Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber

This paper deals with the application of the concept of targeted energy transfer to the field of acoustics, providing a new approach to passive sound control in the low frequency domain, where no efficient dissipative mechanism exists. The targeted energy transfer, also called energy pumping, is a phenomenon that we observe by combining a pure nonlinear oscillator with a linear primary system. It corresponds to an almost irreversible transfer of vibration energy from the linear system to the auxiliary nonlinear one, where the energy is finally dissipated. In this study, an experimental set-up has been developed using the air inside a tube as the acoustic linear system, a thin circular visco-elastic membrane as an essentially cubic oscillator and the air inside a box as a weak coupling between those two elements. In this paper, which mainly deals with experimental results, it is shown that several regimes exist under sinusoidal forcing, corresponding to the different nonlinear normal modes of the system. One of these regimes is the quasi-periodic energy pumping regime. The targeted energy transfer phenomenon is also visible on the free oscillations of the system. Indeed, above an initial excitation threshold, the sound extinction in the tube follows a quasi-linear decrease that is much faster than the usual exponential one. During this linear decrease, the energy of the acoustic medium is irreversibly transferred to the membrane and then damped into this element called nonlinear energy sink. We present also the frequency responses of the system which shows a clipping of the original resonance peak of the acoustic medium and we finally demonstrate the ability of the nonlinear absorber to operate in a large frequency band, tuning itself to any linear system.     

Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers

In order to enhance the robustness and the energy range of efficiency of targeted energy transfer (TET) phenomena in acoustics, we discuss in this paper about the use of multiple nonlinear membrane absorbers (called nonlinear energy sinks or NES) placed in parallel. We show this way, mainly thanks to an experimental set-up with two membranes, that the different absorbers have additional effects that extend the efficiency and the possibilities of observation of TET. More precisely, we present the different behavior of the system under sinusoidal forcing and free oscillations, characterizing the phenomena for all input energies. The frequency responses are also presented, showing successive clipping of the original resonance peak of the system, and strongly modulated regimes (SMR). A model is finally used to generalize these results to more than two NES and to simulate the case of several very similar membranes in parallel which shows how to extend the existence zone of TET.     

Passive damping enhancement of a two-degree-of-freedom system through a strongly nonlinear two-degree-of-freedom attachment

This work reports on the first experimental study of the broadband targeted energy transfer properties of a two-degree-of-freedom (two-DOF) essentially nonlinear energy absorber. In particular, proper design of the absorber allows for an extended range of energy over which it serves to significantly enhance the damping observed in the structural system to which it is attached. Comparisons of computational and experimental results validate the proposed design as a means of drastically enhancing the damping properties of a structure by passive broadband targeted energy transfers to a strongly nonlinear, multidegree-of-freedom attachment.     

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。      

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.     

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。     

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.     

A monopole-dipole resonance absorber in a narrow waveguide

A sound absorber in a narrow waveguide is considered. The absorber consists of one monopole and one dipole resonator placed in a narrow pipe. The optimum parameters of the resonators that provide for the maximum absorption of acoustic power are determined. Results of an experimental study of a two-resonator absorbing system are presented. A 95% absorption is achieved.     

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.     

The impact of the neck material on the sound absorption performance of Helmholtz resonators

Helmholtz resonators with sound absorption materials filling the neck may have an improved sound absorption capacity. In this work, parallel perforated ceramics with different perforation diameters were installed into the neck of a Helmholtz resonator to improve its acoustic impedance to simultaneously achieve a better acoustic absorption coefficient and a wider absorption bandwidth. An experimental system was built to investigate the effect of the perforation diameters on the sound absorption performance of the resonator. It is found that nonlinear effects near the resonance frequency affect the resonator?s neck mouth impedance and further its sound absorption performance significantly. For frequency range 50–500 Hz, a model of the neck mouth impedance is developed based on a revised Forchheimer relationship. The experimental results are in good agreement with the theoretical model.     

Theoretical modeling and experimental realization of dynamically magnified thermoacoustic-piezoelectric energy harvesters

Conventional thermoacoustic-piezoelectric (TAP) harvesters convert thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous medium. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezoelectric diaphragm, placed at the end of the resonator. In this study, the TAP harvester is coupled with an auxiliary elastic structure in the form of a simple spring–mass system to amplify the strain experienced by the piezoelectric element. The auxiliary structure is referred to as a dynamic magnifier and has been shown in different areas to significantly amplify the deflection of vibrating structures. A comprehensive model of the dynamically magnified thermoacoustic-piezoelectric (DMTAP) harvester has been developed that includes equations of motions of the system?s mechanical components, the harvested voltage, the mechanical impedance of the coupled structure at the resonator end and the equations necessary to compute the self-excited frequencies of oscillations inside the acoustic resonator. Theoretical results confirmed that significant amplification of the harvested power is feasible if the magnifier?s parameters are properly chosen. The performance characteristics of experimental prototypes of a thermoacoustic-piezoelectric resonator with and without the magnifier are examined. The obtained experimental findings are validated against the theoretical results. Dynamic magnifiers serve as a novel approach to enhance the effectiveness of thermoacoustic energy harvested from waste heat by increasing the efficiency of their harvesting components.     

