Diffuse Acoustic Field Research Articles

Optimization of Sound Transmission Loss Characteristics of Orthogonally Stiffened Plate

An analytical model is developed to investigate the sound transmission loss from orthogonally rib-stiffened plate structure under diffuse acoustic field excitation. The validity and feasibility of the model are verified by comparing the present theoretical predictions with the numerical results published previously. The influences of structure geometrical parameters on sound transmission loss are subsequently presented. The optimization algorithm is used to search for the optimal structural parameters with the objective to maximize the sound transmission loss over a frequency band. Furthermore, the sensitivity of structural parameters on the overall vibration and acoustic performance of the stiffened plates structure is also analyzed.

Vibroacoustic response of panels under diffuse acoustic field excitation from sensitivity functions and reciprocity principles

This paper aims at developing an experimental method to characterize the vibroacoustic response of a panel to a diffuse acoustic field (DAF) excitation with a different laboratory setup than those used in standards (i.e., coupled rooms). The proposed methodology is based on a theoretical model of the DAF and on the measurement of the panel's sensitivity functions, which characterize its vibroacoustic response to wall plane waves. These functions can be estimated experimentally using variations of the reciprocity principle, which are described in the present paper. These principles can either be applied for characterizing the structural response by exciting the panel with a normal force at the point of interest or for characterizing the acoustic response (radiated pressure, acoustic intensity) by exciting the panel with a monopole and a dipole source. For both applications, the validity of the proposed approach is numerically and experimentally verified on a test case composed of a baffled simply supported plate. An implementation for estimating the sound transmission loss of the plate is finally proposed. The results are discussed and compared with measurements performed in a coupled anechoic-reverberant room facility following standards.

A boundary element based method for accurate prediction of the surface pressure cross-spectral density matrix

Accurate prediction of the surface pressure cross-spectral density matrix is necessary to predict the dynamic response of a structure loaded by a diffuse acoustic field. The cross-spectral density matrix describes the frequency dependence of the correlation between the surface pressure at all pairs of points on the structure. Most often the cross-spectral density matrix is obtained from either a uniform distribution of incident plane waves or direct application of the diffuse field spatial cross-correlation function. While the method of plane waves is relatively more accurate, especially at low frequencies, the necessary distribution of incidence angles and ensemble size can be problematic. This talk shall present a boundary element based methodology for determining the surface pressure cross-spectral density for any structure and frequency, including the effects of scattering and shielding. The method involves a power spectral density formulation of the boundary element method and takes advantage of the underlying foundations in potential theory. The method can be generalized beyond diffuse fields and can be applied to structures having a known surface impedance.

Impact of random failures and tolerances on ensemble average array beampattern and array gain

Analytic expressions for expected array beampattern with random element failures and random perturbations in element amplitude and phase response have been long available for arrays of omnidirectional elements. This work extends prior results to address random failures and tolerances of directive as well as omni-directional elements in curved as well as rectilinear array geometries and to blocks or groups of elements as well as single elements. The analytic result for both failures and multiple types of tolerances is concisely expressed in a single simple universal expression with explicit parametric dependencies. This expression is amenable to efficient numerical evaluation and quantitative results are trivially scaled to any combination of failure probabilities and standard deviation of various types of tolerances. Insightful interpretation of the results in terms of response of an ideal array plus a perturbation array is provided. The impact of failures and tolerances on array beampattern is translated to again simple expressions for array noise response and array gain for an incident diffuse acoustic noise field of arbitrary directionality. The emphasis on concise physically interpretable expressions is due to my training as a young engineer by Ira Dyer and the group of outstanding scientists and engineers he assembled at BBN.

