非规则封闭空间声场建模的Chebyshev-变分法及其固有声学特性分析

针对非规则封闭空间声场建模问题,提出了一种基于Chebyshev-变分原理的声场建模方法。该方法首先选取包络非规则声场的矩形空间并将此矩形空间内的声压函数展开成三重Chebyshev级数形式,然后通过坐标变换得到定义域空间中的声场势能和声场动能,最后按照里茨方法对声场的拉格朗日泛函进行求解,得到声场的特征方程并求得声场固有频率和模态。通过与曲面声场的数值结果对比,验证了本建模方法的正确性和有效性。在此基础上研究具有不同倾角的梯形声场固有特性,分析内部凹槽深度对"凹"型声场频率和模态的影响。结果表明,梯形声场模态会随着倾角增大而逐步演变;"凹"型声场低阶频率随凹槽深度的增加而逐渐减小,但第一阶频率却呈现先减小后增大的特点。      

Radiation from finite cylindrical shell with irregular-shaped acoustic enclosure

In practical situations, large machinery is usually placed in an underwater vessel and changes the acoustic enclosure shape into an irregular one. The existence of machinery causes the difficulties in expressing sound transmission and radiation analytically. In this study, the sound radiation of a cylindrical shell excited by an internal acoustic source is modeled and analyzed. The cylindrical shell contains a machine modeled as a rectangular object, which is attached to a shell with a spring-mass system. The acoustic field of the cavity is computed by the integro-modal approach. The effect of object size on the coupling between acoustic mode and structural mode is investigated. The relationship between object volume and sound radiation is also studied. Numerical results show that the existence of objects inside vessels leads to a more effective coupling between the structure and acoustic enclosure than the existence of no objects in a regular-shaped cavity(i.e. empty vessel).     

A finite element method for determining the acoustic modes of irregular shaped cavities

A twenty node, isoparametric acoustic finite element model is developed for analysing the acoustic modes of irregular shaped cavities. The element is first used to analyse a rectangular enclosure. This indicates that good accuracy can be obtained if one element is used between each nodal plane. Experiments are described on a model van enclosure. A finite element analysis of the model shows very good agreement with the measured results.     

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

Prediction of the absorption exponent in rectangular enclosures with a single absorbent boundary

It is known that the classical theory of room acoustics cannot be strictly applied to the study of the sound field in a rectangular enclosure with only five boundaries (i.e., with a single absorbent boundary), as the sound field in the enclosure is not diffuse. A theoretical method is developed for the prediction of the absorption exponent in a rectangular enclosure with a single absorbent boundary, and the absorption exponent is used to describe the exponential decay of the sound energy. The method is based on the radiosity-based theoretical/computer model and is used for diffusely reflecting boundaries. The predicted absorption exponent is compared with the Kuttruff values and the simulation results from Monte-Carlo computations. It is found that the predicted absorption exponent of the proposed method shows better agreement with the simulation results from Monte-Carlo computations than the Kuttruff values. With the more accurately predicted absorption exponent, the slope of the energy decay curve and other acoustic parameters in an enclosure with a single absorbent boundary can be obtained accurately.     

适用于任意形状封闭空间的声场预测相干模型

针对现有几何声学的方法对封闭空间内声场进行预测时在中低频段出现较大误差的问题,该文提出一种近似圆锥声束追踪法和相干反射场理论相结合的声场预测新模型。在近似圆锥声束追踪法基础上,考虑声束轴线在边界多次反射时声压和相位的改变,最后计算不同声波之间的干涉效应,建立一种适用于任意形状封闭空间的声场预测相干模型。利用该模型对某一矩形封闭空间进行声场预测,通过对边界元法、Raynoise软件相干和非相干算法的预测结果和本模型的数值模拟结果对比。结果表明,文中提出的方法和边界元法的计算结果在中低频段非常吻合,两者的计算结果平均绝对误差为1.1 d B。本模型在中低频率下与同样考虑了相位的Raynoise相干算法相比有更好的准确性,在较高频率上,本模型计算结果与Raynoise相干算法计算结果非常吻合。     

