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.     

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时提高了计算效率;在随机激励下,箱梁顶板和左右翼板的声贡献量高达87.3%,底板和腹板的声贡献量仅为13.7%;箱梁结构各子系统声贡献量规律与箱梁结构各子系统的振动大小规律保持一致。     

怠速工况下燃油系统的噪声评价和改善*

在实车怠速工况下的噪声振动性能评价过程中,燃油系统是发动机诸多子系统当中一个重要的声源。针对这一子系统产生的车内脉动噪声偏大的问题,总结出了对燃油类液体的脉动噪声振动控制机理、原因及诊断方法。首先,采用在燃油轨内追加阻尼器的方案很好地抑制了谐频噪声;然后,从燃油泵这一主要激振源出发,提出了设定燃油泵单品噪声振动、声品质等目标值的策略,即从源头上控制关键产品的噪声性能。在此基础之上,与之相应的解决方案实施之后,怠速工况下的车内噪声提升到了较好的水平,而且,燃油系统噪声的主观评价结论也认为得到了明显改善。     

Mathematical model for characterizing noise transmission into finite cylindrical structures

This work presents a theoretical study of the sound transmission into a finite cylinder under coupled structural and acoustic vibration. Particular attention of this study is focused on evaluating a dimensionless quantity, "noise reduction," for characterizing noise transmission into a small cylindrical enclosure. An analytical expression of the exterior sound pressure resulting from an oblique plane wave impinging upon the cylindrical shell is first presented, which is approximated from the exterior sound pressure for an infinite cylindrical structure. Next, the analytical solution of the interior sound pressure is computed using modal-interaction theory for the coupled structural acoustic system. These results are then used to derive the analytical formula for the noise reduction. Finally, the model is used to predict and characterize the sound transmission into a ChamberCore cylindrical structure, and the results are compared with experimental data. The effects of incidence angle and internal acoustic damping on the sound transmission into the cylinder are also parametrically studied.     

Application of a Bayesian algorithm for the Statistical Energy model updating of a railway coach

The classical statistical energy analysis (SEA) theory is a common approach for vibroacoustic analysis of coupled complex structures, being efficient to predict high-frequency noise and vibration of engineering systems. There are however some limitations in applying the conventional SEA. The presence of possible strong coupling between subsystems and the lack of diffuseness result in a significant uncertainty. This is the main motivation for the present study, where a procedure to update SEA models is proposed. The proposed procedure is the combination of the classical SEA method and a Bayesian technique. Due to reasons such as finding a limited number of important parameters, using a limited search range, avoiding matrix inversion and taking the effect of noise into account, the proposed strategy can be considered as a proper alternative to the experimental SEA approach. To investigate the performance of the proposed strategy, the SEA model updating of a railway passenger coach is carried out. First, a sensitivity analysis is carried out to select the most sensitive parameters of the SEA model. For the selected parameters of the model, prior probability density functions are then taken into account based on published data on comparison between experimental and theoretical results, so that the variance of the theory is estimated. The Monte Carlo Metropolis Hastings algorithm is employed to estimate the modified values of the parameters. It is shown that the algorithm can be efficiently used to update the SEA models with a high number of unknown parameters.     

Investigation of structural response and noise reduction of an acoustical enclosure using SEA method

Noise reduction capability of acoustical enclosures has been extensively investigated and is commonly quantified by noise reduction. Although much work has been done in predicting the noise reduction by using statistical energy analysis (SEA) method, discrepancy often exists between the predicted and measured results, especially at the low and intermediate frequencies. This is largely due to the fact that some physical mechanisms which affect the prediction of noise reduction were not addressed in the available SEA models. In this paper, the sources of the discrepancy were identified by investigating the limitation of SEA for energy transfer in the entire frequency range and the effect of structural–structural coupling, acoustical–structural coupling on the prediction of noise reduction. An improved SEA model including the non-resonant response and more accurate transmission coefficient of finite panels is presented. Finally, the predicted structural response and noise reduction of an acoustical enclosure were compared with measured results, and the improved agreement between the prediction and experiment was observed.     

