Vincent Cotoni

Response variance prediction in the statistical energy analysis of built-up systems

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.

Response variance prediction for uncertain vibro-acoustic systems using a hybrid deterministic-statistical method

Imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures. Any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance. Recently a hybrid method has been developed to predict the ensemble average response of a built-up system by combining a deterministic model of parts of the system with a statistical model of other components [Shorter, P. J., and Langley, R. S. (2005) J. Sound. Vib., 288, 669-700]. In this paper the method is extended to predict the ensemble variance of the response. Expressions are derived for the variance of the vibrational energies in the statistical components, and for the variance of the cross spectrum of the response of the deterministic components, which augment the mean values of these quantities predicted by the original theory. The method employs a nonparametric model of uncertainty, in the sense that the statistical components are taken to carry diffuse wave fields, and this obviates the requirement for a detailed description of the system uncertainties. The method is validated by application to a range of coupled plate structures, and good agreement with detailed Monte Carlo simulations is found.

The ensemble statistics of the vibrational energy density of a random system subjected to single point harmonic excitation

This paper is concerned with the ensemble statistics of the energy density of a random system subjected to a harmonic point load. Both the mean and variance of the reverberant energy density (i.e., the total response minus the direct field) are investigated. It is shown that the ensemble average of the reverberant energy density is not spatially homogeneous, but rather the value at the drive point is between two and three times the spatially averaged value, depending on the modal overlap factor. This result is closely analogous to established results regarding the case of transient excitation. Expressions are also derived for the relative variance of the reverberant energy density both remote from the drive point and at the drive point, and a number of anomalies are found in existing results. A comparison is made with simulation results for a randomized plate, and this comparison highlights the importance of the ensemble size considered in the simulations. The present analysis is based on a random point p...

Prediction of Interior Noise in a Sedan Due to Exterior Flow

Aero-vibro-acoustic prediction of interior noise associated with exterior flow requires accurate predictions of both fluctuating surface pressures across the exterior of a vehicle and efficient models of the vibro-acoustic transmission of these surface pressures to the interior of a vehicle. The simulation strategy used in this paper combines both CFD and vibro-acoustic methods. An accurate excitation field (which accounts for both hydrodynamic and acoustic pressure fluctuations) is calculated with a hybrid CAA approach based on an incompressible unsteady flow field with an additional acoustic wave equation. To obtain the interior noise level at the drivers ears a vibro-acoustic model is used to calculate the response of the structure and interior cavities. The aero-vibro-acoustic simulation strategy is demonstrated for a Mercedes-Benz S-class and the predictions are compared to experimental wind tunnel measurements.

Application of the Hybrid FE-SEA Method to Predict Sound Transmission Through Complex Sealing Systems

Currently, the use of numerical and analytical tools during a vehicle development is extensive in the automotive industry. This assures that the required performance levels can be achieved from the early stages of development. However, there are some aspects of the vibro-acoustic performance of a vehicle that are rarely assessed through numerical or analytical analysis. An example is the modeling of sound transmission through vehicle sealing systems. In this case, most of the investigations have been done experimentally, and the analytical models available are not sufficiently accurate. In this paper, the modeling of the sound transmission through a vehicle door seal is presented. The study is an extension of a previous work in which the applicability of the Hybrid FE-SEA method was demonstrated for predicting the TL of sealing elements. A numerical validation of simplified Hybrid FE-SEA model is performed, which is followed by the application of the method to the TL of a car door seal. A full non-linear deformation/contact analysis is used to estimate the deformed geometry of the door seal in real conditions. The geometry is then used in a vibro-acoustic analysis to predict the in-situ transmission loss of the seal using a local Hybrid FE-SEA model. The channel between the door and the car structure where the seal is located is also included in the analysis. Results for the transmission loss are compared with experimental data, showing a good correlation.

