Contribution to the extension of modal analysis to non-linear structure using Volterra functional series

Mechanical Systems and Signal Processing

Volumn 17, Issue 2, 2003, Pages 379-407

  Tawfiq, I ^a   Vinh, T ^a  

^a Laboratory of Rheology and Struct   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; FOURIER TRANSFORMS; IMPULSE RESPONSE; INTEGRAL EQUATIONS; ITERATIVE METHODS; MATRIX ALGEBRA; MODAL ANALYSIS; PARAMETER ESTIMATION; POLYNOMIALS; TRANSFER FUNCTIONS; VIBRATIONS (MECHANICAL);

CHEBYSHEV POLYNOMIALS; HILBERT TRANSFORM; NONLINEAR STRUCTURES; RESTORING FORCE SURFACE METHOD; SUPERPOSITION PRINCIPLES; VOLTERRA FUNCTIONAL SERIES;

STRUCTURAL ANALYSIS;

EID: 0037344009     PISSN: 08883270     EISSN: None     Source Type: Journal    
DOI: 10.1006/mssp.2002.1499     Document Type: Article

References (41)

1. K. Worden 1989 Ph. D. thesis, Heriott Watt University, Edinburgh, U.K. Parametric and non parametric identification of non-linearity in structural dynamics.
2. H. Leaderman 1943 Elastic and Creep Properties of Filamentous Materials. Washington, DC: Textile Foundation.
3. M. Simon and G. Tomlinson 1984 Journal of Sound and Vibration 96, 421-436. Use of the Hilbert transform in modal analysis of linear and non-linear structures.
4. T. Vinh, A. Haoui, B.J. Fei and Y. Chevalier 1985 Annals of CIRP 35, 315-318. New approach of non-linear system by special integral transform.
5. T. Vinh, A. Haoui and B.J. Chevalier 1984 Proceedings of the 2nd International Modal Analysis Conference, Orlando FL, February, 852-857. Extension of modal analysis to non-linear structures Hilbert transform.
6. M. Feldman 1984 Mechanical System and Signal Processing 8, 119-127. Non linear system vibration analysis using Hilbert transform I-Free vibration analysis method FREEVIB.
7. M. Feldman 1994 Mechanical System and Signal Processing 8, 309-338. Non linear system vibration analysis using Hilbert transform II-forced Vibration analysis method FORCEVIB.
8. K. Worden and G.R. Tomlinson 2001 Nonlinearity in Structural Dynamics. Bristol and Philadelphia: Institute of Physics Publishing.
9. M. Frechet 1907 Comptes-rendus Académie Des Sciences de Paris - Second half year. Généralisation d'un théorème de Weierstrass.
10. E. Gilbert 1977 Functional expansion for the response of non-linear differential systems. IEEE Transactions Ac 22, 909-921.
11. M. Schetzen 1980 The Volterra and Wiener Theories of Nonlinear Systems. New York: John Wiley and Sons.
12. S.N. Obidegwu and H.A. Barker 1973 Proceedings of IEEE 120, 1293-1300. Effects of non linearities on the measurements of weighting functions by cross correlation using pseudo random signals.
13. N. Wiener 1942 Report no. 129, Radiation Laboratory, MIT, Cambridge, MA. Response of non-linear device to noise.
14. A.A. Khan and N.S. Vyas 1999 Journal of Sound and Vibration 221, 805-821. Non-linear parameter estimation using Volterra and Wiener theories.
15. K. Schwartz 1966 Théorie des distributions, 2nd edn. Paris: Hermann.
16. A. Zemanian 1965 Distribution Theory and Transform Analysis - An introduction to generalised functions with applications, 57-67. New York: McGraw-Hill.
17. J. Hadamard 1952 Lectures on Cauchy's Problem in Linear Partial Differential Equations. New York: Dover Publications.
18. H. Liu 1989 Ph. D. thesis (in French), Conservatoire National des Arts et Métiers de Paris, April 28. Multidimensional signal processing and Volterra series application to non-linear dynamics of structures.
