混响声场条件下水声互易传递函数的测量及应用

对不规则的混响声场情况的互易测量方法进行了理论研究,对相关测量误差提出了修正方法。通过测量结果的空间平均和混响环境对声能密度影响的评估,修正了声源体积速度的计算值,并在水中进行了试验验证。经修正后的互易测量结果与正向实测结果基本一致。表明混响声场不影响互易原理有效性的成立,但影响了声源体积速度的计算,进而影响了应用互易原理对传递函数的测量。提出的修正方法在不规则的混响声场情况下简单有效,结论为今后基于互易原理的工程应用提供了参考和依据。      

Application and measurement of underwater acoustic reciprocity transfer functions in reverberant sound field

The reciprocity measurement theory in anomalous reverberant sound fields was investigated.An improved method Was proposed due to the interrelated errors.The source volume velocity Was corrected by spatial average of measurement results and evaluation of the reverberant sound field influence on acoustic energy density.The result was validated in underwater experiment,corrected reciprocity measurement results were almost the same as direct measurement results.It indicates that reverberant sound field does not affect the validitv of the principle,but influences the obtainment of source volume velocity,then influences the measurement of transfer functions with the principle.The proposed method is simple and effective in anomalous reverberant sound fields.The study mav be valuable for the applications which are based on the principle.     

基于声能密度模型的中高频复杂声场预报方法

提出并推导了一种基于声能密度分布方程的声场预报方法。在能量和功率流的本构关系基础上建立声能密度平衡方程。应用直达声场和反射混响声场的叠加原理和边界面散射模型,建立了面向中高频复杂声场细节预报的数值计算方法。通过有限元计算结果在一个简单声场模型上对此方法做了验证,对比结果显示了声能密度法预报有可靠的精度和准确度。      

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.     

一种预测扩散声场在非规则形状刚性壁面附近干涉图样的方法

扩散声场会在反射边界附近形成干涉图样,研究方法包括平面波模型、简正模态分析、渐进模态分析等,但仅适用于尺度远大于声波波长的矩形声腔。提出一种预测扩散声场在非规则刚性壁面结构附近形成的干涉图样的数值方法,表明结构附近“受挡”声压的互谱矩阵取决于:(1)假定该结构在自由空间中振动辐射声音时其表面法向振速到表面及场点声压的边界元系数矩阵;(2)假定结构置于自由空间中且表面刚性时,点声源辐射声波入射到结构表面上产生的散射声场的边界元系数矩阵;(3)扩散声场均方声压。仿真表明,该途径预测的干涉图样与理论值完全吻合。该预测方法还可用于混响环境下声源附近直达声压均方值的空间分布估计,为混响环境下设备的声源定位提供帮助。      

Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part I: Formulation of 1-D and 2-D cases

This paper proposes a hybrid method for the prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the power flow analysis (PFA) algorithm and statistical energy analysis (SEA) coupling concepts. The main part of this method is the application of the coupling loss factor (CLF) of SEA to the boundary condition of PFA in reverberant system. First, for hybrid PFA, the hybrid boundary conditions on 1-D and 2-D cases were derived in the general form. To verify the derived boundary conditions, numerical analyses for each case were performed. The hybrid PFA solutions using derived boundary conditions were compared with the classical PFA solutions with various reverberance factors including the effects of the characteristic length, excitation frequency and group velocity besides damping loss factor of the subsystem. Additionally, the hybrid PFA on 3-D case and the hybrid power flow finite element method (PFFEM) for hybrid PFA of built-up structures are described in the other companion paper.     

Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties

Comparisons between the experimental and predicted sound transmission loss values obtained from statistical energy analysis are presented for two foam-filled honeycomb sandwich panels. Statistical energy analysis (SEA) is a modeling procedure which uses energy flow relationships for the theoretical estimation of the sound transmission through structures in resonant motion. The accuracy of the prediction of the sound transmission loss using SEA greatly depends on accurate estimates of: (1) the modal density, (2) the internal loss factor, and (3) the coupling loss factor parameters of the structures. A theoretical expression for the modal density of sandwich panels is developed from a sixth-order governing equation. Measured modal density estimates of the two foam-filled honeycomb sandwich panels are obtained by using a three-channel spectral method with a spectral mass correction to allow for the mass loading of the impedance head. The effect of mass loading of the accelerometer is corrected in the estimations of both the total loss factor and radiation loss factor of the sandwich panels.     

A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft

This paper describes a hybrid technique that combines Statistical Energy Analysis (SEA) predictions for structural vibration with acoustic modal summation techniques to predict interior noise levels in rotorcraft. The method was applied for predicting the sound field inside a mock-up of the interior panel system of the Sikorsky S-92 helicopter. The vibration amplitudes of the frame and panel systems were predicted using a detailed SEA model and these were used as inputs to the model of the interior acoustic space. The spatial distribution of the vibration field on individual panels, and their coupling to the acoustic space were modeled using stochastic techniques. Leakage and nonresonant transmission components were accounted for using space-averaged values obtained from a SEA model of the complete structural-acoustic system. Since the cabin geometry was quite simple, the modeling of the interior acoustic space was performed using a standard modal summation technique. Sound pressure levels predicted by this approach at specific microphone locations were compared with measured data. Agreement within 3 dB in one-third octave bands above 40 Hz was observed. A large discrepancy in the one-third octave band in which the first acoustic mode is resonant (31.5 Hz) was observed. Reasons for such a discrepancy are discussed in the paper. The developed technique provides a method for modeling helicopter cabin interior noise in the frequency mid-range where neither FEA nor SEA is individually effective or accurate.     

A novel hybrid ES-FE-SEA for mid-frequency prediction of Transmission losses in complex acoustic systems

The widely-used numerical modeling approaches such as the finite element method (FEM) and statistical energy analysis (SEA) often have limited applicability to the transmission loss prediction in mid-frequency range. In this paper, a novel hybrid edge-based smoothed FEM coupled with statistical energy analysis (ES-FE-SEA) method is proposed to further improve the accuracy of “mid-frequency” transmission loss predictions. The application of ES-FEM will “soften” the well-known ‘‘overly-stiff’’ behavior in the standard FEM solution and reduce the inherent numerical dispersion error. While the SEA approach deals with the physical uncertainty in the relatively higher frequency range. The plate of interest is appropriately described by an ES-FEM model, due to its relative robustness to perturbations. Its adjacent reverberation cavities are modeled by employing the SEA approach, because of their high model density. The coupling and interaction between SEA subsystems and the FE subsystem is governed by the “reciprocity relationship” theorem. A standard numerical example for benchmarking is examined and excellent agreement was achieved between the prediction and reference results. The proposed ES-FE-SEA is also verified by various numerical examples. The method is finally applied to the modeling a complicated engineering problem–acoustic fields on both sides of the front windshield in a passenger car.     

Prediction of noise inside an acoustic cavity of elongated shape using statistical energy analyses with spatial decay consideration

In this paper, Statistical Energy Analysis (SEA) is used to predict the interior noise of an acoustic cavity of elongated shape. The disadvantage of the conventional SEA method, which quantifies the response in terms of the energy averaged over each subsystem, is overcome by introducing a one-dimensional spatial decay relation, through which information about the acoustic energy variation in the elongated direction is taken into account. The modified SEA is experimentally validated using a 1:5 scaled space station prototype, having the longitudinal dimension much larger than the cross-sectional dimension. It is also compared with a model reported in the literature. It is shown that, in the region where the acoustic pressure level decays at a constant rate, the two models agree well with each other and are capable of estimating the acoustic pressure variation along the space station cabin. However, near the end walls where the decay rate of the acoustic pressure level is not constant, the proposed model provides better accuracy.     