Using reciprocity principles and sensitivity functions for the vibroacoustic response of panels under random excitations

The vibroacoustic characterization of panels submitted to random pressure fields is of great interest for the industry. The test means associated with those excitations (i.e., wind tunnel, reverberant room) are expensive and can hardly be controlled. An alternative method to experimentally characterize the behavior of a panel under random pressure fields is therefore proposed. The mathematical formulation of the problem allows describing the vibroacoustic behavior of a panel as a function of the cross spectral density function of the considered excitation and so-called “sensitivity functions.” These functions can be estimated experimentally using reciprocity principle, which can either be applied for characterizing the structural response by exciting the panel with a normal force at the point of interest or for characterizing the acoustic response (radiated pressure, acoustic intensity) by exciting the panel with a monopole and a dipole source. For validation purposes, the method is applied numerically and experimentally for the case of a diffuse acoustic field. Based on indicators such as the vibratory response and the transmission loss factor, the method is finally confronted to measurements in coupled anechoic-reverberant rooms facility following standards.

Absorption and transmission of boundary layer noise through flexible multi-layer micro-perforated structures

This paper describes analytical and experimental studies conducted to understand both the absorption and transmission performance of non-fibrous micro-perforated partitions excited by a turbulent boundary layer (TBL). This is of relevance in surface and air transport systems for the airframe design of external liners. A fully-coupled modal formulation is established that predicts the absorption coefficient and the transmission loss (TL) of finite-sized and infinite-sized partitions made up of a micro-perforated panel (MPP) backed by an air cavity and a thin plate. The front MPP undergoes random wall-pressure fluctuations with prescribed auto- and cross- correlation properties such as a TBL and/or an acoustic diffuse field (ADF). An experimental methodology is proposed to evaluate in a closed wind tunnel both the absorption and insulation performance of a TBL-excited MPP partition. This leads to an approximation of the frequency-averaged power flow injected by the TBL into the MPP partition. Both the predictions and the measurements show significant differences in the absorption and TL curves when considering either a low speed TBL or an ADF excitation. These properties are examined considering a weighted contribution of the acoustic and turbulent components, as it is the case for an aeroacoustic excitation. A hole-based transitional Strouhal number is found below which low-back scattering of the wall-pressures occurs and above which the MPP apertures efficiently convert turbulence into back-scattered sound whatever the magnitude of the acoustic component. As for the TL, a minute increase of the acoustic component generates most of the TL decrease. Finally, the effects of adding a second MPP within the cavity are assessed for both the absorption and the TL.

外部から拡散音場加振される隙間を有するカバー内音場のアクティブ制御

To increase the noise proof performance of a cover with aperture excited by diffuse acoustic fields from the outside, it is a problem to prevent the occurrence of the inner acoustic mode at the lower frequencies. Authors had suggested the feed forward active noise control (ANC) for the acoustic field inside the cover. Diffuse acoustic field excitation experiment using reverberant room has been examined to comprehend acoustic characteristics inside the cover. The results show that the inner cover field is in the state of locally coherent at the frequencies of inner acoustic mode, so that it is good environment for the active noise control. Then, a calculation with two-dimensional finite difference time domain (FDTD) method has been done to examine the feasibility of feed forward ANC. The results show that it is possible to realize ANC for the acoustic field inside the cover by proper design of control filter. Finally, experimental measurement of diffuse acoustic field excitation in the reverberant room has been done again to examine the ANC with the design method mentioned above. The results show that feed forward ANC can reduce noise level by 5dB at the peak frequency caused by the inner acoustic mode. Furthermore, the inner acoustic pressure distribution is also reduced uniformly at the frequency. Therefore, it is concluded that it is possible to realize feed forward active noise control for the acoustic field inside the cover with aperture excited by diffuse acoustic fields from the outside, even if the excitation is random or the causality of I/O is not satisfied.

Identification of spatially correlated excitations on a bending plate using the Virtual Fields Method

This paper aims at identifying the autospectral density and spatial correlation functions of random excitations acting on the surface of a thin plate, from its measured vibration response. The general framework is the Virtual Fields Method (VFM), which was previously applied by the authors to the identification of deterministic excitations on plates. In the present paper, the VFM framework is extended to the case of spatially correlated excitations. It is shown that extraction of the loading power spectral density requires measuring power spectral density functions of transverse displacements and bending curvatures, which can be typically derived from contactless Laser Doppler Vibrometry measurements. The paper details the implementation of the VFM for random excitations, presents numerical simulations and experimental results for diffuse acoustic field excitation of a plate.

