Flexural vibration of perforated plates and porous elastic materials under acoustic loading

This paper presents a method of theoretical treatment of acoustic coupling due to flexural vibration of perforated plates and plates of porous elastic materials. The analytical model is developed by introducing flow continuity at the plate surface in a spatially mean sense and air-solid interaction within the plate material. To demonstrate the method of application, some fundamental acoustic problems based on a classical thin-plate theory are analyzed and discussed in relation to the interactive effect of flexural vibration and plate permeability. For acoustic radiation from a vibrating plate excited by a harmonic point-force, the attenuation effect of power radiation appears at frequencies below the critical frequency of coincidence. In the problem of sound absorption of a perforated plate or a plate of porous elastic material backed by an air layer, as permeability decreases, the effect of plate vibration increases. For perforated absorber systems including plate vibration effects, the trend of variation from ordinary theory depends on plate thickness.     

Sound radiation from perforated plates

A practical engineering noise control measure that can often be used for plate-like structures is to construct them from perforates. This can dramatically reduce the sound radiation from such structures. Here, a prediction model is developed to quantify this effect. It is an extension of Laulagnet's model for the radiation from an unbaffled plate, which expresses the surface pressure difference as well as the plate velocity as a sum over plate modes. The perforation is included in terms of a continuously distributed surface impedance, which for moderately sized holes is predominantly inertial. Results show that the radiation efficiency reduces, not only as the perforation ratio increases but also as the hole size reduces for a given perforation ratio. Experimental validation is given which shows a good agreement with the predictions. An approximate formula is also proposed for the effect of perforation which corresponds well with the analytical calculations up to half the critical frequency and could be used for an engineering application to predict the noise reduction due to perforation. A model for the case of a perforated plate embedded in an equally perforated baffle is also discussed for comparison.     

弯曲振动阶梯圆盘辐射阻抗的计算方法

辐射阻抗是描述声学振动系统声转换效率的一个重要物理量.具有强功率的阶梯圆盘辐射器在流体介质,尤其是在空气中有着重要的应用.但对阶梯圆盘的辐射阻抗而言,运用传统理论计算时,由于辐射面不在同一几何面,积分上下限很难选取而无法计算.本文从辐射声功率角度,基于叠加原理,提出了利用叠加法计算阶梯盘的辐射阻抗.作为算例,文中计算了带有一个阶梯的阶梯盘的辐射阻抗. 关键词： 阶梯圆盘 辐射功率 辐射阻抗 叠加原理     

The characteristics of sound radiation from a cylindrical shell coated with multiple compliant layers

The effect of multiple compliant layers on sound radiation from a finite cylindrical shell immersed in an infinite acoustic medium is studied. The transfer matrix is derived according to the continuous boundary conditions at each adjacent interface of the multi-layer system. With the shell theory and the acoustic wave equation, the theoretical model is developed to estimate the characteristics of sound radiation. The numerical calculation results show that the amount of the acoustic radiation power reduction increases as the wave speed or the density of the compliant layer decreases, and using multi-layer system could be more effective on noise reduction than the corresponding uniform single layer.     

Reduction of acoustic radiation by perforated board and honeycomb layer systems

A perforated system, proposed previously for reducing the radiated sound from a plate at arbitrary frequencies, is applied to three-dimensional problem. Plates are assumed to be supported in a duct of a finite cross-section and excited by a harmonic point force. The sound radiation is investigated from the viewpoint of acoustic power and it is discussed whether the attenuation effect shown previously in the one-dimensional system can be obtained with the three-dimensional system. The effect of support conditions on attenuation characteristics is discussed by using clamped and simply supported circular models. Allowing for the effect, a simply supported rectangular model is studied in detail and its problems are revealed. In order to overcome the problems, a new system including subdivided air cavities in the form of a honeycomb layer instead of a undivided backing cavity is proposed. Each of the honeycomb cells can create local one-dimensional sound fields. Calculated theoretical results are compared to data obtained in a 1/5th scale reverberation chamber. The results for the reduction effect, which are in good agreement, show that the honeycomb layer system can achieve the same reduction of the radiated sound power at arbitrary frequencies as the one-dimensional perforated system.     

