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Advanced Strategies for Nonlinear System Identification

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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 518))

Abstract

This chapter contains a review of the past and recent developments in system identifi cation of nonlinear dynamical structures. The objective is to present several approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations.

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Bibliography

  1. G. Kerschen, K. Worden, A.F. Vakakis, J.C. Golinval, Nonlinear normal modes, Past, present and future of nonlinear system identification in structural dynamics, Mechanical Systems and Signal Processing 20 (2006), 505–592.

    Article  Google Scholar 

  2. P. Ibanez, Identification of dynamic parameters of linear and nonlinear structural models from experimental data, Nuclear Engineering and Design 25 (1973), 30–41.

    Article  Google Scholar 

  3. S.F. Masri, T.K. Caughey, A nonparametric identification technique for nonlinear dynamic problems, Journal of Applied Mechanics 46 (1979), 433–447.

    Article  MATH  Google Scholar 

  4. T.K. Caughey, Response of Van der Pol’s oscillator to random excitations, Journal of Applied Mechanics 26 (1959), 345–348.

    MATH  MathSciNet  Google Scholar 

  5. T.K. Caughey, Random excitation of a system with bilinear hysteresis, Journal of Applied Mechanics 27 (1960), 649–652.

    MathSciNet  Google Scholar 

  6. I.E. Kazakov, Approximate probabilistic analysis of the accuracy of operation of essentially nonlinear systems, Automatika i Telemekhanika 17 (1956), 423–450.

    MathSciNet  Google Scholar 

  7. L. Socha, M. Pawleta, Are statistical linearization and standard equivalent linearization the same methods in the analysis of stochastic dynamic systems?, Journal of Sound and Vibration 248 (2001), 387–394.

    Article  MathSciNet  Google Scholar 

  8. W.D. Iwan, A.B. Mason, Equivalent linearization for systems subjected to non-stationary random excitation, International Journal of Nonlinear Mechanics 15 (1980), 71–82.

    Article  MATH  MathSciNet  Google Scholar 

  9. J.B. Roberts, P.D. Spanos, Random Vibrations and Statistical Linearization, Wiley, New York, 1990.

    Google Scholar 

  10. P. Hagedorn, J. Wallaschek, On equivalent harmonic and stochastic linearization, Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamic Engineering Systems, Berlin, 23–32, 1987.

    Google Scholar 

  11. O. Fillatre, Identification of weakly nonlinear dynamic systems by means of random excitations, La Recherche Aéerospatiale 3 (1992), 11–22.

    MathSciNet  Google Scholar 

  12. H.J. Rice, Identification of weakly non-linear systems using equivalent linearization, Journal of Sound and Vibration 185 (1995), 473–481.

    Article  MATH  Google Scholar 

  13. R.N. Miles, An approximate solution for the spectral response of Duffing’s oscillator with random input, Journal of Sound and Vibration 132 (1989), 43–49.

    Article  MathSciNet  Google Scholar 

  14. S.H. Crandall, Les vibrations forcées dans les systèmes non-linéaires, Colloques Internationaux du CNRS, Marseille, 1963.

    Google Scholar 

  15. R. Bouc, The power spectral density of response for a strongly nonlinear random oscillator, Journal of Sound and Vibration 175 (1994), 317–331.

    Article  MATH  Google Scholar 

  16. C. Soize, Stochastic linearization method with random parameters and power spectral density calculation, Proceedings of the International Conference on Structural Safety and Reliability, Rotterdam, 1994.

    Google Scholar 

  17. C. Soize, Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: prediction and identification procedures, Probabilistic Engineering Mechanics 10 (1995), 143–152.

    Article  Google Scholar 

  18. C. Soize, O. Le Fur, Modal identification of weakly non-linear multidimensional dynamical systemsusing a stochastic linearisation method with random coefficients, Mechanical Systems and Signal Processing 11 (1997), 37–49.

    Article  Google Scholar 

  19. S. Bellizzi, R. Bouc, M. Defilippi, P. Guihot, Response spectral densities and identification of a randomly excited non-linear squeeze film oscillator, Mechanical Systems and Signal Processing 12 (1998), 693–711.