Single half-wavelength ultrasonic particle filter: predictions of the transfer matrix multilayer resonator model and experimental filtration results

The quantitative performance of a "single half-wavelength" acoustic resonator operated at frequencies around 3 MHz as a continuous flow microparticle filter has been investigated. Standing wave acoustic radiation pressure on suspended particles (5-microm latex) drives them towards the center of the half-wavelength separation channel. Clarified suspending phase from the region closest to the filter wall is drawn away through a downstream outlet. The filtration efficiency of the device was established from continuous turbidity measurements at the filter outlet. The frequency dependence of the acoustic energy density in the aqueous particle suspension layer of the filter system was obtained by application of the transfer matrix model [H. Nowotny and E. Benes, J. Acoust. Soc. Am. 82, 513-521 (1987)]. Both the measured clearances and the calculated energy density distributions showed a maximum at the fundamental of the piezoceramic transducer and a second, significantly larger, maximum at another system's resonance not coinciding with any of the transducer or empty chamber resonances. The calculated frequency of this principal energy density maximum was in excellent agreement with the optimal clearance frequency for the four tested channel widths. The high-resolution measurements of filter performance provide, for the first time, direct verification of the matrix model predictions of the frequency dependence of acoustic energy density in the water layer.     

Improving low-frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plate combined with Helmholtz resonators

The traditional Micro-perforated plate (MPP) is a kind of clean and non-polluting absorption structure in the middle and high frequency and has been widely used in the field of noise control. However, the sound absorption performance is dissatisfied at low frequencies when the air-cavity depth is restricted. In this paper, a mechanical impedance plate (MIP) is introduced into the traditional MPP structure and a Helmholtz resonator is attached to the MIP. Mechanical impedance plate (MIP) provides a good absorption at low frequency by using mechanism of mechanical resonance and the acoustic energy is dissipated in the form of heat with viscoelastic material. Helmholtz resonator can fill in the defect of the poor absorption effect between the Micro-perforated plate (MPP) and the mechanical impedance plate (MIP). The acoustic impedance of the proposed sound absorber is investigated by using acoustic electric analogy method and impedance transfer method. The influence of the tube’s length of Helmholtz resonator and the number of Helmholtz resonator on the sound absorption is studied. The corresponding results are in agreement with the theoretical calculation and prove that the composite structure has the characteristics of improving the low frequency sound absorption property.     

Identification of a parametric loudspeaker system using an adaptive Volterra filter

Due to the parametric acoustic array effect in air, the input audible signal of a parametric loudspeaker system can be reproduced with high directivity at the target region. However, the reproduced audible signal suffers from harmonic distortion, which is the by-product of nonlinear interaction between the primary waves. In order to investigate this inherent nonlinear phenomenon, a nonlinear system identification model is developed based on an adaptive Volterra filter. Unlike the conventional loudspeaker, the nonlinear characteristic of a parametric loudspeaker system is dependent on several primary parameters in nonlinear acoustics, which include the initial pressure of the primary waves, the observing distance and angle, as well as ambient temperature and relative humidity. By using a truncated Volterra series up to the 2nd-order kernel, numerical simulations are conducted to develop a system model with one group of parameters and examine the quadratic nonlinear intensity for different parameters’ settings. Experimental measurements, which take into account of emitter’s response, are carried out to verify the modeling result and evaluate the model performance. Based on the Volterra system model, the sound pressure level and the harmonic distortion can be accurately predicted.     

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.     

扬声器异常音的快速检测方法及其实验研究

提出了一种对扬声器声响应中的低阶次谐波失真与高阶次谐波失真和进行综合分析的方法,以实现对扬声器异常音的快速检测。文章分析了扬声器异常音的时域和频域特征,并对人耳听测异常音的机理进行了讨论。通过对扬声器系统Volterra建模并选择连续对数扫频信号作为激励信号,推导出了该模型在此激励下的响应表达式.该表达式揭示了提取各阶冲激响应的方法,由该表达式给出一种可以快速提取各阶次谐波失真的跟踪滤波器,以实现对扬声器异常音的检测。实验室测试和多次工厂生产线测试初步验证了该方法的准确性、快速性和可行性。      

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.     

Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators

Single-degree-of-freedom (SDOF) nonlinear energy sinks (NESs) can efficiently mitigate broadband disturbances applied to primary linear systems by means of passive targeted energy transfer (TET), but for a rather limited range of energies. We demonstrate that the TET can be significantly enhanced for broad range of energies by introducing additional internal degrees of freedom to the NES in a highly asymmetric fashion. Numerical simulations demonstrate that the enhanced performance is due to a positive synergistic effect of the internal degrees of freedom of the proposed NES with highly asymmetric stiffnesses.     

An alternative method to measure the on-axis difference-frequency sound in a parametric loudspeaker without using an acoustic filter

The self-demodulation characteristic of finite-amplitude ultrasonic sound waves can be applied with parametric loudspeaker to reproduce audible sound with highly directivity. But measuring the difference-frequency sound is still a problem due to the spurious sound generated as a result of nonlinearity caused by the product of the primary waves at the receiving system. In this paper, based on the phase-cancellation method and the Gaussian beam expansion technique, an alternative method is proposed to measure the on-axis difference-frequency sound accurately without using any traditional acoustic filter, where the spurious sound can be greatly reduced or even eliminated. The proposed method is more suitable for the case where the piston source in the parametric loudspeaker comprises multiple small piezoelectric transducers (PZTs) and each transducer element in the array may have different frequency response. The validity of the proposed method is confirmed both by simulations and experiments.     

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.