拡散音場加振された準閉空間内のアクティブ吸音

Application of active noise control (ANC) was discussed as method to prevent the occurrence of an inner acoustic mode inside the semi-closed cover placed in the diffuse acoustic field. The effect was validated by the experimental measurement using a reverberant room. The results show that the acoustic mode formed by semi-closed cavity has locally-coherency at its occurrence frequency and the inside cover acoustic mode can be controlled by applying ANC. It has been confirmed that noise reduction of ANC for the peak level caused by the acoustic mode is approximately 5dB.

Numerical hybrid TMM-modal finite element method prediction of the vibroacoustic of sandwich panels with add-on damping

This paper discusses the numerical modeling of the vibroacoustic response of sandwich-composite panels with add-on damping, under a diffuse acoustic field (DAF) excitation. A modal synthesis approach is used for the calculation of the structural response and the Rayleigh’s integral is used for the acoustic response. Since the panel has a viscoelastic core, a methodology is presented to handle efficiently the modeling of the frequency depended properties of the viscoelastic layer. A hybrid TMM-modal FEM method is used to predict the acoustic response at high frequency, using the equivalent damping of panel which are calculated from strain energies. Next, a parameters study on the effect of the viscoelastic layer location is presented. In particular, three locations are compared: within the Honeycomb core, within the skins and added to the skin with a constraining layer. The effects of the excitation type on the vibration and acoustic response are also discussed. Key words: Sandwich NIDA, Modal FEM method, TMM method, viscoelastic damping, acoustic response, equivalent properties.

Numerical hybrid TMM-modal FEM method prediction of the vibroacoustic of sandwich panels with add-on damping

This paper discusses the numerical modeling of the vibroacoustic response of sandwich-composite panels with add-on damping, under acoustic excitation, diffuse acoustic field (DAF). A modal synthesis approach is used for the calculation of the structural response and the Rayleigh’s integral is used for the acoustic response. Since the panel has a viscoelastic core, a methodology is presented to handle efficiently the modeling of the frequency depended properties of the viscoelastic layer. A hybrid TMM-modal FEM method is used to predict the acoustic response in high frequency, using the equivalents properties of panel, which are calculated from strain energies’ panel. Next, a parameters' study on the effect of the viscoelastic layer location is presented. In particular, three locations are compared: within the Honeycomb core, within the skins and added to the skin with a constraining layer. The effects of the excitation type on the vibration and acoustic response are also discussed using the hybrid: TMM-modal FEM method. Key words: Sandwich NIDA, Modal FEM method, TMM method, viscoelastic damping, acoustic response, equivalent properties.

Vibroacoustic Tailoring of a Rod-Stiffened Composite Fuselage Panel with Multidisciplinary Considerations

An efficient multi-objective design tailoring procedure seeking to improve the vibroacoustic performance of a fuselage panel while maintaining or reducing weight is presented. The structure considered is the pultruded rod stitched efficient unitized structure, a highly integrated composite structure concept designed for a noncylindrical, next-generation flight vehicle fuselage. Modifications to a baseline design are evaluated within a six-parameter design space including spacing, flange width, and web height for both frame and stringer substructure components. The change in sound power radiation attributed to a design change is predicted using finite-element models sized and meshed for analyses in the 500 Hz, 1 kHz, and 2 kHz octave bands. Three design studies are carried out in parallel while considering a diffuse acoustic field excitation and two types of turbulent boundary-layer excitation. Kriging surrogate models are used to reduce the computational costs of resolving the vibroacoustic and weight objective Pareto fronts. The resulting Pareto optimal designs are then evaluated under a static pressurization ultimate load to assess structural strength and stability. Results suggest that choosing alternative configurations within the considered design space can reduce weight and improve vibroacoustic performance without compromising strength and stability of the structure under the static load condition considered, but the tradeoffs are significantly influenced by the spatial characteristics of the assumed excitation field.