    Article  Google Scholar 

  20. S. Bellizzi, M. Defilippi, Non-linear mechanical systems identification using linear systems with random parameters, Mechanical Systems and Signal Processing 17 (2003), 203–210.

    Article  Google Scholar 

  21. K. Yasuda, S. Kawamura, K. Watanabe, Identification of nonlinearmulti-degree-of-freedom systems (presentation of an identification technique), JSME International Journal Series III 31(1988a), 8–14.

    MathSciNet  Google Scholar 

  22. K. Yasuda, S. Kawamura, K. Watanabe, Identification of nonlinear multi-degree-of-freedom systems (identification under noisy measurements), JSME International Journal Series III 31 (1988b), 302–309.

    MathSciNet  Google Scholar 

  23. Y. Benhafsi, J.E. Penny, M.I. Friswell, A parameter identification method for discrete nonlinear systems incorporating cubic stiffness elements, International Journal of Analytical and Experimental Modal Analysis 7 (1992), 179–195.

    Google Scholar 

  24. S. Meyer, M. Weiland, M. Link, Modelling and updating of local nonlinearities using frequency response residuals, Mechanical Systems and Signal Processing 17 (2003), 219–226.

    Article  Google Scholar 

  25. M.E. Ozer, H.N. Ozgüven, T.J. Royston, Identification of structural non-linearities using describing functions and Sherman-Morrison method, Proceedings of the 23rd Internation Modal Analysis Conference, Orlando, 2005.

    Google Scholar 

  26. E.F. Crawley, K.J. O’Donnell, Identification of nonlinear system parameters in joints using the force-state mapping technique, AIAA Paper 86–1013 (1986), 659–667.

    Google Scholar 

  27. E.F. Crawley, A.C. Aubert, Identification of nonlinear structural elements by force-state mapping, AIAA Journal 24 (1986), 155–162.

    Article  Google Scholar 

  28. S.F. Masri, H. Sassi, T.K. Caughey, A nonparametric identification of nearly arbitrary nonlinear systems, Journal of Applied Mechanics 49 (1982), 619–628.

    Article  MATH  Google Scholar 

  29. Y. Yang, S.R. Ibrahim, A nonparametric identification technique for a variety of discrete nonlinear vibrating systems, Journal of Vibration, Acoustics, Stress, and Reliability in Design 107 (1985), 60–66.

    Google Scholar 

  30. S.F. Masri, R.K. Miller, A.F. Saud, T.K. Caughey, Identification of nonlinear vibrating structures: part I — formalism, Journal of Applied Mechanics 54 (1987a), 918–922.

    Article  MATH  Google Scholar 

  31. S.F. Masri, R.K. Miller, A.F. Saud, T.K. Caughey, Identification of nonlinear vibrating structures: part II — applications, Journal of Applied Mechanics 54 (1987b), 923–929.

    Article  MATH  Google Scholar 

  32. M.A Al-Hadid, J.R. Wright, 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 (1989), 269–290.

    Article  MATH  Google Scholar 

  33. M. A Al-Hadid, J.R. Wright, Application of the force-state mapping approach to the identification of non-linear systems, Mechanical Systems and Signal Processing 4 (1990), 463–482.

    Article  Google Scholar 

  34. M.A Al-Hadid, J.R. Wright, Estimation of mass and modal mass in the identification of nonlinear single and multi DOF systems using the force-state mapping approach, Mechanical Systems and Signal Processing 6 (1992), 383–401.

    Article  Google Scholar 

  35. K. Worden, Data processing and experiment design for the restoring force surface method, Part I: integration and differentiation of measured time data, Mechanical Systems and Signal Processing 4 (1990a), 295–319.

    Article  Google Scholar 

  36. K. Worden, Data processing and experiment design for the restoring force surface method, Part II: choice of excitation signal, Mechanical Systems and Signal Processing 4 (1990b), 321–344.

    Article  Google Scholar 

  37. K.S. Mohaad, K. Worden, G.R. Tomlinson, Direct parameter estimation for linear and nonlinear structures, Journal of Sound and Vibration 152 (1991), 471–499.

    Google Scholar 

  38. K. Shin, J.K. Haond, Pseudo forcestate mapping method: incorporation of the embedding and forcestate mapping methods, Journal of Sound and Vibration 211 (1998a), 918–922.

