Abstract
MODal ENergy Analysis (MODENA) is an energy-based approach which is proposed recently to provide a pure tone analysis of power flow. The net exchanged power between two coupled oscillators is proportional to the weighted difference of total energies of oscillators. Contrary to Statistical Energy Analysis (SEA) or Statistical modal Energy distribution Analysis (SmEdA), the MODENA approach can deal with strong coupling case where the power can flow from the oscillator with lower energy to the one with higher energy. The level of coupling strength between oscillators may affect the accuracy of the MODENA approach. This research work aims to propose a criterion to determine the level of coupling in the MODENA approach. A non-dimensional parameter named coupling strength factor is defined to clearly demonstrate the level of coupling strength. Two numerical examples: (a) a two-oscillators coupling case and (b) a multi-modal coupling case are conducted to show the effectiveness of the proposed criterion.
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References
Totaro, N., Guyader, J.L.: Modal energy analysis. J. Sound Vib. 332(16), 3735–3749 (2013)
Lyon, R.H., Dejong, R.G.: Theory and Application of Statistical Energy Analysis. Butterworth-Heinemann, London (1995)
Lyon, R.H., Maidanik, G.: Power flow between linearly coupled oscillators. J. Acoust. Soc. Am. 34(5), 623–639 (1962)
Newland, D.E.: Calculation of power flow between coupled oscillators. J. Sound Vib. 3(3), 262–276 (1966)
Scharton, T.D., Lyon, R.H.: Power flow and energy sharing in random vibration. J. Acoust. Soc. Am. 43, 1332–1343 (1968)
Maxit, L., Guyader, J.L.: Extension of the SEA model to subsystems with non-uniform modal energy distribution. J. Sound Vib. 265(2), 337–358 (2003)
Totaro, N., Dodard, C., Guyader, J.L.: SEA coupling loss factors of complex vibro-acoustic systems. J. Vib. Acoust. 131(2), 041009 (2009)
Totaro, N., Guyader, J.L.: Extension of the statistical modal energy distribution analysis for estimating energy density in coupled subsystems. J. Sound Vib. 331, 3114–3129 (2012)
Le Bot, A., Vincent, C.: Validity diagrams of statistical energy analysis. J. Sound Vib. 329(2), 221–235 (2010)
Pankaj, A.C., Sastry, S., Murigendrappa, S.M.: A comparison of different methods for determination of coupling factor and velocity response of coupled plates. J. Vibroeng. 15(4), 1885–1897 (2013)
Souf, B., Bareille, O., Ichchou, M.N., et~al.: Variability of coupling loss factors through a wave finite element technique. J. Sound Vib. 332(9), 2179–2190 (2013)
Secgin, A.: Numerical determination of statistical energy analysis parameters of directly coupled composite plates using a modal-based approach. J. Sound Vib. 332(2), 361–377 (2013)
Ji, L., Huang, Z.: A simple statistical energy analysis technique on modeling continuous coupling interfaces. J. Vib. Acoust. 136(1), 014501 (2014)
Maxit, L., Berton, M., Audoly, C., et al: Discussion about different methods for introducing the turbulent boundary layer excitation in vibroacoustic models. In: Flinovia-Flow Induced Noise and Vibration Issues and Aspects, pp. 249–278. Springer, Switzerland (2015)
Fahy, F.J.: Statistical energy analysis: a critical overview. Philos. Trans. R. Soc. Lond. Ser. A Phy. Eng. Sci. 346(1681), 431–447 (1994)
Ji, L., Mace, B.R.: Statistical energy analysis modelling complex structures as coupled sets of oscillators: ensemble mean and variance of energy. J. Sound Vib. 317, 760–780 (2008)
Cotoni, V., Langley, R.S., Kidner, M.R.F.: Numerical and experimental validation of variance prediction in the statistical energy analysis of built-up systems. J. Sound Vib. 288, 701–728 (2005)
Xie, S.L., Zhang, Y.H., Xie, Q., et~al.: Identification of high frequency loads using statistical energy analysis method. Mech. Syst. Signal Process. 35(1), 291–306 (2013)
Legault, J., Woodhouse, J., Langley, R.S.: Statistical energy analysis of inhomogeneous systems with slowly varying properties. J. Sound Vib. 333(26), 7216–7232 (2014)
DÃaz-Cereceda, C., Poblet-Puig, J., RodrÃguez-Ferran, A.: Automatic subsystem identification in statistical energy analysis. Mech. Syst. Signal Process. 54, 182–194 (2015)
Aragonès, À., Guasch, O.: Ranking paths in statistical energy analysis models with non-deterministic loss factors. Mech. Syst. Signal Process. 52, 741–753 (2015)
Maxit, L., Guyader, J.L.: Estimation of SEA coupling loss factors using a dual formulation and FEM modal information, Part I: theory. J. Sound Vib. 239(5), 907–930 (2001)
Karnopp, D.: Coupled vibratory-system analysis, using the dual formulation. J. Acoust. Soc. Am. 40(2), 380–384 (1966)
Maxit, L., Guyader, J.L.: Estimation of SEA coupling loss factors using a dual formulation and FEM modal information, Part II: numerical applications. J. Sound Vib. 239(5), 931–948 (2001)
Maxit, L., Ege, K., Totaro, N., et~al.: Non resonant transmission modelling with statistical modal energy distribution analysis. J. Sound Vib. 333(2), 499–519 (2014)
Acknowledgments
The work described in this paper was supported by a Program for New Century Excellent Talents in University (NCET-11-0086), a Research Grant from National Natural Science Foundation of China (No. 10902024) and also funded by Jiangsu Natural Science Foundation (No. BK2010397).
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Zhang, P., Wu, S., Li, Y., Fei, Q. (2016). Demarcation for the Coupling Strength in the MODENA Approach. In: De Clerck, J., Epp, D. (eds) Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-30084-9_18
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