Noise transmission from a curved panel into a cylindrical enclosure: analysis of structural acoustic coupling

Much of the research on sound transmission through the aircraft fuselage into the interior of aircraft has considered coupling of the entire cylinder to the acoustic modes of the enclosure. Yet, much of the work on structural acoustic control of sound radiation has focused on reducing sound radiation from individual panels into an acoustic space. Research by the authors seeks to bridge this gap by considering the transmission of sound from individual panels on the fuselage to the interior of the aircraft. As part of this research, an analytical model of a curved panel, with attached piezoelectric actuators, subjected to a static pressure load was previously developed. In the present work, the analytical model is extended to consider the coupling of a curved panel to the interior acoustics of a rigid-walled cylinder. Insight gained from an accurate analytical model of the dynamics of the noise transmission from the curved panels of the fuselage into the cylindrical enclosure of an aircraft is essential to the development of feedback control systems for the control of stochastic inputs, such as turbulent boundary layer excitation. The criteria for maximal structural acoustic coupling between the modes of the curved panel and the modes of the cylindrical enclosure are studied. For panels with aspect ratios typical of those found in aircraft, results indicate that predominately axial structural modes couple most efficiently to the acoustic modes of the enclosure. The effects of the position of the curved panel on the cylinder are also studied. Structural acoustic coupling is found to not be significantly affected by varying panel position. The impact of the findings of this study on structural acoustic control design is discussed.     

随钻声波测井隔声体刻槽影响的数值模拟研究*

针对随钻声波测井中钻铤波干扰以及刻槽后散射波问题，该文 利用时域有限差分法模拟钻铤波在随钻隔声体中的传播规律，首先考察在无限大流体中钻铤波在凹槽分界面处的散射特征，利用波场快照直观显示了钻铤波会有一部分能量在刻槽的固液界面转化为斯通利波。同时在有地层时分别对比了均匀内刻槽和外刻槽对钻铤波的衰减效果，发现在选择均匀内刻槽还是外刻槽时结果不仅与频率范围有关，而且与刻槽的深度也有关系。最后对比了槽宽较大的均匀凹槽隔声体和槽宽较小的渐变凹槽隔声体。可以得出结论，在设计随钻隔声体时，在10 kHz以下选择均匀外刻槽方式相对于内刻槽隔声效果会更好。随着刻槽槽深增加，外刻槽在10 kHz以下相比于内刻槽隔声性能优势更加明显。渐变刻槽在满足衰减钻铤波幅度要求的同时，散射波对后续地层波和斯通利波影响也更小。     

Identification of a dynamical model for an acoustic enclosure using the wavelet transform

This paper presents results of research work in the identification of a dynamical model for an acoustic enclosure, a duct with rectangular cross-section, closed ends, and side-mounted speaker enclosures. An acoustic enclosure is excited randomly and random decrement functions are built to convert the random responses to free acoustic responses. It is shown that the estimation of resonance frequencies is possible using the wavelet transform of the system’s free response. Using a particular form of the son wavelet function, results are improved compared to those obtained with the traditionally Morlet wavelet function. An optimal value of a parameter of the son wavelet function is obtained by minimization of the wavelet entropy. The accuracy of this new technique is confirmed by applying it to a numerical example, and to an acoustic enclosure. The advantage of using the wavelet transform method over the Fourier-based modal analysis that would normally be used for the enclosure modes problem is established.     

Development of a hybrid computer model for simulating the complicated virtual sound field in enclosures

A hybrid computer model, SOFIS, has been developed for the simulation of an enclosed virtual sound field in an arbitrary shaped enclosure. It can be used to calculate the impulse response and acoustical parameters of different positions in a virtual enclosure. This paper describes the way in which SOFIS models the sound source, the receiver and the sound propagation throughout the enclosed space with curved surfaces or barriers. A phase tracing method and the calculation of acoustic indexes are also discussed in this paper.     

