Statistical Energy Analysis Model Research Articles

Decay Processes in Rooms with Non-Diffuse Sound Fields. Part II: Effect of Irregularities

The effect of sound scattering objects in a rectangular room with high absorption at the ceiling and low absorption at the walls and floor was investigated. In Part I of this paper a two-system Statistical Energy Analysis (SEA) model was developed in order to predict the gross features of the decay process. The sound field is subdivided into a grazing and nongrazing part. The main effect of introducing irregularities is to divert some of the energy in the grazing group into the nongrazing group. The energy transfer between the groups is taken into account by introducing a coupling loss factor. In order to quantify the effect of scattering objects and other irregularities, a measure called equivalent scattering area is introduced. The model demonstrates how the equivalent scattering area can be determined from measurements.

Decay Processes in Rooms with Non-Diffuse Sound Fields Part I: Ceiling Treatment with Absorbing Material

The decay process in rooms with non-diffuse sound fields was the subject of this investigation. A rectangular room with high absorption at the ceiling and low absorption at the walls and floor constituted the basic configuration for the study. Several alterations of the room were carried out, including changes of room dimensions and the type of ceiling absorber, also additional treatment with absorbent material. The effects of these alterations on the decay curves were analysed. In order to predict the gross features of the decay curves, a two-system Statistical Energy Analysis model was developed. The sound field was subdivided into a grazing and nongrazing part. The grazing part comprised modes with propagation direction almost parallel to the ‘principal’ surface (generally the absorbent ceiling). The nongrazing part comprised the oblique modes, of importance for the decay process. The angle dependent absorbent properties of the principal surface were taken into account when subdividing the sound field into a grazing and nongrazing part. Measured and calculated decay curves for different room configurations were compared.

Virtual acoustic prototyping

In this paper the re-creation of 3-D sound fields so the full psycho-acoustic impact of sound sources can be assessed before the manufacture of a product or environment is examined. Using head related transfer functions (HRTFs) coupled with a head tracked set of headphones the sound field at the left and right ears of a listener can be re-created for a set of sound sources. However, the HRTFs require that sources have a defined location and this is not the typical output from numerical codes which describe the sound field as a set of distributed modes. In this paper a method of creating a set of equivalent sources is described such that the standard set of HRTFs can be applied in real time. A structural-acoustic model of a cylinder driving an enclosed acoustic field will be used as an example. It will be shown that equivalent sources can be used to recreate all of the reverberation of the enclosed space. An efficient singular value decomposition technique allows the large number of sources required to be simulated in real time. An introduction to the requirements necessary for 3-D virtual prototyping using high frequency Statistical Energy Analysis models will be presented. [Work supported by AuSim and NASA.]

Estimation of the SEA coupling loss factors by means of spectral element modeling

The coupling loss factors are of critical importance when building and solving Statistical Energy Analysis (SEA) models. This paper proposes a methodology to numerically estimate these factors for frame-type structures. The estimated factors are compared with those obtained through analytical expressions for frame structures, where members are joined at right angles. The example used to verify the proposed technique consists of two infinite beams connected at a right angle modeled via the Spectral Element Method (SEM) using throw-off elements. It is shown that the obtained coupling loss factors compare very well with the analytical expressions that may be derived for this simple right-angle connection case. By using the SEM approach, the coupling loss factors can be obtained for arbitrary frame structure connections, thus facilitating the analysis via SEA.

Measurement and simulation of brick wall sound reduction index

This paper presents the procedures and results of an experimental, numerical simulation and analytical model of sound reduction index of solid brick wall. The solid brick used has the following dimensions: 22×10×5 cm and density of 1850 kg/m3. The physic-mechanical characteristics: density, resistance, and elasticity modulus were measured using a set of small walls (0.60×0.63 m). One wall of 4.10×3.20×0.10 m (length/height/thickness) was built between two reverberant rooms, with 60 and 63 cubic meters in volume, respectively. Two kinds of junctions were used between the wall and the concrete walls of the reverberant rooms: elastic junction (with a thin layer of rubber, sealed with silicon rubber on both sides and the top of the wall) and rigid junction (using the normal mortar). The sound reduction index was measured according to ISO 140-3 using airborne transmission. The brick characteristics were used as input data for the statistical energy analysis (SEA) model. The results from SEA, analytical, and measured models are compared.

