Statistical Energy Analysis Theory Research Articles

Uncertainty quantification of diffuse sound insulation values

The sound transmission loss of a partitioning structure depends on the nature of the sound fields in the source and receiver spaces. In an indoor setting, both sound fields are often taken to be diffuse. A diffuse field may represent the sound field of a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in the diffuse transmission loss values. In this paper, closed-form expressions are derived for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room–wall–room system may deviate from the nominal, ensemble-averaged diffuse value which corresponds to omni-directional incidence and halfspace radiation. First, an exact expression is derived for the harmonic or band-averaged diffuse transmission loss variance, based on hybrid deterministic–statistical energy analysis theory. Its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. Subsequently, an approximate expression is derived, which depends on energy-related quantities only, making it also applicable in an experimental setting. Furthermore, it is demonstrated that the diffuse transmission loss is approximately normally distributed, such that a complete uncertainty quantification is possible from the mean and variance values. The expressions are verified in a Monte-Carlo simulation study involving a single wall and then validated with experimental data of double-leaf plasterboard walls containing flexible steel studs.

Study on Sound Radiation Characteristics and Sound Insulation of Extruded Aluminium Plate

The use of extruded aluminium plates in the subway car body can reduce the weight of the car body, but it will bring about the negative result of increased noise in the car. The extruded aluminium panels belong to rib-stiffened plate structure in which both local short wave deformation and whole long wave deformation coexist. Studying the vibro-acoustic characteristics of this structure helps to effectively control the noise in the car. In this paper, Acoustic model of extruded aluminium plate and equivalent plate were both built up based on the hybrid method of finite element and statistical energy analysis(FE-SEA) and the statistical energy method (SEA) respectively. According to the theory of statistical energy analysis(SEA), the equivalent modelling method of the aluminium extrusion was presented using a single plate This paper focuses on the sound radiation characteristics and sound insulation of extrude and equivalent structures. Results show that no matter what method is used, the calculation of the sound power and sound insulation of the two structures has the same trend. However, the results of the FE-SEA method can capture the natural frequency of the board and be more accurate reflect vibro-acoustic characteristics of extruded aluminium panels in the middle and low frequency. Equivalent plate can well predict the sound radiation characteristics and sound insulation in the mid and high frequency by using the SEA parameters of the aluminium extrusion.

Sound insulation of lightweight partition walls with regard to structural sound transmission

The known methods of acoustical calculation in buildings disregard the phenomenon of structural sound transmission, whereas its effect can reach from 2 to 12 dB. The purpose of this paper is to develop the calculation method for sound transmission and vibrations in connected vibroacoustic systems. Theoretical research methods were used based on the theory of statistical energy analysis (SEA) and the theory of self-consistent sound fields with regard to dual nature of sound formation - resonance and inertia. Based on M. Sedov's method of sound fields consistency, a calculation method for sound insulation was developed with integration in SEA methodology. Use of the developed method allows predicting sound transmission through a double-panel partition with the account of adjacent structures.

Identification of impact load using transient statistical energy analysis method

A new identification method for impact loads is proposed based on the transient statistical energy analysis theory. The load identification problems of structure subjected to single excitation are classified into three cases according to the completeness of load location information and subsystem response set. The input energy of impact load and the load location is firstly identified from the averaged vibration energy responses of subsystems according to energy balance equation for three cases. The load amplitude spectrum is thereafter derived under the assumption of constant value of itself from the identified input energy within each analytical frequency band. Finally, the time history of impact load is further determined for the given load time domain waveform using a developed fitting method. The experimental studies of impact load identification are conducted on a plate-shell assembled structural system. The results show that the location and input energy of impact load can be identified with fairly accuracy using the presented identification method. Besides, both the load spectrum and time history of impact load have good agreements with the measured ones.

Simulated and experimental studies on identification of impact load with the transient statistical energy analysis method

A new identification method of impact load is proposed based on the transient statistical energy analysis theory in the paper. Firstly, the location and input energy of impact load are identified according to the energy balance equation with a two-stage identification scheme from the averaged kinetic energy responses of subsystems. Secondly, the impact load amplitude spectrum is derived from the identified impact load input energy based on the Parseval theorem under the constant value assumption within each analysis frequency band. Lastly, a parametric fitting approach is developed to reconstruct further the time history of impact load for the given time domain waveform from the identified impact load amplitude spectrum. The impact load identification approach is qualified through the simulated and experimental studies for a two-plate coupling structural system and the simulated study for a three-plate coupling structure system. The results show that the location and input energy of impact load can be identified accurately using the presented method. The derived impact load amplitude spectrums have reasonable agreements with the real ones. As a result, the reconstructed impact load time histories by the fitting method agree well with the real impact load time histories. The present approach provides an effective and feasible way for impact load identification of engineering structures.