Computational studies of steady-state sound field and reverberant sound decay in a system of two coupled rooms

The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thusthey were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.      

A coherent model for predicting noise reduction in long enclosures with impedance discontinuities

A theoretical model has been developed for the prediction of sound propagation in a rectangular long enclosure with impedance discontinuities. Based on the image-source method, the boundaries are assumed to be geometrically reflective. An infinite number of image sources are generated by multiple reflections. The sound pressure of each image is obtained by an approximate analytical solution, known as the Weyl-van der Pol formula. The total sound field is then calculated by summation of the contribution from all images. The phase information of each image and the phase change upon reflection are included in the model. A single change of impedance in a two-dimensional duct is focused on as the fundamental problem of the current study. The diffraction effect at the impedance discontinuity is proved to be insignificant, and it is ignored in the formulation. On the assumption that the diffraction effect is not important, the investigation is moved on to a rectangular long enclosure. Measurements are conducted in two model tunnels to validate the proposed prediction model. The predictions are found to give good approximations of the experimental results. The theoretical model serves as the first attempt to optimize the position and pattern of sound absorption materials in a long enclosure, such as an underground railway station or a building corridor, for the reduction of noise and improvement of sound quality.     

Reduction of radiated exterior noise from the flexible vibrating plate of a rectangular enclosure using multi-channel active control

This study attempted to control the radiated exterior noise from a rectangular enclosure in which an internal plate vibrates by acoustic excitation and noise is thus radiated from that plate. Multi-channel active control was applied to reduce the vibration and external radiation of this enclosed plate. A piezoelectric ceramic was used as a distributed actuator for multiple mode control of the vibration and radiated noise in the acoustically excited plate. To maximize the effective control, an approach was proposed for attachment the piezoelectric actuator in the optimal location. The plate and internal acoustic space in the enclosure are coupled with each other. This will change dominant frequency characteristics of the plate and, thus, those of the externally radiated noise. Active noise control was accomplished using an accelerometer attached to the plate and a microphone placed adjacent to that plate as an error sensor under acoustic excitation of sine wave and white noise. It was found that the control of radiated external radiation noise requires a microphone as an error sensor, a sound pressure sensor due to vibration of the plate, differences in the dominant frequency of externally radiated noise, and complex vibration modes of the plate.     

New modeling method and mechanism analyses for active control of interior noise in an irregular enclosure using piezoelectric actuators

A new modeling method is developed in this paper for the active minimization of noise within a three-dimensional irregular enclosure using distributed lead zirconate titanate piezoelectric (PZT) actuators, and the control mechanisms for irregular enclosure are analyzed. The irregular enclosure is modeled with four rigid walls and two simply supported flexible panels, and PZT actuators are bound to one of the flexible panels. The process of the new modeling method is as follows. First, the modal coupling method is used to establish the motion equations, which contain important coefficients such as modal masses and modal coupling coefficients, etc., of acoustic-structural-piezoelectric coupling system. Then, the acoustic modes and the modal masses of irregular enclosure are calculated by numerical methods. Last, the modal coupling coefficients in motion equations are calculated according to the numerical results of the acoustic modes of irregular enclosure and the modes of two panels. The validity of this modeling method is verified by a regular hexahedron enclosure. Two cost functions are applied to this model. With the two cost functions, good results are obtained in minimizing the sound-pressure level (SPL) within irregular enclosure according to numerical investigations. By comparing the results obtained under controlled and uncontrolled states, the control mechanisms of the system are discussed. It is found that the control mechanisms vary with disturbance frequencies. At most disturbance frequencies, the SPL within enclosure is reduced by restructuring the modes of two panels simultaneously. When the disturbance frequency comes close to one of the natural frequencies of panel a, the dominant mode of panel a is suppressed, while the modes of panel b are reconstructed. While the disturbance frequency is near one of the natural frequencies of panel b, the modes of two panels are restructured at the same time.     

