Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

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.     

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.     

Characterisation of valves as sound sources: Structure-borne sound

Taps and other valves are major sound sources in piping systems and can cause unacceptable noise levels in buildings. The noise results from the fluid-, structure- and air-borne sound emission. At present the acoustic emission of water appliances is tested according to a European standard, the shortcomings of which are apparent as a result of a round robin test of different European laboratories. As a result, there are currently neither acceptable measurement methods for water appliances available nor input data for prediction models. This paper considers methods of characterizing water appliances as sources of structure-borne sound. The concepts of mobility and free velocity are employed for a source characterisation based on power. Taps are considered alone and also in combination with a basin, where again the mobility and free velocity are used. A reception plate method is assessed as an alternative. The two methods each provide an independent characterisation of a structure-borne sound source as a single value. The values are on a power basis and provide input data suitable for prediction of the installed structure-borne power and thence the resultant sound pressure in adjacent rooms. Measured and predicted values of sound pressure level, caused by a wash-basin installed in an adjacent room, are compared.     

Reception plate method for characterisation of structure-borne sound sources in buildings: Assumptions and application

A method for characterisation of structure-borne sound sources is proposed and investigated for the special but common case of machines in heavy-weight homogeneous building structures. The method is based on the concept of the reception plate where the total structure-borne sound power from the machine under test is assumed equal to the power dissipated by a plate attached to the machine. The method is relatively simple and allows comparison of sources on a power basis, and of tests results at different laboratories. Additionally the data obtained is in a form suitable for transformation into an installed structure-borne power and thence for the resultant sound pressure generated in buildings. The method is validated by cross-spectral and mobility methods. A study of the uncertainty of the power estimate was performed by numerical modelling and measurement.     

Experimental example of the pseudo-forces method used in characterisation of a structure-borne sound source

In the analysis of machinery noise the aspect of sound source characterisation is of importance. Unlike for airborne sources, no widely applicable methods are available yet for structure-borne sound sources. In previous work a ‘pseudo-forces' methodology was suggested. In this approach fictitious forces on the outer surface replace the internal excitation in a source. The application of this approach is illustrated by experiments using a small air-compressor. In this example the pseudo-forces gave a good reconstruction of the response field (within 3 dB). Confidence intervals are derived for the results, which are 2-3 dB wide. This spread is separated into spread caused by inefficiencies of the method, spread caused by random measurement errors and the spread which is inherently generated by the source itself. These causes together enable the explaination of most of the deviations. Therefore, the pseudo-forces method is expected to serve well for particular structure-borne noise related questions.     

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.     

Untersuchung zur anwendbarkeit impulsförmiger anregung für ein meßverfahren zur bestimmung von körperschallanregung und -übertragung

A procedure has been developed for measuring the structure-borne sound sensitivity of building structures to stationary excitation. This procedure has the advantage that it can be conducted with simple sound pressure and vibration measurements. The precision and reproducibility of the measurement procedure have been tested. This method permits the measurement of the vibratory point forces due to structure-borne sound sources in buildings or other systems.In order to determine the structure-borne sound sensitivity and the vibratory point forces to transient excitation, impulses were tested and compared with the results obtained with stationary excitation.     

Circulation pumps as structure-borne sound sources: emission to semi-infinite pipe systems

Circulation pumps are an important source of noise from domestic central heating systems. Pumps can generate airborne, liquid-borne and structure-borne sound and although standards exist for airborne and liquid-borne sources, none do for structure-borne sources. This is primarily because the structure-borne acoustic power delivered by the pump not only depends on the pump but also on the connected receiving system, which can be a complicated combination of pipes, valves and radiators. Also pumps deliver liquid-borne and structure-borne acoustic power simultaneously and their relative contributions to the sound radiated from the pipe system is not obviously obtainable. The approach proposed is to estimate the emission from the pump into semi-infinite pipes of material and cross-section typical of heating systems. Then to estimate the ‘mixing’ effect of bends, joints and other pipe discontinuities, due to wave mode conversion, as described in a companion paper. In the present paper, it is demonstrated that the structure-borne power can be calculated from the measured free velocity and mobility of the pump for each component of vibration and from receiver mobilities of idealized pipe systems. The structure-borne power is compared with the liquid-borne power measured directly by intensimetry.     

Modal decomposition method for acoustic impedance testing in square ducts

Accurate duct acoustic propagation models are required to predict and reduce aircraft engine noise. These models ultimately rely on measurements of the acoustic impedance to characterize candidate engine nacelle liners. This research effort increases the frequency range of normal-incidence acoustic impedance testing in square ducts by extending the standard two-microphone method (TMM), which is limited to plane wave propagation, to include higher-order modes. The modal decomposition method (MDM) presented includes four normal modes in the model of the sound field, thus increasing the bandwidth from 6.7 to 13.5 kHz for a 25.4 mm square waveguide. The MDM characterizes the test specimen for normal- and oblique-incident acoustic impedance and mode scattering coefficients. The MDM is first formulated and then applied to the measurement of the reflection coefficient matrix for a ceramic tubular specimen. The experimental results are consistent with results from the TMM for the same specimen to within the 95% confidence intervals for the TMM. The MDM results show a series of resonances for the ceramic tubular material exhibiting a monotonic decrease in the resonant peaks of the acoustic resistance with increasing frequency, resembling a rigidly-terminated viscous tube, and also evidence of mode scattering is visible at the higher frequencies.     

