POMs analysis of randomly vibrating systems obtained from Karhunen-Loève expansion

Journal of Sound and Vibration

Volumn 297, Issue 3-5, 2006, Pages 774-793

  Bellizzi, Sergio ^a   Sampaio, Rubens ^b  

^a LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; CORRELATION METHODS; DECOMPOSITION; FUNCTIONS; NONLINEAR SYSTEMS; RANDOM PROCESSES;

MECHANICAL SYSTEMS; NONLINEAR VIBRATING SYSTEMS; PROPER ORTHOGONAL DECOMPOSITION (POD); SPATIO-TEMPORALLY VARYING SYSTEMS;

VIBRATIONS (MECHANICAL);

EID: 33747369833     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2006.04.023     Document Type: Article

References (28)

1. G. Kerschen, J.C. Golinval, A. Vakakis, L. Bergman, The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview, Nonlinear Dynamics, Special issue on Reduced Order Models: Methods and Applications 41 (2005) 141-170.
2. Ghanen R., and Spanos P.D. Stochastic Finite Elements: A Spectral Approach. rev. ed. (2003), Dover, New York
3. F. Poirion, C. Soize, Monte Carlo construction of the Karhunen-Loève expansion for non-Gaussian random fields, in: N. Jones, R. Ghanen (Eds.), Thirteenth ASCE Engineering Mechanics Conference, CDrom, 1999.
4. Sakamoto S., and Ghanem R. Simulation of multi-dimensional non-Gaussian non-stationary random fields. Probabilistic Engineering Mechanics 17 (2002) 167-176
5. Agrawal O.P., and Sonti V.R. Modelling of stochastic dynamic systems using Hamilton's law of varying action. Journal of Sound and Vibration 192 2 (1996) 399-412
6. Smyth A.W., and Masri S.F. Nonstationary response of nonlinear systems using equivalent linearization with a compact analytical form of the excitation process. Probabilistic Engineering Mechanics 17 (2002) 97-108
7. Schenk C.A., Pradlwarter H.J., and Schueller G.I. On the dynamic stochastic response of FE models. Probabilistic Engineering Mechanics 19 (2004) 161-170
8. Graham M.D., and Kevrekidis I.G. Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis. Computers and Chemical Engineering 20 5 (1996) 495-506
9. Atwell J.A., and King B.B. Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations. Mathematical and Computer Modelling 33 (2001) 1-19
10. Kreuzer E., and Kust O. Analysis of long torsional strings by proper orthogonal decomposition. Archive of Applied Mechanics 67 (1996) 68-80
11. Steindl A., Troger H., and Zemann J.V. Nonlinear Galerkin methods applied in the dimension reduction of vibrating fluid conveying tubes. In: Paidoussis M.P., Bajaj A.K., Corke T.C., Farabee T.M., Williams F., and Hara D.R. (Eds). ASME Symposium on Fluid-Structure Interaction, Aeroelasticity, Flow-Induced Vibration and Noise vol. AD53-1 (1997), Dallas, EUA 273-280
12. Ma X., and Vakakis A.F. Karhunen-Loève decomposition of the transient dynamics of a multibay truss. AIAA Journal 37 8 (1999) 939-946
13. Trindade M.A., Wolter C., and Sampaio R. Karhunen-Loève decomposition of coupled axial/bending vibrations of beams subject to impacts. Journal of Sound and Vibration 279 (2005) 1015-1036
14. Feeny B.F., and Kappagantu R. On the physical interpretation of proper orthogonal modes in vibrations. Journal of Sound and Vibration 211 4 (1998) 607-616
15. Kerschen G., and Golinval J.C. Physical interpretation of the proper orthogonal modes using singular value decomposition. Journal of Sound and Vibration 249 5 (2002) 849-865
16. Lin W.Z., Lee K.H., Lu P., Lim S.P., and Liang Y.C. The relationship between eigenfunctions of Karhunen-Loève decomposition and the modes of distributed parameter vibration system. Journal of Sound and Vibration 256 4 (2002) 791-799
17. Feeny B.F. Proper orthogonal modes and normal modes of continuous vibrations systems. Journal of Vibration and Acoustics 124 1 (2002) 157-160
18. Han S., and Feeny B. Application of proper orthogonal decomposition to structural vibration analysis. Mechanical Systems and Signal Processing 17 3 (2003) 989-1001
19. Feeny B.F., and Liang Y. Interpreting proper orthogonal modes of randomly excited vibration systems. Journal of Sound and Vibration 265 (2003) 953-966
20. Kerschen G., and Golinval J.C. Comments on Interpreting proper orthogonal modes of randomly excited linear vibration systems. Journal of Sound and Vibration 274 (2004) 1091-1092
21. Loève M. Probability Theory (1960), Van Nostrand, New York
22. Papoulis A. Probability, Random Variables and Stochastic Process (1965), McGraw-Hill, New York
23. Hochstadt H. Integral Equations (1989), Wiley, New York
24. Sirovich L. Turbulence and the dynamics of coherent structures-Part I: coherent structures. Quarterly of Applied Mathematics 45 3 (1987) 561-571
25. Wolter C., Trindade M., and Sampaio R. Obtaining mode shapes through the Karhunen-Loève expansion for distributed-parameter linear systems. Shock and Vibration 9 4-5 (2002) 177-192
26. Poirion F., and Soize C. Simulation numérique des champs stochastiques gaussiens homogènes et non homogènes. La Recherche Aérospatiale 1 (1989) 41-61
27. Kozin F. The method of statistical linearization for non-linear stochastic vibrations. In: Ziegler F., and Schueller G.I. (Eds). Nonlinear Stochastic Dynamic Engineering Systems (IUTAM Symposium Innsbruck/Austria 1987) (1988), Springer, Berlin
28. Roberts J.B., and Spanos P.D. Random Vibration and Statistical Linearization (2003), Dover, New York