Validity diagrams of statistical energy analysis

Abstract This paper is concerned with the validity domain of statistical energy analysis (SEA) which is defined in terms of four criteria. The mode count N and the modal overlap M must be high, the normalized attenuation factor m ¯ and the coupling strength γ must be small. The application of dimensional analysis on the governing equations of plates gives the space of dimensionless parameters in which the validity domain of SEA must be delimited. This domain is discussed on the basis of geometry of the surfaces delimiting it. The diagrams of validity of SEA are introduced and discussed. A numerical simulation on a couple of rectangular plates coupled along one edge illustrates the theoretical approach.

[1]  H. Ch. Öttinger,et al.  Beyond Equilibrium Thermodynamics , 2005 .

[2]  Richard H. Lyon,et al.  Random Vibration of Connected Structures , 1964 .

[3]  R. Lyon.  Fluctuation theory and (very) early statistical energy analysis (SEA). , 2003, The Journal of the Acoustical Society of America.

[5]  Alain Le Bot.  Entropy in statistical energy analysis , 2009 .

[6]  A. Pratellesi,et al.  A hybrid formulation for mid-frequency analysis of assembled structures , 2008 .

[7]  Andy J. Keane,et al.  Statistical Energy Analysis: An Overview, with Applications in Structural Dynamics , 2005 .

[8]  R. H. Lyon,et al.  Statistical Analysis of Power Injection and Response in Structures and Rooms , 1969 .

[9]  Brian R. Mace,et al.  Statistical energy analysis, energy distribution models and system modes , 2003 .

[10]  L. W.,et al.  The Theory of Sound , 1898, Nature.

[11]  A. Le Bot,et al.  A vibroacoustic model for high frequency analysis , 1998 .

[12]  R. Blevins.  Modal density of rectangular volumes, areas, and lines , 2006 .

[13]  Robin S. Langley,et al.  A wave intensity technique for the analysis of high frequency vibrations , 1992 .

[14]  Robin S. Langley.  SEA: current and future research needs , 2000 .

[15]  K. Renji.  On the number of modes required for statistical energy analysis-based calculations , 2004 .

[16]  Reply to “Comment on ‘Vibrational‐Energy Transmission in a Three‐Element Structure’” [D. E. Newland, J. Acoust. Soc. Am. 39, 755 (L) (1966)] , 1966 .

[17]  Svante Finnveden,et al.  Two observations on the wave approach to SEA : Keynote Lecture , 2007 .

[18]  Robert J. Bernhard,et al.  Simple models of energy flow in vibrating membranes , 1995 .

[19]  Antonio Carcaterra,et al.  An Entropy Formulation for the Analysis of Energy Flow Between Mechanical Resonators , 2002 .

[20]  Laurent Maxit,et al.  Extension of SEA model to subsystems with non-uniform modal energy distribution , 2003 .

[21]  Amitabh Sagar,et al.  Author's reply , 1991, Journal of neurosciences in rural practice.

[22]  A. Le Bot.  ENERGY TRANSFER FOR HIGH FREQUENCIES IN BUILT-UP STRUCTURES , 2002 .

[23]  Vincent Cotoni,et al.  Response variance prediction in the statistical energy analysis of built-up systems. , 2004, The Journal of the Acoustical Society of America.

[24]  E. Buckingham.  On Physically Similar Systems; Illustrations of the Use of Dimensional Equations , 1914 .

[25]  L. Boltzmann.  Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen , 1970 .

[26]  Christian Soize.  A model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy , 1992 .

[27]  Comment on “Vibrational‐Energy Transmission in a Three‐Element Structure” [Richard H. Lyon and Terry D. Scharton, J. Acoust. Soc. Am. 38, 253–261 (1965)] , 1966 .

[28]  Robert J. Bernhard,et al.  Simple models of the energetics of transversely vibrating plates , 1995 .

[29]  David Newland,et al.  Power Flow between a Class of Coupled Oscillators , 1968 .

[30]  Robert J. Bernhard,et al.  Measurement of the Statistical Variation of Structural-Acoustic Characteristics of Automotive Vehicles , 1993 .

[31]  R. Langley,et al.  Vibro-acoustic analysis of complex systems , 2005 .

[32]  Terry D. Scharton,et al.  Power Flow and Energy Sharing in Random Vibration , 1968 .

[33]  P. W. Smith.  Statistical models of coupled dynamical systems and the transition from weak to strong coupling , 1979 .

[34]  G. M.,et al.  A Treatise on the Mathematical Theory of Elasticity , 1906, Nature.

[35]  A. Le Bot,et al.  Derivation of statistical energy analysis from radiative exchanges , 2007 .

[36]  Terry D. Scharton,et al.  Vibrational‐Energy Transmission in a Three‐Element Structure , 1965 .

[37]  Aldo Sestieri,et al.  Is it possible to treat confidentially SEA the wolf in sheep's clothing? , 2006 .

[38]  Andy J. Keane,et al.  Statistical energy analysis of strongly coupled systems , 1987 .

[39]  Michael Möser,et al.  Structure-borne Sound , 2009 .

[40]  Jim Woodhouse.  An approach to the theoretical background of statistical energy analysis applied to structural vibration , 1981 .

[41]  F. J. Fahy,et al.  Statistical energy analysis: a critical overview , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[42]  Pj Shorter.  Modeling noise and vibration transmission in complex systems , 2011 .

[43]  Robin S. Langley.  An introduction to statistical energy analysis , 1994 .

[44]  Robin S. Langley,et al.  The ensemble statistics of the band-averaged energy of a random system , 2004 .

[45]  D. Newland.  Calculation of power flow between coupled oscillators , 1966 .

[46]  A. Sonin.  A generalization of the Pi-theorem and dimensional analysis. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Brian R. Mace.  On The Statistical Energy Analysis Hypothesis Of Coupling Power Proportionality And Some Implications Of Its Failure , 1994 .

[48]  J. D. Polack.  Modifying chambers to play billiards, the foundations of reverberation theory , 1992 .