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.     

水下复杂壳体结构在多源激励下的振动及声辐射特性研究

为了综合评估水下复杂壳体结构在多源激励下的振动与声辐射特性,专门设计了一个多舱段复杂壳体模型,分别进行了单台设备激励、多台设备激励的壳体振动与声辐射试验。试验结果表明,多源激励下的结构响应和辐射声场可以近似为单源激励下结构响应和辐射声场的非相干叠加。通过对激励源与结构响应、辐射声场之间传递关系的理论分析,讨论了以单源激励响应非相干叠加合成得到多源激励响应的合理性和误差。研究结果对复杂壳体结构在实际激励下的振动与噪声预报具有重要价值。      

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。     

Reduction of structure-borne sound in simple ship structures: Results of model tests

A method for the prediction of the transmission of structure-borne sound in ship structures is presented. Various methods to decrease the noise levels in the accomodation spaces in superstructures are investigated in model tests. The attenuation of structure-borne sound in the propagation path between source and receiver is increased by means of damping layers, resilient mounts and changed boundary conditions between main deck and superstructure. Damping layers are found to have only a local effect. Resilent mounts between superstructure and main deck can reduce the noise levels in the superstructure by the order of 10 dB(A).     

The relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is focused on the relationship between the radiation modes and structural modes and its physical mechanisms. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequencies, the first radiation mode is dominant corresponding to (odd, odd) structural modes; the following radiation modes are respectively dominant corresponding to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the design of active control strategy and arrangement of the secondary forces.     

STRUCTURE-BORNE NOISE AND VIBRATION OF CONCRETE BOX STRUCTURE AND RAIL VIADUCT

In this study, the vibration and acoustic resonance, and dominant frequency range of simple concrete box and viaduct are examined from the measurement results. A narrow band analysis—fast Fourier transform (FFT) method is used to analyze the measurement results and finite element method (FEM) is used to validate resonance frequencies for noise and vibration. The experiment of the concrete box structure is a preliminary study of analyzing resonance frequency radiated from the vibrating concrete structure since railway viaduct is a concrete box structure too. According to their noise and vibration spectra, it shows that the vibration resonance is more significant than the acoustics resonance.Based on the measurement results of the rail viaduct structure-borne noise and vibration, the relationship in terms of transfer function and coherence between noise and vibration are evaluated. They show that the dominant frequency range for noise and vibration of concrete viaduct is between 20 and 157 Hz, the resonance frequencies are 43 and 54 Hz and have significant tonal noise characteristics. The experimental results are in good agreement with the theoretical relationship between sound and vibration.     

Ventilation duct with concurrent acoustic feed-forward and decentralised structural feedback active control

This paper presents theoretical and experimental work on concurrent active noise and vibration control for a ventilation duct. The active noise control system is used to reduce the air-borne noise radiated via the duct outlet whereas the active vibration control system is used to both reduce the structure-borne noise radiated by the duct wall and to minimise the structural feed-through effect that reduces the effectiveness of the active noise control system. An elemental model based on structural mobility functions and acoustic impedance functions has been developed to investigate the principal effects and limitations of feed-forward active noise control and decentralised velocity feedback vibration control. The principal simulation results have been contrasted and validated with measurements taken on a laboratory duct set-up, equipped with an active noise control system and a decentralised vibration control system. Both simulations and experimental results show that the air-borne noise radiated from the duct outlet can be significantly attenuated using the feed-forward active noise control. In the presence of structure-borne noise the performance of the active noise control system is impaired by a structure-borne feed-through effect. Also the sound radiation from the duct wall is increased. In this case, if the active noise control is combined with a concurrent active vibration control system, the sound radiation by the duct outlet is further reduced and the sound radiation from the duct wall at low frequencies reduces noticeably.     

Acoustic metamaterials for sound mitigation

We provide theoretical and numerical analyses of the behavior of a plate-type acoustic metamaterial considered in an air-borne sound environment in view of sound mitigation application. Two configurations of plate are studied, a spring-mass one and a pillar system-based one. The acoustic performances of the considered systems are investigated with different approaches and show that a high sound transmission loss (STL) up to 82 dB is reached with a metamaterial plate with a thickness of 0.5 mm. The physical understanding of the acoustic behavior of the metamaterial partition is discussed based on both air-borne and structure-borne approaches. Confrontation between the STL, the band structure, the displacement fields and the effective mass density of the plate metamaterial is made to have a complete physical understanding of the different mechanisms involved.     

The quantification of structure-borne transmission paths by inverse methods. Part 2: Use of regularization techniques

The inversion of an ill-conditioned matrix of measured data lies at the heart of procedures for the quantification of structure-borne sources and transmission paths. In an earlier paper the use of over-determination, singular value decomposition and the rejection of small singular values was discussed. In the present paper alternative techniques for regularizing the matrix inversion are considered. Such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography. The application to structure-borne sound transmission involves matrices, which vary much more with frequency and from one element to another. In this study Tikhonov regularization is used with the ordinary cross-validation method for selecting the regularization parameter. An iterative inversion technique is also studied. Here a form of cross-validation is developed allowing an optimum value of the iteration parameter to be selected. Simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques. Experiments are also performed to validate the results. Both techniques are found to give considerably improved results compared to singular value rejection.