Different Definitions of Entropy for Statistical Energy Analysis

2018 ◽  
Author(s):  
Zahra Sotoudeh
Keyword(s):  
Statistical Mechanics ◽  
Energy Analysis ◽  
Statistical Treatment ◽  
Statistical Energy Analysis ◽  
Vibrating Structures ◽  
Thermodynamic Framework ◽  
Vibrating Systems

This paper explores several definitions of entropy that stem from the fields of statistical mechanics and thermodynamics for vibrating structures. This paper shows that these definitions are equivalent in the context of mechanically vibrating systems. However, one is more suitable for statistical energy analysis. This work is motivated by the usefulness of the entropy concept towards developing a framework for the statistical treatment of vibroacoustic systems. Specifically, entropy provides a thermodynamic framework to justify the methodology of statistical energy analysis.

Statistical Energy Analysis of Vibrating Systems

1967 ◽  
Vol 89 (4) ◽  
pp. 626-632 ◽  
Author(s):  
Eric E. Ungar
Keyword(s):  
Complex Systems ◽  
Energy Analysis ◽  
Energy Approach ◽  
Analysis Approach ◽  
Statistical Energy Analysis ◽  
Random Vibrations ◽  
Vibration Problems ◽  
Energy Balances ◽  
Vibrating Systems

The “statistical energy analysis” approach provides a relatively simple means for understanding and estimating the significant properties of multimodal random vibrations of complex systems, since this approach permits one to treat complex vibration problems in terms of much simpler energy balances. This paper delineates the concepts and relations which form the basis for the statistical energy approach, indicates its range of validity, and illustrates some of its applications.

scholarly journals Experimental validation of variance estimation in the statistical energy analysis of a structural-acoustic system

2019 ◽  
Vol 233 (18) ◽  
pp. 6448-6459
Author(s):  
Luis Andrade ◽  
Robin S Langley ◽  
Tore Butlin ◽  
Matthew de Brett ◽  
Ole M Nielsen
Keyword(s):  
Experimental Evidence ◽  
Variance Estimation ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Acoustic System ◽  
Analysis Model ◽  
Vibrating Structures ◽  
Mean And Variance ◽  
The Mean ◽  
Acoustic Cavities

The Statistical Energy Analysis (SEA) approach has largely been used in vibro-acoustic modelling to predict the averaged energy in coupled vibrating structures and acoustic cavities. The average is performed over an ensemble of nominally identical built-up systems where random responses are observed at high frequencies after excitation. Over the years, this approach has been extended to predict the energy variance employing the statistics of the Gaussian Orthogonal Ensemble, and numerical and experimental evidence has supported the predictions of the mean and variance of energy of coupled vibrating structures. However, little experimental evidence is found to validate the prediction of the variance of energy in coupled structural-acoustic systems. In this work, the mean and variance of energies predicted from a statistical energy analysis model have been validated with experimental measurements on a structural-acoustic system, comprised by a flat thin plate coupled to an enclosed acoustic volume. The structural system has been randomised by adding small masses on arbitrary positions on the plate, whereas the randomisation of the acoustic cavity is achieved by allocating rigid baffles in random positions within the acoustic volume. In general, good agreement is found between the predictions of the model and the experimental results.

The Feasibility of Statistical Energy Analysis in the Modeling of Stringed Musical Instruments

2010 ◽  
Author(s):  
Hossein Mansour
Keyword(s):  
Finite Element ◽  
Structural Modification ◽  
Energy Analysis ◽  
Element Model ◽  
Musical Instruments ◽  
Statistical Energy Analysis ◽  
Reliable Model ◽  
Challenging Tasks ◽  
High Degree ◽  
Vibrating Systems

Stringed musical instruments are complex vibrating systems both from structural and fluid-structure coupling perspectives; hence, their modeling is one of the most challenging tasks in the area of vibration and acoustics. Making a reliable model not only broadens our knowledge of the physics of these instruments, but also it simplifies the procedure of structural modification and optimization on them. In this regard, a Finite Element Model has been previously made from Setar and is verified with the experimental results. Although that model could precisely simulate the instrument in lower frequencies (i.e. below 2.5 KHz), its results showed a weak correlation with reality in higher frequencies. In fact, unreliable results and high computational demand are common drawbacks of finite element method in higher frequencies. To avoid these problems, in this study Setar is modeled with Statistical Energy Analysis (SEA) approach. This method is more efficient in dealing with high degree of uncertainty in the system. SEA does this by averaging the response over the frequency and location to gain a more general and reliable result. Application of SEA in higher frequencies is, in fact, compatible with the nature of musical instruments where in higher frequencies we are mostly interested in the trend of the response rather than the location of each individual peak.

Experimental and Statistical Energy Analysis of the Structure-borne Noise in a Helicopter Cabin

2017 ◽  
Vol 10 (6) ◽  
pp. 323
Author(s):  
Raffaella Di Sante ◽  
Marcello Vanali ◽  
Elisabetta Manconi ◽  
Alessandro Perazzolo
Keyword(s):  
Energy Analysis ◽  
Statistical Energy Analysis

Power Flow and Energy Sharing between an Oscillator and a Continuous Receiver Structure

2011 ◽  
Vol 189-193 ◽  
pp. 1914-1917
Author(s):  
Lin Ji
Keyword(s):  
High Frequency ◽  
Power Flow ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Coupled Subsystems ◽  
Modal Density ◽  
Vibration Problems ◽  
Energy Sharing ◽  
High Modal Density ◽  
Vibration Modeling

A key assumption of conventional Statistical Energy Analysis (SEA) theory is that, for two coupled subsystems, the transmitted power from one to another is proportional to the energy differences between the mode pairs of the two subsystems. Previous research has shown that such an assumption remains valid if each individual subsystem is of high modal density. This thus limits the successful applications of SEA theory mostly to the regime of high frequency vibration modeling. This paper argues that, under certain coupling conditions, conventional SEA can be extended to solve the mid-frequency vibration problems where systems may consist of both mode-dense and mode-spare subsystems, e.g. ribbed-plates.

scholarly journals Ergodic billiard and statistical energy analysis

Wave Motion ◽  
2019 ◽  
Vol 87 ◽  
pp. 166-178 ◽  
Author(s):  
H. Li ◽  
N. Totaro ◽  
L. Maxit ◽  
A. Le Bot
Keyword(s):  
Energy Analysis ◽  
Statistical Energy Analysis
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