Models of the acoustic radiation and transmission properties of complex trimmed structures

A number of advances have been made recently in the development of a hybrid method for rigorously coupling finite element and statistical energy analysis descriptions of the dynamics of a vibro‐acoustic system. The method provides an efficient way to analyze the acoustic radiation and transmission properties of a complex structure across a broad frequency range. In this paper, two case studies of engine components are used to validate the ‘‘hybrid area junction’’ formulation for coupling FE structures with trimmed SEA fluids, and to demonstrate the use of the method in a design process.

Modeling Interior Noise due to Fluctuating Surface Pressures from Exterior flows

There are many applications in which exterior flow over a structure is an important source for interior noise. In order to predict interior “wind noise” it is necessary to model both: (i) the spatial and spectral statistics of the exterior fluctuating surface pressures (across a broad frequency range) and (ii) the way in which these fluctuating surface pressures are transmitted through a structure and radiated as interior noise (across a broad frequency range). One approach to the former is to use an unsteady CFD model. The use of compressible CFD to characterize exterior fluctuating surface pressures for broadband interior noise problems is relatively new; the accurate prediction of both the convective and acoustic wavenumber content of the flow can therefore present some challenges. This paper presents a numerical investigation of the spatial and spectral statistics contained in the flow downstream of a simplified side-mirror. Two distinct concentrations of energy are observed in wavenumber space at the convective and acoustic wavenumbers. Using wavenumber filtering it is then possible to describe a complex windnoise source in terms of the superposition of two simple analytical sources (that can be fit to CFD data). An example is presented in which the fluctuating surface pressures are applied to a side glass and a SEA model is used to predict interior noise.

Modeling the low‐, mid‐, and high‐frequency response of poro‐elastic materials in vibro‐acoustics applications.

A method is presented for representing layered poro‐elastic materials and acoustic fluids in a finite element (FE) model of a structure. The method is based on the hybrid FE‐statistical energy analysis (SEA) formulation that allows the coupling of FE and SEA descriptions of various subsystems in a model. By making use of the dynamic properties of poro‐elastic materials and acoustic fluids (in terms of wavelength and uncertainty), the method is made particularly fast and appropriate for the prediction of the vibro‐acoustic response at midfrequencies. The method allows to quickly incorporate acoustics and/or noise control treatment in an existing finite element model of a structure. Given the frequency range of applicability, it complements the existing low‐frequency methods (structure and poro‐elastic material described with FE, acoustic fluid described with FE, infinite elements, or boundary elements) and high‐frequency methods (structure, poro‐elastic material, and acoustic fluid described with SEA). The...

Turbulent Surface Pressure Field in Low Speed Flow

The external air low speed flow over a flat plate passed a half cylinder shape is computed using an unsteady CFD technique; the turbulent surface pressure field is analyzed in details; a frequency-wavenumber decomposition is used to identify the convective and acoustic energy concentration. A comparison is then made with results obtained using several standard semi-analytical models of turbulent surface pressure. Finally the wall pressure fluctuations are used as a load on an elastic plate in a vibroacoustic analysis and the transmitted noise inside a trimmed acoustic cavity is computed. Some conclusions are drawn on the pertinence of using a semi-analytical model or unsteady LES-type CFD computations to describe the wall pressure loading for a vibroacoustic analysis.

Predicting the Acoustics of Squeak and Rattle

This paper discusses the development of a computationally efficient numerical method for predicting the acoustics of rattle events upfront in the design cycle. The method combines Finite Elements, Boundary Elements and SEA and enables the loudness of a large number of rattle events to be efficiently predicted across a broad frequency range. A low frequency random vibro-acoustic model is used in conjunction with various closed form analytical expressions in order to quickly predict impact probabilities and locations. An existing method has been extended to estimate the statistics of the contact forces across a broad frequency range. Finally, broadband acoustic radiation is predicted using standard low, mid and high frequency vibro-acoustic methods and used to estimate impact loudness. The approach is discussed and a number of validation examples are presented.