    Article  Google Scholar 

  39. W.J. Kim, S.J. Park, Non-linear joint parameter identification by applying the force-state mapping technique in the frequency domain, Mechanical System and Signal Processing 8 (1994), 519–529.

    Article  Google Scholar 

  40. H.R. Lo, J.K. Haond, Identification of a class of nonlinear systems, Preprint Institute of Sound and Vibration Research, Southampton, 1988.

    Google Scholar 

  41. F. Benedettini, D. Capecchi, F. Vestroni Nonparametric models in identification of hysteretic oscillators, Report DISAT N.4190, Dipartimento di Ingegneria delle Strutture, Universita’ dell’Aquila, Italy, 1991.

    Google Scholar 

  42. K. Shin, J.K. Haond, Force-state mapping method of a chaotic dynamical system, Journal of Sound and Vibration 218 (1998b), 405–418.

    Article  Google Scholar 

  43. A. Audenino, G. Belingardi, L. Garibaldi, An application of the restoring force mapping method for the diagnostic of vehicular shock absorbers dynamic behaviour, Preprint, Dipartimento di Meccanica del Politecnico di Torino, 1990.

    Google Scholar 

  44. G. Belingardi, P. Campanile, Improvement of the shock absorber dynamic simulation by the restoring force mapping method, Proceedings of the International Seminar in Modal Analysis and Structural Dynamics, euven, 1990.

    Google Scholar 

  45. C. Surace, K. Worden, G.R. Tomlinson, On the nonlinear characteristics of automotive shock absorbers, Proceedinds of the I. Mech. E., Part D — Journal of Automobile Engineering, 206 (1992), 3–16.

    Article  Google Scholar 

  46. S. Cafferty, K. Worden, G.R. Tomlinson, Characterisation of automotive shock absorbers using random excitation, Proceedinds of the I. Mech. E., Part D — Journal of Automobile Engineering, 209 (1993), 239–248.

    Article  Google Scholar 

  47. S. Duym, R. Stiens, K. Reybrouck, Fast parametric and nonparametric identification of shock absorbers, Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 1996a.

    Google Scholar 

  48. S. Duym, J. Schoukens, P. Guillaume, A local restoring force surface method, International Journal of Analytical and Experimental Modal Analysis 11 (1996b), 116–132.

    Google Scholar 

  49. S. Duym, J. Schoukens, Selection of an optimal force-state map, Mechanical Systems and Signal Processing 10 (1996c), 683–695.

    Article  Google Scholar 

  50. G. Kerschen, J.C. Golinval, K. Worden, Theoretical and experimental identification of a non-linear beam, Journal of Sound and Vibration 244 (2001a), 597–613.

    Article  Google Scholar 

  51. C. Meskell, J.A. Fitzpatrick, H.J. Rice, Application of force-state mapping to a non-linear fluid-elastic system, Mechanical Systems and Signal Processing 15 (2001), 75–85.

    Article  Google Scholar 

  52. G. Dimitriadis, J.E. Cooper, A method for the identification of non-linear multi-degree-of-freedom systems, Proceedings of the Institute of Mechanical Engineers, Part G 212 (1998), 287–298.

    Article  Google Scholar 

  53. M. Haroon, D.E. Adams, Y.W. Luk, A technique for estimating linear parameters of an automotive suspension system using nonlinear restoring force excitation, ASME International Mechanical Engineering Congress, Anaheim, 2004.

    Google Scholar 

  54. M. Haroon, D.E. Adams, Y.W. Luk, A.A. Ferri, A time and frequency domain approach for identifying nonlinear mechanical system models in the absence of an input measurement, Journal of Sound and Vibration 283 (2005), 1137–1155.

    Article  Google Scholar 

  55. G.E.P. Box, G.M. Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco, 1970.

    Google Scholar 

  56. I.J. Leontaritis, S.A. Billings, Input-output parametric models for nonlinear systems, part I: deterministic nonlinear systems, International Journal of Control 41 (1985a), 303–328.

    Article  MATH  MathSciNet  Google Scholar 

  57. I.J. Leontaritis, S.A. Billings, Input-output parametric models for nonlinear systems, part II: stochastic nonlinear systems, International Journal of Control 41 (1985b), 329–344.