Communications/Navigation Outage Forecasting System (C/NOFS) statistical energy analysis

The objective of this study was the assessment of the dynamics response of the Communications/Navigation Outage Forecasting System (C/NOFS) spacecraft due to incident acoustic environments. C/NOFS is space vehicle (SV) launched using a Pegasus launch vehicle (LV). A statistical energy analysis (SEA) model of the SV was developed from a NASTRAN finite-element model (FEM). The study compared the dynamic response of the structural subsystems (panels and structural elements) due to incident acoustic Pegasuss protoflight environment [which is 3 dB above maximum expected flight environment (MEFL)] and compared it against the Mil-340 standard workmanship acoustic levels. A concern was raised as to whether the workmanship acoustics, required by Mil-340, imposed on C/NOFS may induce higher vibration responses than what C/NOFS was qualified for, and may result in unnecessary increases in component test levels. The two incident acoustic spectrums were introduced as reverberant loads on the model. The PSD results at the structural panels were compared to random vibration test levels performed on the components for C/NOFS.

AN ASSESSMENT OF TRANSDUCER MASS LOADING EFFECTS ON THE PARAMETERS OF AN EXPERIMENTAL STATISTICAL ENERGY ANALYSIS (SEA) MODEL

The effects of transducer mass and moments of inertia on frequency response functions (FRFs) were assessed. The relationships between the affected and unaffected values were determined through direct substructuring and then analysed with a finite element model. Subsequently, the effects of transducer mass loading on a structure were investigated with a special focus on the errors introduced in an experimental statistical energy analysis model built from the FRFs. Comparison with the experimental data validated the theoretical results. The data were acquired with different instrumentation sets, each of which was capable of highlighting a specific error. The results showed that the model's internal and coupling loss factors were never affected by the measurement errors, whereas the other parameters could be affected by the type of measuring instrumentation selected.

Radiation from nonhomogeneous structures using SEA

Prediction of the acoustic radiation from vibrating structures at high frequencies can be accomplished using statistical energy analysis models. However, the basic formulations of radiation efficiency used in these models are often based on assumptions regarding boundary conditions and structural homogeneity that are not valid. Recent work carried out for nonhomogeneous structures with realistic boundary conditions is presented. An impedance approach is used that allows the radiation to be defined in terms of the forces acting on the structure from boundaries and added components. Examples are used to demonstrate the changes in radiation efficiency resulting from realistic boundaries, frame stiffeners, and added components.

Experimental statistical energy analysis in the time domain

A technique for identifying an experimentally based power flow model from transient measurements is described. The technique was validated using a range of test simulations and then with true physical tests conducted on a structure comprised of coupled thin plates. The identified power flow model was used to successfully update and improve an existing computational statistical energy analysis (SEA) model. It was found that utilization of time domain data allowed for an overdetermined power balance providing favorable numerical conditions for the identification. Useful insight into system order/dimension was obtained during the identification process. It was observed that a full matrix of measured inputs and outputs was not required. However, inclusion of the extra measurements was seen to further increase overdetermination, yielding an even better least squares estimate of model parameters. It was found that the identification procedure indicated true parameters that were easily distinguished from those associated with noise in the data and, hence, seemed well suited for this SEA application. Results indicate that the methodology has the potential to enhance standard experimental SEA procedures.

Internal fuselage noise: comparison of computations and tests on a Falcon airframe

An unequipped Falcon 2000 airframe, a complex heterogeneous structure reduced to the fuselage alone, was subjected to vibro-acoustic characterization within the framework of a cooperative effort by Aerospatiale, Dassault-Aviation, and Onera. Onera's Structural Dynamics and Coupled Systems Department measured the structure's vibro-acoustic responses for four mechanical excitation configurations, and analysed three structural configurations: fuselage alone without floor, with floor, and with floor and internal wall. The resulting database of vibratory and acoustic level measurements is used for validating numerical models in the low- and medium-frequency range, as well as statistical energy analysis (SEA) models in the medium- and high-frequency range. The database was analysed by Dassault-Aviation and Onera. We present here the computation/test comparisons and the limitations of the methods in use. All of the data and comparisons validate the predictive vibro-acoustic response models and methods for a Falcon fuselage subjected to a mechanical excitation.

Sound transmission through lightweight parallel plates. Part II: structure-borne sound

In Part I of this paper sound transmission through double leaf lightweight partitions was examined. It was shown that an important part of the overall transmission is determined by structure-borne sound transmission between the two leaves of the wall. In this report, Part II of the paper, structural coupling is examined in more detail. Two theories are presented. One is appropriate where the connection behaves as a series of points and the other where the connection behaves as a continuous line. It was found that an appropriate transition frequency between these two theories was where a half bending wavelength on the plate fitted between the nails or screws that form the coupling. In the most common forms of construction the connection will behave as a series of independent points for most of the frequency range. The continuous line model included the frame either as a beam or as a short plate. It was found that the agreement with the experimental data was better when the frame was modelled as a plate.There was good agreement between the measured and predicted data for transmission between the two leaves of the wall for a wide variety of structures. These theories can be incorporated into a statistical energy analysis model to enable the sound transmission throughout the entire structure to be predicted as was shown in Part I of this paper.

Experimentally validated statistical energy analysis models of wood and metal frame walls

Statistical energy analysis models were developed, using commercially available programs, for insulated and uninsulated wood and metal frame walls with various gypsum configurations. Material properties were taken from the literature. The 1/3 octave band results over the frequency range from 100 to 6300 Hz were compared with measured data from tests conducted in accordance with ASTM E 90. The predicted sound transmission losses were found to compare favorably with the measured data. The predicted power flows gave some insight into which paths were most significant, and the opportunity to alter them with changes in material properties.

Probability Distribution of Statistical Energy Analysis Model Responses Due to Parameter Randomness

The Statistical Energy Analysis (SEA) methodology has been widely used in aerospace, ship and automotive industry for high frequency noise analysis and acoustic designs. SEA models are treated here as baseline representations of a population of models for systems such as automotive vehicles. SEA responses from the population of all possible models for a vehicle have a random distribution because of the unavoidable uncertainty in the physical parameters due to fabrication imperfection, manufacturing and assembly variations. The random characteristics of the SEA responses can be described by the response probability distribution. In this work, SEA energy response probability distributions due to parameter randomness in a small neighborhood of nominal design values in frequency bands are proven through the Central Limit Theorem to be Gaussian for infinite number of design parameters. Mean squared sound pressure and velocity are directly proportional to SEA energy responses, their distributions are also shown to be Gaussian. In engineering applications, the number of design parameters is always finite for any SEA models. A Monte Carlo test and Statistical Hypothesis test on a simple 3-element SEA model show that the theoretical, infinite order, Gaussian distributions are good approximations for response distributions of a finite parameter SEA model.

Flanking paths between walls and lightweight wood frame floors using statistical energy analysis

Previous work has examined flanking paths from a floor/ceiling assembly to a load-bearing wall (where the floor joists were oriented normal to the supporting wall). It was shown that beams at the joint (plates and joist header) must be considered when predicting transmission at this type of joint. The dominant flanking path was from the floor deck to the supporting wall which reduced the apparent sound insulation from FSTC 59 to 53. The path from the upper to the lower wall was insignificant. This paper presents the results of a similar study that examined flanking paths from a nominally identical floor/ceiling assembly to a non-load-bearing wall (where the joists were parallel to the joint axis). Measured velocity level differences and apparent sound insulation are compared to the load-bearing wall configuration. Flanking paths involving a non-load-bearing wall are shown to have no appreciable impact. Joint models are presented using both standard wave methods and dynamic stiffness methods. The joint models are incorporated into a statistical energy analysis model of the system. Measured and predicted results for the two joint configurations are compared and show good agreement between 100–3150 Hz.