Influence of circumferential partial coating on the acoustic radiation from a fluid-loaded shell

Acoustic compliant coatings are a common approach to mitigate the radiation and scattering of sound from fluid-loaded submerged structures. An acoustic compliant coating is a coating that decouples an acoustic source from the surrounding acoustic medium; that is, it provides an acoustic impedance mismatch (different density and speed of sound product). Such a coating is distinct from an ordinary compliant coating in that it may not be resilient in the sense of low stiffness, but still provides an acoustic impedance mismatch. Ideally, the acoustic coating is applied uniformly over the entire surface of the fluid-loaded structure to minimize the acoustic radiation and scattering. However, in certain instances, because of appendages, it may not be practically possible to completely cover the surface of a fluid-loaded structure to decouple it from the adjacent acoustic medium. Furthermore, there may be some inherent advantages to optimizing the distribution of the coating around areas from which the acoustic radiation appears to be dominant. This would be analogous to the application of damping treatment to a vibrating structure in areas where the vibration levels are highest. In the case of the acoustic radiation the problem is more complex because of the coupling between the acoustic fluid and the structure. In this paper, the influence of a partial coating on the acoustic radiation from a fluid-loaded, cylindrical shell of infinite extent and excited by either a line force or an incident plane acoustic wave is examined. The solution to the response and scattered pressure is developed following the procedure used by the authors in previous work on the scattering from fluid-loaded plates and shells. The coating is assumed to be normally reacting providing a decoupling layer between the acoustic medium and the structure; that is, it does not add mass or stiffness to the base structure. The influence of added mass or stiffness of the coating can be included as an added inhomogeneity and treated separately in the solution.     

Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels

This paper experimentally investigates the holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels. The theoretical formulations are based on a semi-empirical approach and the use of Fok’s function to model the acoustic surface impedance. For the high sound level regime, an empirical power law involving three coefficients is adapted. It is shown theoretically and experimentally that these coefficients can lead to optimized absorption performance and particularly, a formula relating the critical Reynolds number (Reynolds number value after which the absorption coefficient decreases with the increase of sound level) and the center-to-center distance between the perforations is derived. It is demonstrated that the first coefficient of the nonlinear acoustic resistance strongly depends on the separation distance between the apertures and decreases with a decrease of this latter distance. Analysis of the data reveals the fact that even with Holes Interaction Effect (HIE), the nonlinear reactance dependence on velocity is still very low compared to the resistance-velocity dependence. Four perforated panels of 1.5 mm thickness with different separation distances between the holes (from widely to closely separation) were built and tested. Experimental results performed with an impedance tube are compared with the described model for HIE. To test the dependence of the coefficients on frequency, the experiments are carried out for two different excitation frequencies (292 Hz and 506 Hz). The results can be used for designing optimal perforated panels for ducts, silencers and for the automotive industry.     

Sound radiation from a vibrating plate with uncertainty

Sound radiation into open space from a vibrating structure has been investigated since Rayleigh. On the other hand the sound power transferring into neighboring reverberant subsystems has also been rigorously studied using statistical energy analysis, particularly for the high frequency range. Falling between the two well-known problems, pressure and intensity fields from the sound radiation have not yet been widely studied using statistical methods. In this paper, the sound radiation from a vibrating thin plate having uncertain dynamic properties is investigated. Estimates are developed for the reverberant vibration field in the uncertain plate subjected to a point-excitation, and for the ensemble average of pressure from the direct field and from the reverberant field, leading to an estimate of the average sound intensity. The power radiated from the plate and the radiation efficiency is also derived. Monte Carlo simulations are conducted with an ensemble of plates with randomly-distributed point masses, and the simulation results compare well with the estimates.     

Some physical insights for active acoustic structure

Active acoustic structure (AAS) proposed in recent years has been viewed as an encouraging approach to actively control sound radiation from vibrating structures. Much work of AAS has been done on theoretical model, arrangement of the secondary panel and error sensing, and experimental investigation of AAS system, but physical mechanisms is little understanding. In this study, under minimization of the total sound power output, the physical mechanism of noise reduction is investigated by analyzing the sound power output change of primary and secondary structures and the distribution of sound intensity. The results show that there are two kinds of energetic behaviors, which includes the suppression of the sound power radiated by the primary panel and absorption of sound power by the primary and secondary panels.     

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.     