    Article  MATH  MathSciNet  Google Scholar 

  58. M. Korenberg, S.A. Billings, Y.P. Liu, P.J. McIlroy, An orthogonal parameter estimation algorithm for nonlinear stochastic systems, International Journal of Control 48 (1988), 193–210.

    Article  MATH  MathSciNet  Google Scholar 

  59. S.A. Billings, S. Chen, R.J. Backhouse, Identification of linear and nonlinear models of a turbocharged automotive diesel engine, Mechanical Systems and Signal Processing 3 (1989c), 123–142.

    Article  Google Scholar 

  60. S.A. Billings, H.B. Jamaluddin, S. Chen, Properties of neural networks with applications to modelling non-linear dynamical systems, International Journal of Control 55 (1991a), 193–224.

    Article  MathSciNet  Google Scholar 

  61. S. Chen, S.A. Billings, C.F.N. Cowan, P.M. Grant, Practical identification of models using radial basis functions, International Journal of Control 52 (1990a), 1327–1350.

    Article  MATH  MathSciNet  Google Scholar 

  62. E. Bedrosian, S.O. Rice, The output properties of systems driven by harmonic and Gaussian inputs, Proceedings IEEE5 9 (1971), 1688–1707.

    Article  MathSciNet  Google Scholar 

  63. S.A. Billings, K.M. Tsang, Spectral analysis for nonlinear systems, part I: parametric non-linear spectral analysis, Mechanical Systems and Signal Processing 3 (1989a), 319–339.

    Article  MATH  Google Scholar 

  64. S.A. Billings, K.M. Tsang, Spectral analysis for nonlinear systems, part II: interpretation of nonlinear frequency response functions, Mechanical Systems and Signal Processing 3 (1989b), 341–359.

    Article  MATH  Google Scholar 

  65. F. Thouverez, L. Jezequel, Identification of models on a modal base, Journal of Sound and Vibration 189 (1996), 193–213.

    Article  Google Scholar 

  66. M. Feldman, Nonlinear system vibration analysis using the Hilbert transform —I. Free vibration analysis method ‘FREEVIB’, Mechanical Systems and Signal Processing 8 (1994a), 119–127.

    Article  Google Scholar 

  67. M. Feldman, Nonlinear system vibration analysis using the Hilbert transform —I. Forced vibration analysis method ‘FORCEVIB’, Mechanical Systems and Signal Processing 8 (1994b), 309–318.

    Article  Google Scholar 

  68. O. Gottlieb, M. Feldman, S.C.S. Yim, Parameter identification of non-linear ocean mooring systems using the Hilbert transform, Journal of Offshore Mechanics and Arctic Engineering 118 (1996), 29–36.

    Article  Google Scholar 

  69. M. Feldman, Non-linear free vibration identification via the Hilbert transform, Journal of Sound and Vibration 208 (1997), 475–489.

    Article  MathSciNet  Google Scholar 

  70. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society of London, Series — Mathematical, Physical and Engineering Sciences 454 (1998), 903–995.

    Article  MATH  MathSciNet  Google Scholar 

  71. J.N. Yang, Y. Lei, S.W. Pan, N. Huang, System identification of linear structures based on Hilbert-Huang spectral analysis; Part 1: Normal modes, Earthquake Engineering and Structural Dynamics 32 (2003a), 1443–1467.

    Article  Google Scholar 

  72. J.N. Yang, Y. Lei, S.W. Pan, N. Huang, System identification of linear structures based on Hilbert-Huang spectral analysis; Part 2: Complex modes, Earthquake Engineering and Structural Dynamics 32 (2003b), 1533–1554.

    Article  Google Scholar 

  73. J.N. Yang, S. Lin, Hilbert-Huang based approach for structural damage detection, Journal of Engineering Mechanics 130 (2004b), 85–95.

    Article  Google Scholar 

  74. S.L. Lacy, D.S. Bernstein, Subspace identification for nonlinear systems that are linear in unmeasured states, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, 3518–3523, 2001.

    Google Scholar 

  75. V.N. Pilipchuk, C.M. Tan, Non-linear system identification based on the Lie series solutions, Mechanical Systems and Signal Processing 19 (2005), 71–86.