In-plane wave propagation in buildings

When structural vibration measurements are made it is usually bending wave motion that is measured and compared with theoretical predictions. However, in-plane motion is also important for transmission through buildings, particularly if this occurs over large distances and involves transmission across many joints. In this paper a simple procedure for measuring in-plane motion is reviewed and used to study in-plane vibration transmission through a building. It is found that the technique can be used at lower frequencies but that interference associated with bending waves will usually limit its application at high frequencies unless the in-plane vibration is very high. The measured vibration agrees well with the results predicted using a statistical energy analysis model.

Modal densities of simple dynamic systems

Modal densities are parameters that participate in the specification of a statistical energy analysis (SEA) model of a complex composed of a number of coupled dynamic systems. The modal density n(ω) of a dynamic system in this context, is defined by the equation: (Δω)n(ω)=N(ω), where a frequency band {ω,Δω} is identified by the bandwidth (Δω) centered at the frequency (ω) and N(ω) is the number of resonant modes, in this dynamic system, for which the resonance frequencies lie within this frequency band. Usually, it is assumed that the modal density n(ω) is a continuous and/or a monotonic function of the frequency (ω). Moreover, it is often argued that the modal densities are identical for dynamic systems that possess the same propagation speeds and the same spatial extents, i.e., the same volumes, areas, or lengths. The implication that the assumption and the argument are particularly valid for the higher frequency range, has designated SEA suitable for ‘‘a high-frequency analysis only.’’ The modal densities are examined, for a few simple dynamic systems, in an attempt to reassess the assumption, the argument, and the designation.

Sound transmission across a separating and flanking cavity wall construction

Two parameters that can be difficult to model accurately for cavity wall constructions are the cavity damping and the foundation coupling. In order to investigate dominant sound transmission paths across masonry cavity wall constructions, measured cavity damping and foundation coupling data have been incorporated in a statistical energy analysis (SEA) model for a test construction in the BRE flanking laboratory. This paper presents measured data to validate the SEA predictions for the direct and flanking transmission paths that were dominant. For the masonry cavity wall construction that was tested, structural coupling due to the separating wall foundations was found to be a dominant path for transmission across the separating cavity wall.

Sound transmission through a double leaf partition with edge flanking

Lightweight double leaf partitions are widely used and with proper design give good sound isolation. However, when these walls are used as party walls between dwellings, then precautions are necessary to prevent the transmission of fire and smoke. This is usually carried out by placing a firestop in the cavity. This firestop introduces flanking transmission paths reducing the airborne transmission loss of the wall. A simple model is developed which can predict vibration transmission across this type of structural connection. The structural vibration transmission loss can then be used with a more general statistical energy analysis model to give the sound transmission through the entire system. Predicted airborne transmission loss results for a variety of different materials are compared with measured results and good agreement is obtained.

Implementing and improving statistical energy analysis models using quality technology

Implementing and improving statistical energy analysis models using quality technology

Sound transmission through parallel plates coupled along a line

This paper presents a theoretical model to predict bending wave transmission through double walls where the two leaves are coupled by a line joint. The model assumes that the joint comprises four semi-infinite plates connected at their edges by an inertia-less rigid beam and allows the structural transmission loss between the plates to be computed. These values can then be used in a standard statistical energy analysis model to predict either the structural transmission from one plate to another or airborne transmission through the wall. The predicted results show good agreement with measurements performed both on a cavity masonry wall and a dry-lined wall tested in a transmission suite.