for homogeneous, thermoviscous fluids. Calculations are performed exclusively in the time domain, and all harmonic components are obtained by one resolution. The fully nonlinear differential equation is written in Lagrangian coordinates. It is solved without truncation. Effects of absorption are included. Displacement and pressure wave forms are calculated at different locations and results are shown for different excitation levels and tube lengths. Amplitude distributions along the resonator axis for every harmonic component are also evaluated. Simulations are performed for amplitudes ranging from linear to strongly nonlinear and weak shock. A very good concordance with classic experimental and analytical results is obtained.