    Article  Google Scholar 

  76. B.F. Feeny, J.W. Liang, A decrement method for the simultaneous estimation of coulomb and viscous friction, Journal of Sound and Vibration 195 (1996), 149–154.

    Article  Google Scholar 

  77. J.W. Liang, B.F. Feeny, Identifying Coulomb and viscous friction from free-vibration decrements, Nonlinear Dynamics 16 (1998), 337–347.

    Article  MATH  Google Scholar 

  78. J.W. Liang, B.F. Feeny, Identifying Coulomb and viscous friction in forced dual-damped oscillators, Journal of Vibration and Acoustics 126 (2004a), 118–125.

    Article  Google Scholar 

  79. R. Singh, P. Davies, A.K. Bajaj, Initial condition response of a viscoelastic dynamical system in the presence of dry friction and identification of system parameters, Journal of Sound and Vibration 239 (2001), 1086–1095.

    Article  Google Scholar 

  80. A. Chatterjee, J.P. Cuano, Asymptotic parameter estimation via implicit averaging on a nonlinear extended system, Journal of Dynamic Systems, Measurement, and Control 125 (2003), 11–18.

    Article  Google Scholar 

  81. K. Yasuda, K. Kamiya, Experimental identification technique of non-linear beams in time domain, Nonlinear Dynamics 18 (1999),185–202.

    Article  MATH  MathSciNet  Google Scholar 

  82. M. Schetzen, The and Wiener Theories of Nonlinear Systems. John Wiley & Sons, New York, 1980.

    MATH  Google Scholar 

  83. F. Thouverez, L. Jezequel, Identification of a localized non-linearity, International Journal of Non-Linear Mechanics 33 (1998), 935–945.

    Article  MATH  MathSciNet  Google Scholar 

  84. S.J. Gifford, Series Analysis of Nonlinear Structures, Ph.D. Thesis, Department of Mechanical Engineering, Heriot-Watt University, 1989.

    Google Scholar 

  85. D.M. Storer, Dynamic Analysis of Nonlinear Structures Using Higher Order Frequency Response Functions, Ph.D. Thesis, Department of Engineering, University of Manchester, 1991.

    Google Scholar 

  86. D.M. Storer, G.R. Tomlinson, Recent developments in the measurements and interpretation of higher order functions from non-linear structures, Mechanical Systems and Signal Processing 7 (1993), 173–189.

    Article  Google Scholar 

  87. A.A. Khan, N.S. Vyas, Non-linear parameter using and Wiener theories, Journal of Sound and Vibration 221 (1999), 805–821.

    Article  Google Scholar 

  88. A. Chatterjee, N.S. Vyas, Non-linear parameter estimation through series using the method of recursive iteration through harmonic probing, Journal of Sound and Vibration 268 (2003), 657–678.

    Article  Google Scholar 

  89. A.A. Khan, N.S. Vyas, Nonlinear bearing stiffness parameter estimation in flexible rotor-bearing systems using and Wiener approach, Probabilistic Engineering Mechanics 16 (2001b), 137–157.

    Article  Google Scholar 

  90. A. Chatterjee, N.S. Vyas, Non-linear parameter estimation in multidegree-of-freedom systems using multi-input series, Mechanical Systems and Signal Processing 18 (2004), 457–489.

    Article  Google Scholar 

  91. A.A. Khan, N.S. Vyas, Application of and Wiener theories for non-linear parameter estimation in a rotor-bearing system, Nonlinear Dynamics 24 (2001a), 285–304.

    Article  MATH  Google Scholar 

  92. I. Tawfiq, T. Vinh, Contribution to the extension of modal analysis to non-linear structure using functional series, Mechanical Systems and Signal Processing 17 (2003), 379–407.

    Article  Google Scholar 

  93. I. Tawfiq, T. Vinh, Nonlinear behaviour of structures using the seriessignal processing and testing methods, Nonlinear Dynamics 37 (2004), 129–149.

    Article  MATH  MathSciNet  Google Scholar 

  94. J.B. Roberts, J.F. Dunne, A. Debonos, A spectral method for estimation of non-linear system parameters from measured response, Probabilistic Engineering Mechanics 10 (1995), 199–207.