STATISTICAL ENERGY ANALYSIS OF COUPLED PLATE SYSTEMS WITH LOW MODAL DENSITY AND LOW MODAL OVERLAP

Finite element methods, experimental statistical energy analysis (ESEA) and Monte Carlo methods have been used to determine coupling loss factors for use in statistical energy analysis (SEA). The aim was to use the concept of an ESEA ensemble to facilitate the use of SEA with plate subsystems that have low modal density and low modal overlap. An advantage of the ESEA ensemble approach was that when the matrix inversion failed for a single deterministic analysis, the majority of ensemble members did not encounter problems. Failure of the matrix inversion for a single deterministic analysis may incorrectly lead to the conclusion that SEA is not appropriate. However, when the majority of the ESEA ensemble members have positive coupling loss factors, this provides sufficient motivation to attempt an SEA model. The ensembles were created using the normal distribution to introduce variation into the plate dimensions. For plate systems with low modal density and low modal overlap, it was found that the resulting probability distribution function for the linear coupling loss factor could be considered as lognormal. This allowed statistical confidence limits to be determined for the coupling loss factor. The SEA permutation method was then used to calculate the expected range of the response using these confidence limits in the SEA matrix solution. For plate systems with low modal density and low modal overlap, relatively small variation/uncertainty in the physical properties caused large differences in the coupling parameters. For this reason, a single deterministic analysis is of minimal use. Therefore, the ability to determine both the ensemble average and the expected range with SEA is crucial in allowing a robust assessment of vibration transmission between plate systems with low modal density and low modal overlap.     

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.     

Non-resonant sound transmission through double walls using statistical energy analysis

Although SEA is a suitable framework for predicting sound transmission through double walls it has been found that the standard method of computing the non- resonant coupling loss factor from a room to cavity underestimates the coupling. A revised model for computing this coupling loss factor is presented which gives much better agreement with measured data. This allows better predictions to be made of sound transmission through lightweight double walls.     

SOUND TRANSMISSION THROUGH ELASTOMERIC BULB SEALS

The sound barrier performance of elastomeric vehicle weather seals was investigated. Experiments were performed on a single bulb seal specimen using a reverberation room method. The seal wall velocity was measured using a laser Doppler vibrometer. The sound pressure near the velocity measurement location was measured simultaneously, which allowed the sound intensity on both sides of the seal and the sound transmission loss to be determined. The vibration response and the sound transmission loss of the bulb seal were then computed using finite element analysis. Acoustic-structure interactions were considered for a partially coherent spatially distributed pressure excitation. The experimental data obtained using the reverberation room method allowed the validation of the numerical models. The resonance frequency due to the mass-air-mass mode of vibration was accurately predicted. The model was then used to numerically investigate the influence of various design parameters. It was found that the elastic modulus significantly affects the bulb seal resonance frequency, and that the loss factor of the material has major effects on the sound transmission loss around resonance.     

The prediction of sound transmission through buildings using statistical energy analysis

Measurements were carried out on a building to evaluate the uses of statistical energy analysis for determining sound transmission performance. Coupling loss factors were measured and compared with predicted values. It was found that, in general, good agreement was obtained. The coupling loss factors were also used to calculate the sound pressure level, or surface velocity, of each subsystem in the building for a number of different sources. Comparison with the measured results gave an average error of 4 dB. Some large errors were obtained but these were due mainly to the omission of airborne flanking paths from the SEA model or due to the breakdown of the theory for specific coupling loss factors.     

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.     

Passive and active interior noise control of box structures using the structural intensity method

This paper presents passive and active vibro-acoustic noise control methods for attenuating the interior noise level in box structures which can be an analogy of cabins of vehicle and aircraft. The structural intensity (SI) approach is adopted to identify the predominant vibration panels and interior noise sources for box structures. In the study, the finite element method is used to determine the structural vibration and structural intensity in the box surfaces. According to structural intensity vectors plot and structural intensity stream lines presentation, the possible effective control positions where the dampers may be attached and the active control forces may act to reduce vibration and interior noise, are identified. From the study, it can be demonstrated that the structural intensity approach and stream line presentation are possible methods for identifying the vibro-acoustic interior noise source and predominant panels which may be modified to reduce the interior noise level. The structural intensity methodology, passive and active noise control results can be extended to the further study of the vibration and interior noise control of actual cabins of vehicles and aircraft.     

有限元-统计能量分析法的拖拉机驾驶室噪声研究*

对某拖拉机驾驶室内中频噪声进行预测,建立了拖拉机驾驶室FE-SEA(有限元统计能量分析)混合模型,通过理论计算和试验方法获取驾驶室结构内损耗因子等数据；加载振动和噪声激励后进行有限元-统计能量分析联合仿真,将仿真获取的驾驶室声压级与实测数据进行对比,分析对比表明该模型在中频段利用FE-SEA混合法分析所得结果与试验测试值拟合程度较高,分析各子系统对驾驶室声腔的能量贡献度,确定对驾驶室噪声贡献较大的子系统,针对性对驾驶室声学包进行整改,获得一定降噪效果。     

Frequency average loss factors of plates and shells

This paper describes a thorough investigation of the measurement of frequency band average loss factors of structural components for use in the statistical energy analysis (SEA) method of computation of vibration levels. The “traditional” method of measurement is to excite the structure by a random force having a flat spectral density in the frequency band of interest. The force is then cut off and the decay of the modes excited in the band is noted. The average loss factor is deduced from the decay curve. The alternative energy method is the subject of this study. In this test the power input from the band limited random force is measured and the spatial average vibration level of the structure is estimated from several surface accelerometers. It is shown that when the modes in the band have similar loss factors (as is usually the case) the energy method gives a result which is very close to that obtained from the decay method. These in turn are close to the arithmetic average of the loss factors of the individual modes in the band. It is shown that only when the band contains one or two very lightly damped modes amongst several more heavily damped modes is there a difference between the two methods. In this case it is better to use the energy result in the SEA calculations.     