Virtual sensors for active noise control in acoustic-structural coupled enclosures using structural sensing: robust virtual sensor design

The work was aimed to develop a robust virtual sensing design methodology for sensing and active control applications of vibro-acoustic systems. The proposed virtual sensor was designed to estimate a broadband acoustic interior sound pressure using structural sensors, with robustness against certain dynamic uncertainties occurring in an acoustic-structural coupled enclosure. A convex combination of Kalman sub-filters was used during the design, accommodating different sets of perturbed dynamic model of the vibro-acoustic enclosure. A minimax optimization problem was set up to determine an optimal convex combination of Kalman sub-filters, ensuring an optimal worst-case virtual sensing performance. The virtual sensing and active noise control performance was numerically investigated on a rectangular panel-cavity system. It was demonstrated that the proposed virtual sensor could accurately estimate the interior sound pressure, particularly the one dominated by cavity-controlled modes, by using a structural sensor. With such a virtual sensing technique, effective active noise control performance was also obtained even for the worst-case dynamics.     

Theory and calculation for acoustic radiation mode of weak coupled enclosure

Active structural acoustic control(ASAC)is an efficient method in acoustic radiation control of coupled enclosure.In the past research of ASAC,the concept of "acoustic radiation mode(ARM)of coupled enclosure"was proposed,which was a set of basis functions of structural mode amplitude.However,there was an incompatibility with the ARM definition in free space radiation case which was a set of basic functions of normal velocity or pressure on the vibrating surface.Also,there was severe inconvenience for application as structural modes were required while accurate and useful structural modes were difficult to be extracted in practice.To overcome these problems,by analogy to ARM theory of free space,the acoustic potential energy was expressed in quadratic form of normal velocity on coupling surface and ARM of coupled enclosure was redefined.Furthermore,theoretic derivation showed that ARM of coupled enclosure could be replaced simply by corresponding acoustic mode projection of enclosure when the coupling surface was discretized into equal size elements.Therefore,the ARM theory of coupled enclosure which was consistent with that of free space and convenient for application was formed.Finally,numerical calculation was performed and the results proved that the presented theory was very efficient in ARM calculation of coupled enclosure and ASAC.     

封闭腔体噪声控制中亥姆霍兹共振器的优化设计方法

提出用亥姆霍兹共振器控制声腔内噪声时计算共振器最优阻尼比和最优工作带宽的理论公式,并进行实验验证。首先,建立共振器与待控腔体的声学耦合方程,以最小化腔体内目标声压幅值为参考,对共振器的阻尼比和工作带宽进行理论分析,求出最优阻尼比和最优工作带宽的计算公式。接着,提出在声腔噪声控制中使用最优亥姆霍兹共振器的实施步骤。最后,以一维声学腔体内的噪声为控制对象,通过对比控制前后的理论结果与实测数据,验证最优阻尼比和最优工作带宽的理论公式。结果表明,本文开发的亥姆霍兹共振器优化设计方法能准确地预报共振器的最优阻尼比与最优工作带宽,在声腔中低频噪声控制中有广泛的应用前景。      

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。      

The prediction of speech intelligibility in underground stations of rectangular cross section

Long enclosures are spaces with nondiffuse sound fields, for which the classical theory of acoustics is not appropriate. Thus, the modeling of the sound field in a long enclosure is very different from the prediction of the behavior of sound in a diffuse space. Ray-tracing computer models have been developed for the prediction of the sound field in long enclosures, with particular reference to spaces such as underground stations which are generally long spaces of rectangular or curved cross section. This paper describes the development of a model for use in underground stations of rectangular cross section. The model predicts the sound-pressure level, early decay time, clarity index, and definition at receiver points along the enclosure. The model also calculates the value of the speech transmission index at individual points. Measurements of all parameters have been made in a station of rectangular cross section, and compared with the predicted values. The predictions of all parameters show good agreement with measurements at all frequencies, particularly in the far field of the sound source, and the trends in the behavior of the parameters along the enclosure have been correctly predicted.     

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.