Acoustic characteristics of a heavy duty vehicle cooling module

Studies dedicated to the determination of acoustic characteristics of an automotive cooling package are presented. A shrouded subsonic axial fan is mounted in a wall separating an anechoic- and a reverberation room. This enables a unique separation of the up- and downstream sound fields. Microphone measurements were acquired of the radiated sound as a function of rotational speed, fan type and components included in the cooling module. The aim of the present work is to investigate the effect of a closely mounted radiator upstream of the impeller on the SPL spectral distribution. Upon examination of the SPL spectral shape, features linked specifically to the source and system are revealed. The properties of a reverberant sound field combined with the method of spectral decomposition permit an estimation of the source spectral distribution and the acoustic transfer response, respectively. Additionally, purely intrinsic acoustic properties of the radiator are scrutinized by standardized ISO methods. A new methodology comprising a dipole sound source is adopted to circumvent limitation of transmission loss measurement in the low frequency range. The sound attenuation caused by the radiator alone was found to be negligible.     

SEA and contribution analysis for interior noise of a high speed train

This paper presents a detailed Statistical Energy Analysis (SEA) and contribution analysis of the interior noise of a high-speed train through extensive simulations and measurements. The SEA model was developed based on the actual geometrical parameters of a benchmark high-speed coach. Sound transmission loss levels of the structural components of the car body, which are required in the SEA model, were tested in a dedicated acoustic laboratory following international standard ISO 140-3:1995. Modal densities of these structural components were derived from measured frequency response functions using the modal counting method. Damping loss factors were obtained using the half-power bandwidth method and the vibration attenuation method. By considering the relationship between sound radiation and power transmission, coupling loss factors between structures and cavities were estimated. Source inputs to the SEA model were derived from field experiment data. Interior noise due to those sources was predicted using the SEA model and the prediction was generally in good agreement with measurement. Contribution analysis was then performed using this validated model through parametric study, and this analysis was further examined experimentally. In conclusion, for the coach that was investigated in this paper, the key factors for interior noise are sidewall vibration, bogie area noise, and floor sound transmission loss. Based on this and other engineering considerations, an interior noise control strategy can be defined.     

An improved model to predict energy-based acoustic parameters in Apulian-Romanesque churches

In this paper an improved model to predict energy relations in churches is proposed. A detailed acoustic survey was carried out of nine Romanesque churches having volumes ranging from 33 000 to 1500 m³. The measured sound level and early/late ratio showed significant correlation with the source-receiver distance, but the comparison with values predicted using theoretical models initially gave unsatisfactory results. The main difference was due to the early energy which was underestimated at points near the source and overestimated at distant points. Barron's revised theory proved to be the most reliable among the analysed models, so, in order to improve its prediction accuracy, a modified early reflected energy component was added to the direct and reverberant sound. The improved model was finally validated and the comparison between predicted and measured values gave good results.     

A note on the modal kurtosis and the concentration factor in reverberation rooms

The effect known as "weak Anderson localization," "coherent backscattering," or "enhanced back-scattering" is a physical phenomenon that occurs in random systems, e.g., disordered media and linear wave systems, including reverberation rooms: The mean square response is increased at the drive point. In a reverberation room, this means that one can expect an increase of the reverberant sound field at the position of the source that generates the sound field. This affects the sound power output of the source and is therefore of practical concern. The relative increase of reverberant energy is described by the concentration factor, which is usually assumed to be 2. However, because of the stronger direct sound field at the source position, it is obviously very difficult to measure this quantity directly under steady-state conditions. A related parameter of crucial importance for the ensemble statistics of responses in rooms is the modal kurtosis, which is usually assumed to be 3. The modal kurtosis is also very difficult to measure directly. This paper presents the results of an indirect experimental estimation of the two parameters.     