汽车车内噪声主动控制系统仿真

摘要：降低汽车空腔的振动,是抑制汽车车内噪声的有效途径之一。以激振器、作动器和控制器等为主要部件,搭建了简化的汽车车内噪声主动控制系统,该系统通过将汽车空腔模型简化为板件,以减弱板件振动为目标,实现了汽车车内噪声主动控制。采用简谐正弦及余弦信号作为激振器发出的激励,用于模拟板件的初始振动,控制器通过采用模糊控制算法直接控制压电陶瓷作动器的振动,压电陶瓷作动器的振动用于抑制板件的振动,完成了汽车车内噪声主动控制系统仿真。仿真结果表明,研究采用的汽车车内噪声主动控制系统,使汽车空腔振动降低23%,为解决由汽车发动机和动力总成的振动所引发的汽车车内噪声问题提供了一个有效途径。     

Corrected Statistical Energy Analysis Model in a Non-Reverberant Acoustic Space

Statistical Energy Analysis (SEA) is a well-known method to analyze the flow of acoustic and vibration energy in a complex structure. This study investigates the application of the corrected SEA model in a non-reverberant acoustic space where the direct field component from the sound source dominates the total sound field rather than a diffuse field in a reverberant space which the classical SEA model assumption is based on. A corrected SEA model is proposed where the direct field component in the energy is removed and the power injected in the subsystem considers only the remaining power after the loss at first reflection. Measurement was conducted in a box divided into two rooms separated by a partition with an opening where the condition of reverberant and non-reverberant can conveniently be controlled. In the case of a non-reverberant space where acoustic material was installed inside the wall of the experimental box, the signals are corrected by eliminating the direct field component in the measured impulse response. Using the corrected SEA model, comparison of the coupling loss factor (CLF) and damping loss factor (DLF) with the theory shows good agreement.     

Research on the procedure for analyzing the sound quality contribution of sound sources and its application

Transfer path analysis (TPA) plays an important role for identifying and quantifying the contribution by airborne and structure-borne in the automotive industry. The main bottleneck of the TPA method is the test time consumption and complex procedure. It becomes a key target in many applications to find out the source with dominant contribution to overall noise rather than to identify each source. In recent years the contribution pattern of sources to the vehicle overall interior noise has changed with the reduction of engine noise, which masks all other sources. The panel radiation noise of vehicle body could not be ignored. There is an increasing demand for analyzing the sound quality contribution of sound sources in simple ways. The procedure for analyzing sound quality contribution of panel radiation noise is suggested in this study, in which an operational path analysis (OPA) method combined with partial singular value decomposition (PSVD) analysis is applied and sound quality objective assessment is introduced. The experimental research for verifying the procedure is finished, from which the source with largest sound quality contribution is picked up from three sources. For engineering application, the sound quality contributions of panels to the interior noise of a micro commercial vehicle are analyzed by using the procedure. By investigating the contributions of sound sources to each sound quality attribute, the dominant sound source is determined.     

飞机机体表面声压及舱内降噪优化设计

本文以某型客机为研究对象,从飞行试验数据分析和声学建模两方面研究机体表面声压分布及其对舱内壁板近场辐射声压的影响。首先根据试飞数据分析了机体表面声压分布,然后利用统计能量法建立飞机客舱中后段的声学模型,以试飞数据作为声源输入,研究机体表面声压分布对客舱内部壁板附近声压分布的影响,并在此基础上提出优化设计方案,通过模型验证优化方案的有效性。试飞数据表明：机体表面声压在后应急门前方、靠近地板处最大;巡航速度升高,声压级较大区域的面积随之增加;巡航高度和发动机N1N2频率变化对机体表面声压级分布无明显影响。仿真数据表明：仅蒙皮结构无法有效降低客舱噪声;对声学降噪包进行优化能增加壁板隔声量,降低舱内声压。     

Calculation of the sound transmission between dwellings by partitions and flanking structures

A calculation model is presented for the sound transmission between dwellings by partitions and by flanking structures, based on the application of classical theory.The most important data needed are the sound reduction index for direct transmission of the different structures and the vibration level differences across junctions. Information on the reduction index is given, based on theory, taking into account the influence of boundary conditions by means of the structural reverberation time in situ. The vibration level differences have been determined for different junctions on the basis of in situ measurements. Under some—reasonable—restrictions this model gives the same results as would be achieved by applying the so-called Statistical Energy Analysis (SEA).Comparison between calculation and measurement for seventy-five different situations shows good agreement, the average predictions being correct with a standard deviation of 1·5 dB.