掠过流作用下穿孔板的声阻抗

应用三维时域数值方法研究掠过流对穿孔板声阻抗的影响。建立了掠过流作用下穿孔板声阻抗计算的计算流体动力学(CFD)模型,通过时域计算得到掠过流作用下穿孔板的声阻抗,分析结构参数和掠过流马赫数对穿孔板声阻抗的影响。根据计算结果拟合掠过流作用下穿孔板声阻抗的近似表达式,利用获得的穿孔声阻抗新公式预测穿孔管消声器的传递损失,数值预测和实验结果吻合良好。计算结果表明,掠过流对穿孔板的声阻抗和穿孔管消声器的消声性能有明显影响。     

不同声强宽带噪声激励下结构参数对穿孔板消声器吸声特性影响的实验研究

高声压级激励下,由于非线性效应的存在,穿孔板消声器的吸声特性将发生改变,而改变量的大小与穿孔板的结构参数(穿孔率,孔径,板厚)密切相关。本文设计搭建了实验平台来研究结构参数的变化对穿孔板消声器的吸声特性的影响。根据实验结果发现:随着声压级的升高,由于穿孔板结构的非线性加剧,其声阻抗将发生变化,导致穿孔板消声器的吸收峰值降低,但吸收频带却拓宽了;在穿孔率一定的情况下,孔径越小的穿孔板消声器更适合低声压级环境工作;在孔径一定的情况下,穿孔率越低的穿孔板消声器也更适合低声压级环境工作。     

Broadband control of plate radiation using a piezoelectric, double-amplifier active-skin and structural acoustic sensing

The potential of a piezoelectric, double-amplifier active-skin with structural acoustic sensing (SAS) is demonstrated for the reduction of broadband acoustic radiation from a clamped, aluminum plate. The active-skin is a continuous covering of the vibrating portions of the plate with active, independently controllable piezoelectric, double-amplifier elements and is designed to affect control by altering the continuous structural radiation impedance rather than structural vibration. In simulation, acoustic models are sought for the primary and secondary sources that incorporate finite element methods. Simulation indicates that a total radiated power attenuation in excess of 10 dB may be achieved between 250 and 750 Hz with microphone error sensing, while under SAS the radiated power is reduced by nearly 8 dB in the same frequency range. In experiment, the adaptive feed forward filtered-x LMS (least mean square) algorithm, implemented on a Texas Instruments C40 DSP, was used in conjunction with the 6I6O control system. With microphone error sensing, 11.8-dB attenuation was achieved in the overall radiated power between 175 and 600 Hz, while inclusion of SAS resulted in a 7.3-dB overall power reduction in this frequency band.     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

阶梯圆盘的设计及其声参数计算

由薄圆盘改进而来的阶梯型薄圆盘声波辐射器在空气中有着很好的应用,但由于阶梯的存在,需要根据在节线处位移连续、位移斜率连续、剪切力连续以及弯矩连续,加之其边界条件才能推导出频率方程。多一条节线,则多四个方程。变量多,方程系数复杂,频率方程难解。本文以单节线阶梯圆盘为例,提出了一种数值计算方法,编制了计算程序。计算结果与实验测试值符合较好。更进一步,可计算得到阶梯盘的声场分布、辐射阻抗等声学特性。本文为阶梯圆盘的设计和其声学性能的计算提供了一种方法。      

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。      

ACOUSTIC POWER SUPPRESSION OF A PANEL STRUCTURE USING H∞OUTPUT FEEDBACK CONTROL

This paper presents a robust control system design for suppressing the radiated acoustic power emitted from a vibrating planar structure, and spillover effect caused by neglected high-frequency modes. A state-space model of a simply supported panel structure is derived and an output equation is formed based on the one-dimensional PVDF film sensors. An output feedback H_∞control is designed by introducing a multiplicative perturbation which represents unmodelled high-frequency dynamics in the control system. The simulation and experimental results demonstrated significant decrease in sound radiation for the considered structural power modes in control.     

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.     

基于平面声源进行结构声辐射有源控制的实验研究

采用分布式平面声源作为次级声源,对振动钢板的声辐射进行了抵消实验,验证了以往研究中的一系列关键理论。实验研究结果表明:一个平面声源可以控制钢板奇-奇模态的声辐射,两个平面源可以控制结构偶-奇或奇-偶模态的声辐射,同时也可以控制结构奇-奇模态的声辐射;平面声源的面积和布放位置对降噪效果有重要影响,采用单个平面声源控制时,平面声源面积越大,控制效果越好;基于近场声压的误差传感策略是有效可行的,实际中,将近场测量面的声功率作为有源控制的目标函数与总声功率作为目标函数是一致的;控制后远场声压和声强都得到有效降低,部分区域的声能向声源流动,近场声压及声强分布也发生显著变化。