    Article  Google Scholar 

  95. M. Vasta, J.B. Roberts, Stochastic parameter estimation of non-linear systems using only higher order spectra of the measured response, Journal of Sound and Vibration 213 (1998), 201–221.

    Article  Google Scholar 

  96. J.B. Roberts, M. Vasta, Parametric identification of systems with non-Gaussian excitation using measured response spectra, Probabilistic Engineering Mechanics 15 (2000a), 59–71.

    Article  Google Scholar 

  97. J.B. Roberts, M. Vasta, Energy-based stochastic estimation for non-linear oscillators with random excitation, Journal of Applied Mechanics 67 (2000b), 763–771.

    Article  MATH  MathSciNet  Google Scholar 

  98. M.R. Hajj, J. Fung, A.H. Nayfeh, S. Fahey, Damping identification using perturbation techniques and higher-order spectra, Nonlinear Dynamics 23 (2000), 189–203.

    Article  MATH  Google Scholar 

  99. A. Swami, G.B. Giannakis, G. Zhou, Bibliography on higher-order statistics, Signal Processing 60 (1997), 65–126.

    Article  MATH  Google Scholar 

  100. K. Yasuda, K. Kamiya, Identification of a nonlinear beam (proposition of an identification technique), JSME International Journal Series III 33 (1990), 535–540.

    Google Scholar 

  101. K. Yasuda, K. Kamiya, Experimental identification technique of vibrating structures with geometrical nonlinearity, Journal of Applied Mechanics 64 (1997), 275–280.

    Article  Google Scholar 

  102. C.M. Yuan, B.F. Feeny, Parametric identification of chaotic systems, Journal of Vibration and Control 4 (1998), 405–426.

    Article  Google Scholar 

  103. B.F. Feeny, C.M. Yuan, J.P. Cuano, Parametric identification of an experimental magneto-elastic oscillator, Journal of Sound and Vibration 247 (2001), 785–806.

    Article  Google Scholar 

  104. Y. Liang, B.F. Feeny, Parametric identification of chaotic base-excited double pendulum experiment, ASME International Mechanical Engineering Congress, Anaheim, 2004b.

    Google Scholar 

  105. M. Thothadrai, R.A. Casas, F.C. Moon, R. D’Andrea, C.R. Johnson, Nonlinear system identification of multi-degree-of-freedom systems, Nonlinear Dynamics 32 (2003), 307–322.

    Article  MathSciNet  Google Scholar 

  106. M. Thothadrai, F.C. Moon, Nonlinear system identification of systems with periodic limit-cycle response, Nonlinear Dynamics 39 (2005).

    Google Scholar 

  107. H.J. Rice, J.A. Fitzpatrick, A generalised technique for spectral analysis of non-linear systems, Mechanical Systems and Signal Processing 2 (1988), 195–207.

    Article  MATH  Google Scholar 

  108. H. Esmonde, J. A. Fitzpatrick, H.J. Rice, F. Axisa, Analysis of non-linear squeeze film dynamics: part I — physical theory and modelling. Proceedings of ASME PVP Conference, Nashville, 1990a.

    Google Scholar 

  109. H. Esmonde, F. Axisa, J. A. Fit zpatrick, H.J. Rice, Analysis of non-linear squeeze film dynamics: part II — experimental measurement and model verification. Proceedings of ASME PVP Conference, Nashville, 1990b.

    Google Scholar 

  110. J. S. Bendat, Nonlinear System Analysis and Identification from Random Data, John Wiley & Sons, New York, 1990.

    MATH  Google Scholar 

  111. H.J. Rice, J. A. Fitzpatrick, The measurement of nonlinear damping in single-degree-of-freedom systems, Journal of Vibration and Acoustics 113 (1991a), 132–140.

    Article  Google Scholar 

  112. J.S. Bendat, R.N. Coppolino, P.A. Palo, Identification of physical parameters with memory in non-linear systems, International Journal of Non-Linear Mechanics 30 (1995), 841–860.

    Article  MATH  Google Scholar 

  113. B.A. Zeldin, P.D. Spanos, Spectral identification of nonlinear structures, Journal of Engineering Mechanics 124 (1998), 728–733.

    Article  Google Scholar 

  114. J.S. Bendat, Spectral techniques for nonlinear system analysis and identification, Shock and Vibration 1 (1993), 21–31.

