Statistical Energy Analysis Method Research Articles

Sound Bridging By Wall Ties in Cavity Brick Walls: Theory and Experiment

In cavity brick wall construction, wall ties are frequently used to provide resistance to water penetration and to transfer lateral forces, thereby increasing the load-carrying capacity of the wall. The presence of such ties, however, introduces an additional path through which sound and vibration transmission can take place. As a consequence, the sound insulation performance of cavity walls with ties may be lower than those of identical walls with no ties. In this paper, sound transmission loss results obtained from laboratory measurements on a common cavity wall system with two different types of wall ties are reported. The statistical energy analysis (SEA) method is used to construct a model representing a cavity wall system with or without ties, and predicted airborne sound transmission loss values are compared with experimental results. By considering the wall ties as rigid point bridges that excite the second leaf, which in turn radiates the transmitted sound power, expressions are developed that allow the calculation of the reduction in transmission loss at different frequencies. Reasonable agreement between theory and experimental results has been found by using both methods.

Statistical energy analysis prediction of a liftoff vibration environment in six degrees of freedom

The liftoff vibration environment for a guidance control sensor was predicted in three translational and three rotational degrees of freedom using statistical energy analysis (SEA) methods. Excitations from airborne sound pressure and mechanical transmission from solid rocket motor internal sources were applied to an SEA model of the vehicle and motor structure. Model predictions of translational response and wavenumbers for radial and inplane motions were combined to estimate rotational velocity environments. The rotational velocities from the vibroacoustic response represented out-of-band noise for the control system (that is trying to properly gimbal the motor nozzle) and required pre-flight estimation so that an appropriate filter could be provided.

Statistics of energy flows in spring-coupled one-dimensional subsystems

This paper considers the problem of determining the statistical fluctuations occurring in the vibrational energy flow characteristics of a system of two multimodal, random, one-dimensional subsystems coupled through a spring and subject to single frequency forcing. The subsystems are modelled either as transversely vibrating Euler- Bernoulli beams or as axially vibrating rods. The masses of the subsystems are modelled as random variables. The calculations of energy flows are based on an exact formulation which uses the Green functions of the uncoupled subsystems, which, in turn, are expressed as summations over the uncoupled modes. Factors influencing the number of modes contributing to the response statistics at any specified driving frequency are investigated. A criterion for identifying the driving frequency beyond which the mean power spectra become smooth is proposed. Empirical procedures are developed to predict the 5 % and 95 % probability points given knowledge of the first two moments of the response. The work reported here forms part of a long term study into the reliability of statistical energy analysis (SEA) methods.

A Study of Vibration Transmission in a Framed Building

Sound transmission through large buildings can be studied using Statistical Energy Analysis (SEA). In this study measurements were carried out to investigate sound transmission through a framed building. Sound transmission between columns, beams, walls and floors is investigated. Sound transmission through the building is investigated and measured and predicted results are shown. Difficulties were encountered when modelling large floor slabs. The work demonstrates the application of Statistical Energy Analysis methods to the study of sound transmission in framed buildings and highlights some of the diiffculties.

Prediction of sound fields in rooms using statistical energy analysis

The method of statistical energy analysis (SEA) has been used to predict the sound field in rooms containing noise sources. Because SEA takes into account the vibration modes both of the boundaries of the room and of the room itself together with the energy transport between them, the predictions of SEA are closer to measured results than those obtained by the statistical acoustical method (SAM) based on Sabine's theory. The validity of prediction by SEA is discussed.

Estimation of the Coupling Loss Factor of Structural Joints

This paper shows how Bishop's receptance method can be used to derive the transmission of vibrational energy across a structural joint. The results are averaged over frequency bands and on the assumption of light damping an approximate formula for the coupling loss factor is obtained. This is an important parameter in the statistical energy analysis method of estimating the response of structures to broad-band random forces. The results compare well with those obtained by the travelling wave method.

The effect of fluid–structural coupling on acoustical decays in a reverberation room in the high‐frequency range

The effect of the fluid–structural coupling between the modes of a sound field and the modes of test panels placed in the sound field upon their decay behavior is investigated in the high‐frequency range. Quasitransient solutions of the average energies in the room and the panels are used to estimate the reverberation times in the room and to calculate the decay curves of a test panel. Experiments are conducted that verify these solutions. The estimated and measured results are in good agreement, which indicates that the average decay behavior of the room and panels can be analyzed in terms of the average modal parameters. The average modal parameters of the test panels and the reverberation room can be related to the Sabine absorption coefficient αSab of the panels. This result suggests an interpretation for the Sabine absorption coefficient of a modally reactive surface and provides a way to estimate this quantity using the statistical energy analysis (SEA) method. The dependence of the αSab upon the room properties, in which the panel is measured, is demonstrated both experimentally and analytically.

Estimation of noise power radiated from gear bodies. 1st Report: The basic theory for estimation of radiated sound power and its application to circular plates with a solid shaft.