Численное моделирование вибраций панели летательного аппарата при воздействии акустических пульсаций давления

Investigation vibration characteristics of thin-walled shell when excitation of random pressure fields defined of wall pressure fluctuations in a turbulent boundary layer at flow regime of maximum dynamic pressure and fluctuations induced by the noise of a jet engine at the start. Is assumed that the noise from the jet engine is described a longitudinal acoustic wave propagating along the product's enclosure and diffuse acoustic field, in particular emerging as a result reflection of acoustic waves from the launch facility. As a thin-walled structure is considered streamlined panel fairing products made of a composite materials. In structure of the panel, except shell, included reinforcing circumferential ribs with two frames. The mathematical model presented for described external effects and algorithms for determining of a random vibration characteristics when exposed to fields random pressure. The calculation of the frequency response of the system is produced by the superposition of forms. The spatial correlation function of wall pressure fluctuations in turbulent boundary layer is determined according to the expression Corcos, in which the coefficients the damping of the spatial correlation function are corrected according to the model Efimtsov. The spectral density of wall pressure fluctuations in the turbulent boundary layer is determined according to the model Efimtsov. The levels sound of acoustic pressure caused by the noise of a jet engine at the start is determined by calculating of gas dynamics, and are given as the initial data. It shows the spectral characteristics of the vibration acceleration thin-walled structure depending on the frequency and distribution of the surface of the structure in a neighborhood of the central frequency at which there is maximum loading. It is assumed that the calculated levels of loads will be used as loading conditions during experimental testing of parts.

Численное моделирование вибраций панели летательного аппарата при воздействии акустических пульсаций давления

Investigation vibration characteristics of thin-walled shell when excitation of random pressure fields defined of wall pressure fluctuations in a turbulent boundary layer at flow regime of maximum dynamic pressure and fluctuations induced by the noise of a jet engine at the start. Is assumed that the noise from the jet engine is described a longitudinal acoustic wave propagating along the product's enclosure and diffuse acoustic field, in particular emerging as a result reflection of acoustic waves from the launch facility. As a thin-walled structure is considered streamlined panel fairing products made of a composite materials. In structure of the panel, except shell, included reinforcing circumferential ribs with two frames. The mathematical model presented for described external effects and algorithms for determining of a random vibration characteristics when exposed to fields random pressure. The calculation of the frequency response of the system is produced by the superposition of forms. The spatial correlation function of wall pressure fluctuations in turbulent boundary layer is determined according to the expression Corcos, in which the coefficients the damping of the spatial correlation function are corrected according to the model Efimtsov. The spectral density of wall pressure fluctuations in the turbulent boundary layer is determined according to the model Efimtsov. The levels sound of acoustic pressure caused by the noise of a jet engine at the start is determined by calculating of gas dynamics, and are given as the initial data. It shows the spectral characteristics of the vibration acceleration thin-walled structure depending on the frequency and distribution of the surface of the structure in a neighborhood of the central frequency at which there is maximum loading. It is assumed that the calculated levels of loads will be used as loading conditions during experimental testing of parts.

Multi-objective vibro-acoustic optimization of stiffened panels

A multi-objective vibro-acoustic design optimization of straight or curvilinearly stiffened panels excited by an acoustic diffuse field is performed. During design optimization, the panel mass and the radiated acoustic power are the two objectives to be minimized while satisfying constraints on buckling, von Mises stress and crippling. Based on the concept of plane wave propagation, a diffuse acoustic field is developed for use along with a finite element model. To represent the panel's structural behavior, the dynamic analysis of the panel is performed for the developed diffuse acoustic excitation and the radiated acoustic power is calculated using the velocities obtained from the dynamic analysis. A baseline design is obtained by optimization study with mass as an objective to be minimized while constraints are put on buckling, von Mises stress and crippling. The obtained baseline grid stiffened panel is used for a comparative study of a panel with curvilinear stiffeners in vibro-acoustics with diffuse sound field as the source of the excitation.

