Identification of multi-degree of freedom non-linear systems using an extended modal space model

Mechanical Systems and Signal Processing

Volumn 23, Issue 1, 2009, Pages 8-29

  Platten, M F ^a   Wright, J R ^b   Dimitriadis, G ^c   Cooper, J E ^d  

^a Romax Technology Limited   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

^c UNIVERSITY OF LIÈGE   (Belgium)

^d UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Force appropriation; Non linear system identification; Non linear systems; Resonant decay method

Indexed keywords

AIRCRAFT; DEGREES OF FREEDOM (MECHANICS); LINEAR CONTROL SYSTEMS; LINEAR SYSTEMS; NONLINEAR SYSTEMS;

DEGREE OF FREEDOM; DEGREES OF FREEDOM; FORCE APPROPRIATION; IDENTIFICATION APPROACH; IDENTIFICATION METHODS; MODAL SPACE; NON-LINEAR; NON-LINEAR CHARACTERISTICS; NON-LINEAR DYNAMIC SYSTEMS; NON-LINEAR IDENTIFICATION; NON-LINEAR RESONANT DECAY METHOD; NON-LINEAR SYSTEM IDENTIFICATION; NON-LINEARITIES; POTENTIAL APPLICATIONS; REAL ENGINEERING; REDUCED ORDER MODELLING; RESONANT DECAY METHOD; RESTORING FORCES; SIMULATED SYSTEMS; SMALL SYSTEMS;

CURVE FITTING;

EID: 53849101419     PISSN: 08883270     EISSN: 10961216     Source Type: Journal    
DOI: 10.1016/j.ymssp.2007.11.016     Document Type: Article

References (44)