Aiming to establish the estimation method of gear noises, the authors derived the basic theory for estimation of radiated sound power from the definition of the loss factor given by Ungar and Kerwin, without using the statistical energy analysis method. The theory was applied to the circular plates with a solid shaft as a simple model of gear bodies, and the vibration modes of the plates were analyzed under the assumption of mode damping. By using the result of the modal analysis, the equations for calculating the frequency spectrum of the three important parameters for estimation, the total loss factor, the driving point mobility and the radiation loss factor of the plates, were theoretically derived.

Prediction of Transient Vibration Envelopes Using Statistical Energy Analysis Techniques

The prediction, by the statistical energy analysis (SEA) method, of transient vibration envelopes for coupled systems is investigated. The relation between the time-varying energy transferred between two coupled subsystems and time-varying energies of the subsystems is studied numerically and experimentally. These studies indicate that time-varying energy transmitted between two subsystems is related to the subsystem energies by an apparent time-varying coupling loss factor. It is shown that the apparent coupling loss factor approaches the asymptotic (or steady-state) coupling loss factor as response energies and transferred energies are integrated over progressively larger times. Both the apparent time-varying coupling loss factor and the asymptotic coupling loss factor, determined experimentally, are used in energy balance equations to predict the time-varying vibration envelopes of a system of two point-coupled plates and the results are compared. Although overall response predictions are similar, considerable differences are noted in individual frequency bands. However, no general method for a priori determination of the apparent time-varying coupling loss factor is suggested.

Modeling of transient vibration envelopes using statistical energy analysis techniques

The modeling, by the statistical energy analysis (SEA) method, of transient vibration envelopes of coupled systems is investigated. The relation between the time‐varying energy transferred between two coupled subsystems and time‐varying energies of the individual subsystem is studied numerically and experimentally. These studies indicate that time‐varying energy transmitted between two subsystems can be related to the subsystem energies by an appparent time‐varying coupling loss factor. It is shown that the apparent coupling loss factor approaches the asymptotic (or steady‐state) coupling loss factor as response energies and transferred energies are integrated over progressively larger times. Both the apparent time‐varying coupling loss factor and the asymptotic coupling loss factor, determined experimentally, are used in energy balance equations to predict the time‐varying vibration envelopes of a system of two point‐coupled plates and the results are compared. Although overall response predictions are similar, considerable differences are noted in individual frequency bands

A functional prediction method on the response probability for linear sound systems on energy scale based on the stochastic information and its application to room acoustics.

As is well-known, the conventional standard identification methods for stochastic systems are usually employed under the optimum selection of the system order and system parameters, by use of the linear correlation technique and the usual least squares error method. In this paper, a new trial of finding some object-oriented system identification method matched to the prediction of output response probability distribution has been proposed in the functional and hierarchical forms. More explicitly, the indoor sound system on an energy scale is firstly described by a linear time series model supported by the well-known Sabine's equation or Statistical Energy Analysis method. Then, a generalized series expansion type probability density expression matched to an energy state variable has been proposed for the system output response in the form matched to the variety of fluctuation form, under the introduction of statistical information reflected hierarchically in expansion coefficients. Furthermore, instead of the usual system order and system parameters in the time series type system model, several kinds of functionally introduced system orders and system parameters have been estimated hierarchically in the matched form to the above hierarchical structure in the probability density expression. Finally, the validity and the effectiveness of the proposed theory have been experimentally confirmed too by applying it to the actual data observed in a reverberation room.

Effect of fluidal‐structural coupling on the acoustical decays in a reverberation room in high‐frequency range

The effect of the coupling between a sound field and test panels upon their decay behavior is investigated in high‐frequency range. Quasitransient solutions of the average energies in the room and the panels are used to estimate the reverberation times in the room and to calculate the decay curves of a test panel. Experiments are conducted to verify these solutions. The estimated and measured results are in good agreement in high‐frequency range, which indicates that the average decay behavior of the room and panels can be analyzed in terms of the average modal parameters. The amalgamation of the average modal parameters (of the test panels and the reverberation room) can be related to the Sabine absorption coefficient αSab of the panels. This result provides a possible interpretation for the αSab of a modally reactive surface and suggests a way to estimate this quantity by statistical energy analysis (SEA) method. The dependence of the αSab upon the room properties, in which the panel is measured, is demonstrated both experimentally and analytically.

A Vibroacoustic Database Management Center for Shuttle and Expendable Launch Vehicle Payloads

A Vibroacoustic Database Management Center has recently been established at the Jet Propulsion Laboratory (JPL). The center uses the Vibroacoustic Payload Environment Prediction System (VAPEPS) computer program to maintain a database of flight and ground-test data and structural parameters for both shuttle and expendable launch-vehicle payloads. Given the launch-vehicle environment, the VAPEPS prediction software, which employs Statistical Energy Analysis (SEA) methods, can be used with or without the database to establish the vibroacoustic environment for new payload components. This paper summarizes the VAPEPS program and describes the functions of the Database Management Center at JPL.