Passive-only damage detection by reciprocity of Green’s functions reconstructed from diffuse acoustic fields with application to wind turbine blades

The increasing demand for renewable and clean power generation has resulted in the increased size of rotor blades in wind turbine systems. The operational environments have introduced the need for structural health monitoring of the blades to help prevent unexpected failures. A new passive approach is here presented to detect damage in a wind turbine blade using the reciprocity of Green’s function. This is achieved using the derivative of an ensemble average of cross-correlation functions to reconstruct the forward and backward time-domain Green’s functions between any two detection points on the structure within a diffuse acoustic field. Damage is detected when the similarity between the forward and backward signals decreases due to the wave nonlinearities introduced by the discontinuity that break the field reciprocity condition. Proof-of-principle results are presented first for an aluminum plate and then for a 9-m-long composite wind turbine blade containing known, simulated damage.

Measurement of the absorption coefficient of sound absorbing materials under a synthesized diffuse acoustic field.

This letter proposes an experimental method to estimate the absorption coefficient of sound absorbing materials under a synthesized diffuse acoustic field in free-field conditions. Comparisons are made between experiments conducted with this approach, the standard reverberant room method, and numerical simulations using the transfer matrix method. With a simple experimental setup and smaller samples than those required by standards, the results obtained with the proposed approach do not exhibit non-physical trends of the reverberant room method and provide absorption coefficients in good agreement with those obtained by simulations for a laterally infinite material.

Experimental vibroacoustic testing of plane panels using synthesized random pressure fields.

The experimental reproduction of random pressure fields on a plane panel and corresponding induced vibrations is studied. An open-loop reproduction strategy is proposed that uses the synthetic array concept, for which a small array element is moved to create a large array by post-processing. Three possible approaches are suggested to define the complex amplitudes to be imposed to the reproduction sources distributed on a virtual plane facing the panel to be tested. Using a single acoustic monopole, a scanning laser vibrometer and a baffled simply supported aluminum panel, experimental vibroacoustic indicators such as the Transmission Loss for Diffuse Acoustic Field, high-speed subsonic and supersonic Turbulent Boundary Layer excitations are obtained. Comparisons with simulation results obtained using a commercial software show that the Transmission Loss estimation is possible under both excitations. Moreover and as a complement to frequency domain indicators, the vibroacoustic behavior of the panel can be studied in the wave number domain.

Transmission Loss of Variable Cross Section Apertures

Openings in enclosures or walls are frequently the dominant path for sound propagation. In the current work, a transfer matrix method is used to predict the transmission loss of apertures assuming that the cross-sectional dimensions are small compared with an acoustic wavelength. Results are compared with good agreement to an acoustic finite element approach in which the loading on the source side of the finite element model (FEM) is a diffuse acoustic field applied by determining the cross-spectral force matrix of the excitation. The radiation impedance for both the source and termination is determined using a wavelet algorithm. Both approaches can be applied to leaks of any shape and special consideration is given to apertures with varying cross section. Specifically, cones and abrupt area changes are considered, and it is shown that the transmission loss can be increased by greater than 10 dB at many frequencies.

Extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem

Abstract An improvement of the Force Analysis Technique (FAT), an inverse method of vibration, is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate. This method is a significant progress since the usual techniques of measurements with flush-mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high. Moreover, the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate. This underlines the need to extract the acoustic part. In this work, numerical experiments are performed to solve both the direct and inverse problems of vibration. The excitation is a turbulent boundary layer and combines the pressure field of the Corcos model and a diffuse acoustic field. These pressures are obtained by a synthesis method based on the Cholesky decomposition of the cross-spectra matrices and are used to excite a plate. Thus, the application of the inverse problem FAT that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation. Indeed, the discretization of the inverse operator (motion equation of the plate) acts as a low-pass wavenumber filter. In addition, this method is simple to implement because it can be applied locally (no need to know the boundary conditions), and measurements can be carried out on the opposite side of the plate without affecting the flow. Finally, an improvement of FAT is proposed. It regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution. This optimized FAT, in the case of the turbulent flow, has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise.