Comparison of various algorithms for improving acoustic attenuation performance and flow characteristic of reactive mufflers

The parametric optimization of the reactive mufflers is researched by numerical analysis, regarding the performance of the acoustic and flow fields synthetically. The finite element method, based on the Helmholtz equation and the Navier–Stokes equation respectively, is utilized in the analysis of the acoustic and flow fields. And the initial and boundary conditions are set up in the physical fields respectively. The weighting multi-objective function about acoustic and flow fields is formulated. In addition, the optimization results of multidisciplinary, obtained by the Nelder Mead algorithm (NMA) based on the sensitivity analysis, the Monte Carlo algorithm (MCA) and Genetic Algorithm (GA) based on the random sampling, are analyzed comparatively. The optimization results indicate that the NMA can maximize the transmission loss (TL) and minimize the pressure drop with the given weight factor. Finally, numerical optimization examples confirm the validity and reliability of the proposed optimization method in the acoustic-flow field.     

Enhancing micro-perforated panel attenuation by partitioning the adjoining cavity

The sound attenuation performance of micro-perforated panels (MPP) with adjoining air cavity is investigated for a plenum. The sound field inside of a plenum is compared for two cases. In the first case, the plenum is treated with an MPP and adjoining air cavity without any partitioning. For the second case, the adjoining air cavity is partitioned into a number of sub-cavities. The resulting sound pressure fields indicate that partitioning the adjoining air cavity increases the overall sound attenuation due to the MPP by approximately 4 dB. The explanation for this phenomenon was investigated by measuring the sound pressure level on planes in front of the MPP. Additionally, boundary element analyses were conducted to simulate the effect of the MPP and adjoining cavity with and without partitioning on the sound field in the plenum. It was demonstrated that a MPP can be modeled as a transfer impedance and that partitioning the adjoining cavity enhances attenuation to acoustic modes that propagate transverse to the MPP.     

Disorder in a periodic Helmholtz resonators array

This paper considers the disorder in a periodic duct–resonator system. The transfer matrix method is used to investigate wave propagation in the duct. Two cases are investigated: the disorder in periodic distance and the disorder in the geometries of Helmholtz resonators. Different from the original attenuation characteristic brought about by pure periodic system, it is found that the disorder in the geometries of resonators with the periodic distance being kept unchanged provides a useful way for the design of such a system to achieve a relatively wide noise attenuation band and to track some narrow noise peaks within it.     

Feasibility of applying micro-perforated absorbers in acoustic window systems

The paper examines the feasibility of using transparent micro-perforated absorbers (MPA) in a window system to allow noise attenuation whilst at the same time maintaining high levels of comfort ventilation and daylighting. The underlying theory for micro-perforated panels and membranes and the application in silencers is presented. Experiments have been performed between a semi-anechoic and a reverberant chamber using a standard window mock-up, and the effectiveness of MPA has been demonstrated. With a constant air backing, MPA are more effective with a wider ventilation path. With an air flow of up to 2 m/s the performance of the MPA remains unchanged. Current results are based on readily available materials and relatively simple configurations, but the theoretical analysis suggests possibilities for increasing the noise reduction and widening the frequency range by using more strategically designed materials and configurations.     

阻抗复合消声器声学性能有限元预测方法及分析

为计算和分析具有复杂结构的阻抗复合式消声器的宽频消声性能,建立了一种高效声学有限元方法,给出了不同边界条件下的边界积分处理细节,得到有限元全局系数矩阵表达式,设计出计算程序框架以实现这些算法,其求解规模和计算速度与商业软件相比有优势。为计算阻抗复合式消声器的传递损失,通过阻抗管测量和数据拟合得到了吸声材料声学特性的经验公式。计算和测量了两通穿孔阻抗复合式消声器的传递损失,二者良好的吻合验证了声学有限元方法和计算程序的正确性。研究表明,插管长度影响消声器在中高频段的消声特性,右侧隔板上穿孔会消除共振峰,中高频消声性能随着出口管穿孔率的增加而提升。     

水介质管路弹性背腔微穿孔消声器的传递损失特性

为抑制水介质管路系统低频噪声,兼顾结构的紧凑性,提出弹性背腔微穿孔管路消声结构,弹性管壁为橡胶帘线复合材料,并推导了传递损失的数值解法。首先,基于Biot-Allard多孔弹性理论,将弹性微穿孔板等效为弹性多孔材料;然后,利用双尺度法建立帘布的周期性代表单元,求得其刚度矩阵;接着,基于分层理论,建立弹性管壁的多层复合材料模型,并与内部声场耦合计算,得到弹性背腔微穿孔管路消声器的传递损失。在水介质驻波管中,利用双声源法测量弹性背腔微穿孔管路消声器样机的传递损失曲线,并与扩张式管路消声器和刚性背腔微穿孔管路消声器进行对比,理论结果与试验结果吻合良好。研究表明,弹性背腔微穿孔管路消声器属于反射耗散复合式消声器,具有低频域、宽频带的消声特性。样机B2在40~300 Hz和40~1200 Hz频段内的传递损失分别为36 dB和30 dB,而相同尺寸扩张式消声器在对应频段的传递损失分别为7 dB和11 dB。     

Sound absorption of a double-leaf micro-perforated panel with an air-back cavity and a rigid-back wall: Detailed analysis with a Helmholtz-Kirchhoff integral formulation

So far the electro-acoustical equivalent circuit analysis has been widely used to analyse micro-perforated panel (MPP) absorbers, however, as for the double-leaf MPP the equivalent circuit analysis inevitably includes an approximation. In this paper, the sound absorption characteristics of a double-leaf MPP absorber backed by a rigid wall are analysed by wave theory using Helmholtz-Kirchhoff integral formulation to obtain a strict solution. The present wave theory is experimentally validated with existing measured results. The theory is also compared with the equivalent circuit solutions so that the differences between the two theories appear and the effect of the approximation is clarified. The comparison shows that the difference mainly appears in the vicinity of the resonance peaks: the differences occur in the resonance frequencies and the absorption coefficient at frequencies between the two resonance peaks.     

Design of a single layer micro-perforated sound absorber by finite element analysis

Micro-perforated sound absorbers with sub-millimeter size holes can provide high absorption coefficients. This paper presents results of work on the development of an effective single layer micro-perforated sound absorber from the commercial composite material Parabeam^® with micro diameter holes drilled on one side. Parabeam^® is used as a structural material made from a fabric woven out of a E-glass yarn and consists of two decklayers bonded together by vertical piles in a sandwich structure with piles (thick fibers) woven into the decklayers. The paper includes, the analytical model developed for prediction of absorption coefficients, finite element solution using commercial software MSC.ACTRAN and experimental results obtained from impedance tube measurements. A simple optimization is performed based on the developed models to obtain an efficient absorber configuration. It has been anticipated that several different and interesting applications can be deduced by combining structural and sound absorption properties of this new micro-perforated absorber.     

面向微穿孔板吸声结构和吸声特性混合设计的软件平台

微穿孔板吸声结构是由微穿孔板与板后空腔组成的共振吸声结构,被认为是继多孔吸声材料之后发展起来的最有吸引力的吸声结构,其吸声特性与结构参数孔径d、板厚t、孔距b及空腔深度D有关,如何按需设计一个有效的微穿孔板吸声结构已成为目前研究的热点。本文从微穿孔板吸声结构和吸声特性混合设计的角度出发,使用面向对象的编程语言C++开发了微穿孔板吸声结构设计平台。与以往设计方法不同,本文开发的软件平台综合考虑了结构参数和吸声特性参数两方面的限制,根据实际应用要求平衡微穿孔板吸声结构的最大吸声系数与吸声带宽之间的制约关系,并以饱满的吸声曲线为目标,提供满足混合设计要求的优化结构参数。     

Numerical studies on venting system with multi-chamber perforated mufflers by GA optimization

Research on new techniques of perforated silencers has been well addressed and developed; however, the research work in shape optimization for a volume-constrained silence requested upon the demands of operation and maintenance inside a constrained machine room is rare. Therefore, the main purpose of this paper is to not only analyze the sound transmission loss of a multi-chamber perforated muffler but also to optimize the best design shape under space-constrained condition.In this paper, both the generalized decoupling technique and plane wave theory are used. The four-pole system matrix in evaluating the acoustic performance of sound transmission loss (STL) is also deduced in conjunction with a genetic algorithm (GA). To demonstrate the precision of the tuning ability in a muffler, various targeted pure tones are proposed in numerical cases. Results reveal that the maximal acoustical performance precisely occurred in the desired frequency. Furthermore, a noise reduction with respect to full-band exhausted noise emitted from a diesel engine is also introduced and assessed. To achieve a better optimization in GA, several test parameter values were used. Before a GA operation can be carried out, the accuracy of the mathematical models have to be checked by experimental data.The optimal result in eliminating full-band noise reveals that the overall noise reduction of a multi-chamber muffler can achieve 68 dB under space-constraint conditions. Consequently, the approach used for the optimal design of the STL proposed in this study is indeed easy, economical and quite effective.     

多层微穿孔板结构声学性能计算方法对比分析

计算多层微穿孔板结构声学特性方法传统主要用声电类比法,目前出现阻抗转移法和传递矩阵法,对比分析这三种计算方法,同时进行相应的实验验证。结果表明:阻抗转移法和传递矩阵法实质上是相同的,这两种方法计算结果与实验结果吻合良好。声电类比法在空腔较大时计算结果偏离实验值,原因是声电类比法采用集总参数分析,计算多层结构时,空腔单元只考虑声顺,忽略声质量,导致误差。阻抗转移法和传递矩阵法不存在这一误差,计算准确。     

Continuation of periodic solutions in the waveguide array mode-locked laser

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.     

阻性管道消声器消声量方程的一个新算法

将阻性管道消声器消声量特征方程（组）转化为常微分方程（组），由此给出消声量计算的一个新方法。该方法毋需迭代因而不存在计算稳定性问题，计算量小，初值的迭取也很简单，适合于扁矩形、任意矩形及圆形等各种截面管道消声器，尤其对多变量、考虑平均流影响的情形更为有效。     

Experimental study on variation of acoustical resonance frequency of duct with orifice depending on periodic motion

Recently, a linear compressor has been actively developed to improve the energy efficiency of home appliances, such as refrigerators. Unlike a reciprocating compressor, the suction part of a linear compressor is periodically moving. Therefore, the suction valve and the muffler constituting the suction part are periodically moving. However, up to now, there has been no research into the characteristics of the sound propagation in a periodically moving acoustic system. Thus, in this study, characteristics of sound propagation in a periodically moving acoustic system were investigated for the first time. Among a variety of acoustic filters used in a suction muffler, the change in the orifice impedance has been observed because this change is considered to be easily affected by periodically moving. Due to difficulty in measuring the orifice impedance in a periodically moving acoustic system, the change in the orifice impedance was predicted from the change in the input impedance of the suction muffler that included orifice. The experiments were carried out while changing the diameter and the pattern of orifice as well as length of the duct. As a result of experiments, the impedance of periodically moving orifice was changed depending on diameter, pattern of orifice and frequency band. Therefore, if periodically moving orifice was used to design a suction muffler in linear compressor or acoustic system, the change in the orifice impedance should be taken into consideration.     

Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs

Using a periodic expansion by means of the Bloch theorem, the flexural vibration band gaps are studied in a thin plate with two-dimensional ternary locally resonant structures, i.e. a thin epoxy plate containing a periodic square array of lead discs hemmed around by rubber. The full band gaps of flexural vibration in the thin plate are obtained within which sound and vibration will be forbidden. The numerical results are used to show how the width of the first full band gap depends on the radius ratio of lead disc to hemmed disc, filling fraction, lattice constant (distance between the centers of the nearest lead discs) and thickness of the thin plate. It is observed that the gap width can be changed a lot by modulating these physical parameters.     

A generalized scheme for analysis of multifarious commercially used mufflers

Commercial automotive mufflers are often too complex to be broken into a cascade of one-dimensional elements with predetermined transfer matrices. The one-dimensional (1-D) scheme presented in this paper is based on an algorithm that uses user-friendly visual volume elements along with the theory of transfer matrix based muffler analysis. This work attempts to exploit the speed of the one-dimensional analysis with the flexibility, generality and user-friendliness of three-dimensional analysis using geometric modeling. A code based on the developed algorithm has been employed to demonstrate the generality of the proposed method in analyzing commercial mufflers by considering three very diverse classes of mufflers with different kinds of combinations of reactive, perforated and absorptive elements. Though the examples used in the paper are not very complex for they are meant to be just representative cases of certain classes of mufflers, yet the algorithm can handle a large domain of commercial mufflers of high degree of complexity. Results from the present algorithm have been validated through comparisons with both the analytical (plane wave based) and the more general, three-dimensional FEM based results. The forte of the proposed method is its power to construct the system matrix consistent with the boundary conditions from the geometrical model to evaluate the four-pole parameters of the entire muffler and thence its transmission loss, etc. Thus, the algorithm can be used in conjunction with the transfer matrix based muffler programs to analyze the entire exhaust system of an automobile.     

Sound transmission across orthotropic laminates with a 3D model

This investigation examines the propagation of elastic waves in orthotropic materials to explain the sound insulation of FRP (Fiber Reinforced Plastics). The mechanical characteristics of an orthotropic material generally require nine independent parameters: three Young’s moduli, three shear moduli and three Poisson’s ratios. Three-dimensional analysis is performed with the elastic wave equations of an orthotropic material. The transfer matrix method which expresses the relationship between stress and velocity is adopted to calculate the sound transmission loss across an orthotropic material. Further, the transfer matrix method can only be calculated under the continuous boundary condition in the interface of each FRP layer. The boundary conditions which are indicated above are velocity and stress. The numerical results are compared with the experimental results. Additionally, along with varying material properties such as Young’s modulus, the acoustical properties of the orthotropic material are explained and discussed later.     

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.     

A note on the prediction method of reverberation absorption coefficient of double layer micro-perforated membrane

The absorption performance of micro-perforated absorber (MPA) has been usually estimated by equivalent circuit (EC), however, it has been noted that the predicted absorption coefficient by EC does not agree completely with the experiment in some frequency range. Hence impedance transfer method (ITM) is adopted to predict the reverberation absorption coefficient of a double layer micro-perforated membrane (MPM) structure. Experimental studies show that the prediction of ITM is better than that of EC.     

穿孔率和穿孔直径耦合下微穿孔板吸声体整体吸声性能

微穿孔板几何参数的耦合性及其对整体吸声性能的影响,对于设计微穿孔板吸声体和优化其工作性能具有指导作用。根据微穿孔板吸声体基本理论,研究了穿孔率和穿孔直径双参数耦合作用下微穿孔板吸声体的整体吸声性能。穿孔率和穿孔直径之间的耦合性与其本身取值密切相关,而与板厚和板后腔深无明显关系;在穿孔率-穿孔直径参数域上,吸声体存在吸声系数为1.0的吸收峰,整体吸声性能随穿孔率或穿孔直径从小到大变化,呈现出先增强后减弱的变化趋势。该结论能够准确解释微穿孔板受粉尘污染后吸声性能的变化规律和演变路径。论文的工作为设计微穿孔板吸声体提供了一种新的理论依据和实施方法。