Noise Prediction of Offshore Platforms and Working Ships

This paper describes noise prediction methods and some examples applied to offshore structures and working ships.An empirical method based on full-scale measurement data and a statistical energy analysis (SEA) method were worked out as prediction methods of noise level for the living quarters of offshore platforms and working ships.Some coefficients and parameters included in the noise prediction methods were determined from the full-scale measurement data of noise and vibration on 7 offshore platforms and 2 working ships.Noise levels obtained from the full-scale measurements were compared with those calculated by the empirical method and the statistical energy analysis method.The results yielded an average error of 3-5 dB (A). To clarify the vibration propagation characteristics and to discuss the noise and vibration reduction methods, an experiment was conducted using a scale model and the experimental values and predicted values by the SEA method showed agreement in their trends.

New functional evaluation methods of sound insulation system using the SEA method and an [formula omitted] evaluation criterion

Recently, for the purpose of reducing residential environmental noise, many sound insulation systems have often been improved acoustically by changing their geometrical scales and/or acoustical characteristics. In this paper, new functional evaluation and probabilistic prediction methods for these improvements are theoretically and experimentally proposed in practical expression forms by introducing a few functional parameters. These functional parameters introduced only for the prediction are supported by many physical structural factors closely related to the well-known statistical energy analysis method, and are easily estimated in a preliminary experiment. The estimation procedures developed are based on two error criteria using the actual overall frequency band data. The used least-squares error criterion is the most fundamental method and the L x evaluation criterion matches the actual situation of estimating the representative evaluation indices. Finally, by using musical sound as an input noise, the effectiveness of the proposed method is experimentally confirmed by applying it to some actual problems.

Predicting sound power radiation from built-up structures using statistical energy analysis

Statistical Energy Analysis (SEA) methods have been used in conjunction with energy accountancy ideas to develop a technique for the prediction of sound power radiation from machinery and other built-up structures. The methods enable calculation and optimization of the changes in noise radiation associated with modifications to individual parts of a coupled structure. As an initial exercise the techniques have been applied to predict the noise radiation from a coupled system composed of two plates welded at right angles. The predicted noise radiation is compared with values obtained from direct measurements by the surface velocity technique and agreement generally within 2 or 3 dB on overall level is obtained.

Two probabilistic evaluation methods for single and double walls type sound insulation systems with arbitrary random noise excitation.

In the practical engineering field of noise control, it is as important as the sound source countermeasure to improve the sound propagation characteristics by newly setting a sound insulation system. On the other hand, the noise statistics like an Lx (x=5, 10, 50, 90, ) defined as a (100 -x) percentage point of the sound level distribution are very important as well as the lower order energy moment statistics like an Leq in the actual noise evaluation and regulation problems. In this paper, two kinds of probabilistic evaluation methods for sound insulation systems are theoretically proposed from typically different points of view for the probability distribution of the transmitted sound intensity, when a general stationary random noise having an arbitrary distributionform and frequency characteristics is insulated by a wall. To evaluate its sound transmission coefficient, a somewhat modified statistical energy analysis method has been used.The validity of the theoretical results is experimentally confirmed by applying it to the actually observed data on the output response fluctuation of single and double walls type insulation systems inserted between two reverberation rooms.

Statistical energy analysis, structural resonances, and beam networks

The statistical energy analysis method is applied to a beam network in a building structure. A method of taking structural resonances into account is introduced into the analysis via the use of ‘‘discretized’’ modal densities. Transfer functions computed from the model beam network are compared over a wide frequency range to experimentally measured transfer functions from an equivalent beam network in an existing building structure in which one of the beams is vibrationally excited. Our results suggest that by taking resonance effects into account, the predictions of statistical energy analysis can be made to display the fine details found in the frequency dependence of transfer functions for real building structures.

Calculation of sound insulation of ribbed panels using statistical energy analysis

Crocker and Price employed the method of statistical energy analysis to calculate the sound insulation of single and double partitions. As ribbed panels are used in many structures, for example, in the superficial structure of ships, the application of statistical energy analysis to calculate the sound insulation of such panels is discussed. The results of experiments conducted to test the theory are reported. The agreement between theory and experiment is shown to be satisfactory.

Transfer function determination in structures and enclosures using adaptive linear prediction techniques

Given a structure or enclosure with a finite number of bandlimited sources radiating energy into it, the transfer functions between any two points are found using adaptive pole‐zero digital filters with a leasts‐squared‐error criterion when the signals at the points in the structure or enclosure are known. The number of poles and zeros in the adaptive filter is chosen higher than the assumed number of resonances and antiresonances between the points of interest to insure that all the dominant features of the transfer function are matched by the adaptive filters. The mathematical basis for deriving the filter parameters directly from the observed input/output time series can be found from using a lattice method solution to the multichannel Yule‐Walker equations [B. Friedlander, Proc. IEEE 70 (8), 841–852 (1982)]. The computed poles and zeros of the adaptive filter provide more information than traditional Fourier cross spectra or statistical energy analysis methods.