1. Ewins D.J. Modal Testing: Theory, Practice and Application. second edition (1999), Research Studies Press Ltd., Hertfordshire
2. Worden K., and Tomlinson G.R. Nonlinear Vibrations (2000), Sheffield University Press, Sheffield
3. J.R. Wright, M.F. Platten, J.E. Cooper, and M. Sarmast, Identification of multi-degree of freedom weakly non-linear systems using a model based in modal space, in: Proceedings of the COST International Conference on Structural System Identification, Kassel, Germany, 2001.
4. M.F. Platten, J.R. Wright, J.E. Cooper, The use of a non-contact acoustic excitation array for the estimation of damping in aircraft panels, in: Proceedings of the 25th International Seminar on Modal Analysis, ISMA 2002, Leuven, Belgium, September 2002.
5. Masri S.F., Sassi H., and Caughey T.K. Nonparametric identification of nearly arbitrary nonlinear systems. Journal of Applied Mechanics 49 (1982) 619-628
6. Kerschen G., Worden K., Vakakis A.F., and Golinval J.-C. Past, present and future of nonlinear system identification in structural dynamics. Mechanical Systems and Signal Processing 20 3 (2006) 505-592
7. Richards C.M., and Singh R. Identification of multi-degree-of-freedom non-linear systems under random excitations by the 'reverse path' spectral method. Journal of Sound and Vibration 213 (1998) 673-708
8. Garibaldi L. Application of conditioned reverse path method. Mechanical Systems and Signal Processing 17 1 (2003) 227-235
9. Adams D.E., and Allemang R.J. A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback. Mechanical Systems and Signal Processing 14 (2000) 637-656
10. Billings S.A., and Leontaritis I.J. Input-output parametric models for non-linear systems. ii. Stochastic non-linear systems. International Journal of Control 41 2 (1985) 329-344
11. Billings S.A., Tsang K.M., and Tomlinson G.R. Application of the NARMAX method to nonlinear frequency-response estimation. Modal Analysis: the International Journal of Analytical and Experimental Modal Analysis 4 3 (1989) 97-102
12. Thouverez F., and Jezequel L. Identification of NARMAX models on a modal base. Journal of Sound and Vibration 189 2 (1996) 193-213
13. Chen S., Billings S.A., and Luo W. Orthogonal least squares methods and their applications to non-linear system identification. International Journal of Control 50 5 (1989) 1873-1896
14. Billings S.A., Chen S., and Korenberg M.J. Identification of MIMO non-linear systems using a forward-regression orthogonal estimator. International Journal of Control 49 6 (1989) 2157-2189
15. Chen Q., Worden K., Peng P., and Leung A.Y.T. Genetic algorithm with an improved fitness function for ARX modelling. Mechanical Systems and Signal Processing 21 3 (2007) 994-1007
16. Masri S.F., and Caughey T.K. A nonparametric identification technique for nonlinear dynamic problems. Journal of Applied Mechanics 46 2 (1979) 433-447
17. Worden K., Wright J.R., Al-Hadid M.A., and Mohammad K.S. Experimental identification of multi-degree of freedom non-linear systems using restoring force methods. Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis 9 1 (1994) 35-55
18. Lenaerts V., Kershen G., and Golinval J.C. Proper orthogonal decomposition for model updating of non-linear mechanical systems. Mechanical Systems and Signal Processing 15 1 (2001) 31-43
19. Rice H.J., and Fitzpatrick J.A. A procedure for the identification of linear and nonlinear multi-degree-freedom systems. Journal of Sound and Vibration 149 3 (1991) 397-411
20. Marchesiello S., and Garibaldi L. A time domain approach for identifying nonlinear vibrating structures by subspace methods. Mechanical Systems and Signal Processing 22 1 (2008) 81-101
21. Lin R.M., Ewins D.J., and Lim M.K. Identification of nonlinearity from analysis of complex modes. Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis 8 3 (1994) 290-306
22. Al-Hadid M.A., and Wright J.R. Developments in the force-state mapping technique for non-linear systems and the extension to the location of non-linear elements in a lumped-parameter system. Mechanical Systems and Signal Processing 3 3 (1989) 269-290
23. Shaw S.W., and Pierre C. Normal modes for non-linear vibratory systems. Journal of Sound and Vibration 164 1 (1993) 85-124
24. Vakakis A.F., Manevitch L.I., Mikhlin Y.V., Pilipchuk V.N., and Zevin A.A. Normal Modes and Localization in Nonlinear Systems, Non-linear Science (1996), Wiley-Interscience, New York
25. Nayfeh A.H., and Nayfeh S.A. On nonlinear modes of continuous systems. Journal of Vibration and Acoustics 116 1 (1994) 129-136
26. Pesheck E., Pierre C., and Shaw S.W. A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds. Journal of Sound and Vibration 249 5 (2002) 971-993
27. Camillacci R., Ferguson N.S., and White P.R. Simulation and experimental validation of modal analysis for non-linear symmetric systems. Mechanical Systems and Signal Processing 19 1 (2005) 21-41
28. G. Kerschen, M. Peeters, J.-C. Golinval, A. Vakakis, Nonlinear normal modes, part I: a useful framework for the structural dynamicist, Mechanical Systems and Signal Processing, under review, 2007.
29. Gifford S.J., and Tomlinson G.R. Recent advances in the applications of functional series to non-linear structures. Journal of Sound and Vibration 135 2 (1989) 289-317
30. Tawfiq I., and Vinh T. Contribution to the extension of modal analysis to non-linear structure using Volterra functional series. Mechanical Systems and Signal Processing 17 2 (2003) 379-407
31. Chatterjee A., and Vyas N.S. Non-linear parameter estimation in multi-degree-of-freedom systems using multi-input Volterra series. Mechanical Systems and Signal Processing 18 3 (2004) 457-489
32. Vazquez Feijoo J.A., Worden K., and Stanway R. System identification using associated linear equations. Mechanical Systems and Signal Processing 18 3 (2004) 431-455
33. Vazquez Feijoo J.A., Worden K., and Stanway R. Associated linear equations for volterra operators. Mechanical Systems and Signal Processing 19 1 (2005) 57-69
34. Peyton Jones J.C. Simplified computation of the Volterra frequency response functions of non-linear systems. Mechanical Systems and Signal Processing 21 3 (2007) 1452-1468
35. Wright J.R. Flutter test analysis in the time domain using a recursive system representation. Journal of Aircraft 11 12 (1974) 774-777
36. Wright J.R., Cooper J.E., and Desforges M.J. Normal mode force appropriation theory and application. Mechanical Systems and Signal Processing 13 2 (1999) 217-240
37. M.F. Platten, J.R. Wright, J.E. Cooper, Identification of a continuous structure with discrete non-linear components using an extended modal model, in: Proceedings of the International Conference on Noise and Vibration Engineering, ISMA 2004, Leuven, Belgium, 2004, pp. 2155-2168.
38. R. Williams, J. Crowley, H. Vold, The multivariate mode indicator function in modal analysis, in: Proceedings of the 4th International Modal Analysis Conference, Los Angeles, USA, 1986.
39. Atkins P.A., Wright J.R., and Worden K. An extension of force appropriation to the identification of non-linear multi-degree of freedom systems. Journal of Sound and Vibration 237 1 (2000) 23-43
40. Naylor S., Platten M.F., Wright J.R., and Cooper J.E. Identification of multi-degree of freedom systems with nonproportional damping using the resonant decay method. Journal of Vibration and Acoustics 126 2 (2004) 298-306
41. Wright J.R., Holmes P.J., Cooper J.E., and Desforges M.J. Optimum exciter placement for normal mode force appropriation. IMechE Proceedings, Part G, Journal of Aerospace Engineering 212 5 (1998) 325-338
42. Tomlinson G.R. Force distortion in resonance testing of structures with electro-dynamic vibration exciters. Journal of Sound and Vibration 63 3 (1979) 337-350
43. M.F. Platten, J.R. Wright, J.E. Cooper, M. Sarmast, Identification of multi-degree of freedom non-linear systems using an extension of force appropriation, in: Proceedings of the 20th International Modal Analysis Conference, IMAC XX, Los Angeles, USA, 2002.
44. J.R. Wright, M.F. Platten, J.E. Cooper, M. Sarmast, Experimental identification of continuous non-linear systems using an extension of force appropriation, in: Proceedings of the 21st International Modal Analysis Conference, Orlando, Florida, USA, 2003.