Identification of high frequency loads using statistical energy analysis method

The paper proposes an identification method of high frequency loads based on statistical energy analysis theory. The load identification problems of structures subjected to multi excitations are classified into three cases according to the completeness of loads location information and subsystem response set, and the corresponding identification schemes are presented. The approaches for the derivation of load power spectrum from input power are described as well under the assumptions of constant value and linear variation on load power spectrum within each analytical frequency band. The simulated and experimental studies of load identification with the approach were conducted on a plate–shell assembled structural system. The results show that the input power of loads can be identified accurately in three cases using the presented identification method. Besides that, the computed load power spectrums under the constant value assumption have reasonable agreements with the measured load power spectrums.

A review of recent advances in vibro-acoustic system response variance determination in statistical energy analysis: A tribute to Preston Smith, Jr

Since the pioneering work of Preston Smith, Jr. and Richard Lyon in 1959 in the development of the theory of Statistical Energy Analysis (SEA), followed by many others in the 1960’s on through today, the US Navy has utilized the important SEA vibro-acoustic simulation approach for high frequency self- and radiated-noise predictions of a multitude of undersea vehicles and systems. As a tribute to Preston Smith, this talk will review the current state of research in the determination of the variance/probability distribution about the mean response of a system modeled in SEA. While the subject of system response variance (or confidence interval) has obviously been of interest since the inception of this energy-based statistical method, there has been significant recent research in the literature advancing this area that is worth reviewing. As an additional acknowledgement of Preston Smith’s later important work in the area of underwater cylindrical shell acoustics, the current presentation will also revisit the canonical structural acoustic problem of a point-excited, finite cylindrical shell with fluid loading and compare SEA-derived radiated noise level predictions with a variety of different classical analytical and modern day numerical approach solutions (e.g., FEA, EFEA/EBEA, closed form plate and shell theory solutions).

Prediction method of aircraft interior noise and validation testing

VA-one software is based on Statistical Energy Analysis theory. In this paper, acoustic modeling and prediction of interior noise of Fuselage Acoustic Research Facility (FARF) are accomplished with this software. With its support, the subsystem partition method and modeling method of airframe are proposed; further validation by testing method is also studied. With several different kinds of sidewall structures, the FARF is excited by speaker arrays and shakers while acoustic and vibration energy were measured and added into model as input. The interior damping loss factor was obtained by reverberant time measurement. Then the sound pressure level was predicted. Good coherent between prediction and measurement was obtained while methods of testing and data processing are validated. All these are very important to improve the capability of prediction of interior noise of aircraft.

Determination of SEA total loss and coupling loss factors for built-up structures: Theory and numerical experiments.

It is the aim of this paper to develop a strategical method for the determination of SEA total loss factors (TLFs) and some of the coupling loss factors (CLFs) for built-up structures based on the recent development of in situ measurement techniques and the Statistical Energy Analysis theory. An obvious advantage of the method is that the determined TLFs would include the dissipation of coupling, and ‘automatically’ share the dissipation loss of the coupling to each coupled subsystem. The present strategy provides an applicable means for determination of total loss and some coupling loss factors of built-up structures for high frequency structure borne vibration and sound prediction. Satisfactory results of numerical experiments of the present strategy have been achieved.

Improvement of the method of statistical energy analysis for the calculation of sound insulation at low frequencies

In the application of the statistical energy analysis theory to the calculation of sound insulation it has been determined that there is a great discrepancy between the measured and theoretical values at low frequencies. This is one of the disadvantages of statistical energy analysis. Therefore, it was necessary to improve this method at low frequencies. The measured and theoretical values of the sound transmission loss at low frequencies are made to reach good agreement by the introduction of a correction factor.

Criticism of statistical energy analysis for the calculation of sound insulation: Part 2-double partitions

The theory of statistical energy analysis has been applied to the problem of estimating the transmission loss of a single finite panel. This theory was extended to the problem of a finite double-leaf partition structure. This paper deals with the degree of agreement of the measured values with the theoretical results of the sound insulation of double partitions according to this theory. In addition, the advantages and disadvantages of this method compared with classical methods are discussed. A comparison between the method of statistical energy analysis and classical methods for the calculation of the sound insulation of double partitions is given.