Transfer matrix modeling of the vibroacoustic response of multi-materials structures under mechanical excitation

In several automotive and aircraft applications there is a need for simple tools to assess quickly and accurately the performance of sound packages. Statistical energy analysis (SEA) and the transfer matrix method (TMM) are examples of such methods. The used methodology (for modeling sound packages) is well validated for acoustic excitations (airborne). However, a simple and reliable methodology is still lacking for mechanical excitations (structure-borne). This work concentrates on the latter. It presents and compares three different simple approaches to model the vibration and acoustic response of a mechanically excited structure with an added noise control treatment. Various examples are presented to confirm their relevance and accuracy in comparison to more exact and costly methods, such as the finite element method. In particular, it is shown that the TMM with a size correction (FTMM) is accurate enough to eliminate the classical assumption of low coupling classically assumed in SEA modeling of sound packages and/or compute efficiently the structure-borne insertion loss of sound packages used in SEA and FEM models.     

A superdirective array of phase shift sources

A superdirective array of audio drivers is described, which is compact compared with the acoustic wavelength over some of its frequency range. In order to minimize the overall sound power output, and hence reduce the excitation of the reverberant field when used in an enclosed space, the individual drivers are made directional by using phase shift enclosures. The motivating application for the array is the enhancement of sound from a television, in a particular region of space, to aid hearing impaired listeners. The design is initially investigated, using free-field simulations, by comparing the performance of 8 monopoles, 8 phase shift loudspeakers, and a double array of 16 monopoles, with a contrast maximization formulation. The construction and testing of an array of 8 drivers is then discussed, together with its measured response in an anechoic environment. The result of using acoustic contrast maximization is then compared with a least squares formulation, which demonstrates that the performance of the least squares solution can be made similar to that given by acoustic contrast maximization in this application, with a suitable choice of the target field.     

基于混合有限元-统计能量分析的箱梁结构噪声特性分析

为了探讨箱梁的结构噪声辐射规律,提高计算精度及效率,基于混合有限元-统计能量分析理论,建立1/10箱梁有限元-统计能量分析计算模型,并进行模态实验与声学实验验证.在此基础上进行声贡献量以及振动传递规律分析,并与相关文献进行比较.研究结果表明:混合有限元-统计能量分析模型不仅适用于箱梁结构噪声分析,而且在保证计算精度的同...     

Study on the validity region of Energy Finite Element Analysis

The validity domain of Energy Finite Element Analysis (EFEA) is studied in this paper. The validity region and criterion of EFEA are studied theoretically from the formation of reverberant plane wave field, one of the main assumptions of EFEA. The studies are acquired by virtue of the equation of radiative energy transfer method, a similar wave method that can express the direct field and its conversion relationship with reverberant field exactly. The result shows that the SEA criterion of diffuse field derived by Le Bot can be used as a good indicator for the EFEA validity. Numerical simulations on a rectangular plate with different physical parameters are applied to validate the criterion. The validity region and the diagrams of validity of EFEA are assessed and discussed. Some noteworthy conclusions about EFEA are drawn.     

Interaural cross-correlation coefficients in stereo-reproduced sound fields

Interaural cross-correlation coefficients (ICCCs) were measured in stereo-reproduced fields where a KEMAR (Knowles electric manikin for acoustic research) was located. These ICCCs were then compared with those in an ideal, diffuse sound field. The ICCCs in a reverberant field are not reproduced accurately using a conventional two-channel stereo-reproduction technique. In four-channel stereo reproduction, however, the ICCCs can, for the most part, be reproduced accurately as in an ideal, diffuse sound field. Some experimental results are also shown for binaural discrimination of the ICCCs.     

The use of cross-spectral density measurements in partially reverberant sound fields

The cross-spectral densities of sound at two points in a partially reverberant space are shown to be sensitive to the power flow out of the space. A nearly homogeneous sound field is found to possess a co-spectral density which is nearly insensitive to the nature of the field. This spectrum is traditionally obtained as a cross-correlation and its analytical form has been well established. Perhaps less well known is the imaginary part of the cross-spectrum which is shown in this paper to be sensitive to the direction of propagation from a sound scattering enclosure. Specific analytical forms of the spectrum are derived for incidence included within certain cones by using a wavefunction model of the scattered sound field. In some cases the co- and quadrature-spectra are related to each other by the Hilbert transform.