19. T. Vinh 1986 Lecture Note On Transfer Functions and Impulse Responses of Non Linear Structures. Seminar Heriott Watt University.
20. R. Lecourtier F. Lamnabhi-Lagarrigue and E. Walter 1987 In Volterra and Generating Power Series Approaches to Identifiability Testing, 50-66. New York, Pergamon Press. E. Walter (ed.). Ecole Supérieure d'électricité France: Gif Sur Yvette.
21. K. Worden, G. Manson and G.R. Tomlinson 1997 Journal of Sound and Vibration 205, 67-84. A harmonic probing algorithm for the multi input Volterra series.
22. I. Tawfiq and T. Vinh Extension of modal analysis to non-linear structure using Volterra series. Signal processing and testing methods, to be published.
23. S.J. Gifford 1989 Ph. D. thesis, Heriott Watt University, Edinburgh, March. Volterra series analysis of non linear structures.
24. D. Storer 1991 Ph. D. thesis, University of Manchester, October. Dynamic analysis of non linear structures using higher order frequency response.
25. C. Huet 1972 VI th International Congress of Rheology, Lyon, 4-8 September. Series of Volterra functionals in non-linear viscoelasticity.
26. M. Fliess and F. Lamnabhi-Lagarrigue 1983 An algebraic approach to non linear functional expansions. IEEE Transaction on Circuits and Systems CAS 30, 495-502.
27. T. Vinh M. Soula and Y. Chevalier 1997 Journal of Sound and Vibration 205, 185-203. Transient responses of polymers and elastomers deduced from harmonic responses.
28. Y.C. Kim and E.J. Powers 1978 Physics of Fluids 21, 1452-1453. Digital bispectral analysis of self excited fluctuation spectra.
29. T.S. Rao and M.M. Gab 1944 An Introduction to Bispectral Analysis and Bilinear Time Series Models, Lecture Notes in Statistics Vol. 24. Berlin: Springer-Verlag.
30. C.L. Nikias and A. Petropoulos 1993 Higher Order Spectra Analysis - A Non Linear Signal Processing framework, NJ, U.S.A: Prentice-Hall, 57-66.
31. Ditkine V and A. Proudnikov 1975 Operational Calculus, pp. 337-362. Moscow French edition.
32. A.M. Nayfeh and D. Mook D. 1979 Non linear Oscillations. New York: John Wiley and Sons.
33. G. Schmidt and A. Tondl 1986 Non linear Vibrations. London: Cambridge University Press.
34. C.M. Richards and Singh R. 1998 Journal of Sound and Vibration 213, 673-708. Identification of multi degree of freedom non linear systems Under random excitations by the "reverse path" spectral method".
35. B. Kuran, H.N. Ozguven 1996 Journal of Sound and Vibration 189, 315-339. A modal superposition method for non-linear structures.
36. J. Bendat 1990 Non Linear System Analysis and Identification from Random Data. New York: John Wiley.
37. Y.S. Tang S. Boyd L.O. Chua and L.O. Chua 1983 IEEE Transactions on Circuits and Systems 30, 571-577. Measuring Volterra kernels.
38. A.H. Nayfeh and B. Balachandran 1995 Applied Nonlinear Dynamics - Analytical Computational and Experimental Methods. Wiley Series in Non-linear Sciences. New York: Wiley and Sons Inc.
39. T. Vinh and T. Chouychai 1991 IMAC 1991, Vol. 1, pp. 81-88. Multidimensional frequency Hilbert transform applied to transfer functions.
40. H. Cartan 1961 Théorie élémentaire des functions analytiques d'une ou plusieurs variables complexes pp. 135-136. Paris, Hermann Edit.
41. T. Chouychai 1987 Ph.D. thesis in French, ISMCM, Saint-Ouen July Dynamic non linear behaviour of structures (Linearisation, multidimensional Hilbert transform and Volterra series.