    Google Scholar 

  115. H.J. Rice, J.A. Fitzpatrick, A procedure for the identification of linear and non-linear multi-degree-of-freedom systems, Journal of Sound and Vibration 149 (1991b), 397–411.

    Article  Google Scholar 

  116. C.M. Richards, R. Singh, 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.

    Article  Google Scholar 

  117. G. Kerschen, J.C. Golinval, Generation of accurate finite element models of nonlinear systems — Aplication to an aeroplane-like structure, Nonlinear Dynamics 39 (2005a), 129–142.

    Article  MATH  MathSciNet  Google Scholar 

  118. J.A. Fitzpatrick, H.J. Rice, Coents on “Identification of multi-degree-of-freedom non-linear systems under random excitations by the “reverse path’ spectral method“, Journal of Sound and Vibration 237 (2000), 357–358.

    Article  Google Scholar 

  119. C.M. Richards, R. Singh, Coents on “Identification of multi-degree-of-freedom non-linear systems under random excitations by the reverse path’ spectral method” — Authors’ reply, Journal of Sound and Vibration 237 (2000a), 358–360.

    Article  Google Scholar 

  120. C.M. Richards, R. Singh, Comparison of two non-linear system identification approaches derived from “reverse path” spectral analysis, Journal of Sound and Vibration 237 (2000b), 361–376.

    Article  Google Scholar 

  121. C.M. Richards, R. Singh, Feasibility of identifying non-linear vibratory systems consisting of unknown polynomial forms, Journal of Sound and Vibration 220 (1999), 413–450.

    Article  Google Scholar 

  122. G. Kerschen, V. Lenaerts, S. Marchesiello, A. Fasana, A frequency domain versus a time domain identification technique for nonlinear parameters applied to wire rope isolators, Journal of Dynamic Systems, Measurement, and Control 123 (2001b), 645–650.

    Article  Google Scholar 

  123. G. Kerschen, V. Lenaerts, J.C. Golinval, Identification of a continuous structure with a geometrical non-linearity, part I: conditioned reverse path method, Journal of Sound and Vibration 262 (2003a), 889–906.

    Article  Google Scholar 

  124. L. Garibaldi, Application of the conditioned reverse path method, Mechanical Systems and Signal Processing 17 (2003), 227–236.

    Article  Google Scholar 

  125. S. Marchesiello, Application of the conditioned reverse path method, Mechanical Systems and Signal Processing 17 (2003), 183–188.

    Article  Google Scholar 

  126. D.E. Adams, R.J. Allemang, A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback, Mechanical Systems and Signal Processing 14 (2000a), 637–656.

    Article  Google Scholar 

  127. D.E. Adams, R.J. Allemang, A new derivation of the frequency response function matrix for nonlinear vibrating systems, Journal of Sound and Vibration 227 (1999a), 1083–1108.

    Article  Google Scholar 

  128. D.E. Adams, R.J. Allemang, Characterization of nonlinear vibrating systems using internal feedback and frequency response modulation, Journal of Vibration and Acoustics 121 (1999b), 495–500.

    Article  Google Scholar 

  129. J.A. Vazquez Feijoo, K. Worden, R. Stanway, System identification using associated linear equations, Mechanical Systems and Signal Processing 18 (2004), 431–455.

    Article  Google Scholar 

  130. J.X. Zhang, J.B. Roberts, A frequency domain parametric identification method for studying the non-linear performance of squeeze-film dampers, Journal of Sound and Vibration 189 (1996), 173–191.

    Article  Google Scholar 

  131. R.W. Krauss, A.H. Nayfeh, Experimental nonlinear identification of a single mode of a tranversely excited beam, Nonlinear Dynamics 18 (1999), 69–87.

    Article  MATH  Google Scholar 

  132. R Malatkar, A.H. Nayfeh, A parametric identification technique for single-degree-of-freedom weakly nonlinear systems with cubic nonlinearities, Journal of Vibration and Control 9 (2003a), 317–336.

    Article  MATH  Google Scholar 

  133. A.H. Nayfeh, Parametric identification of nonlinear dynamic systems, Computers and Structures 20 (1985), 487–493.

    Article  MATH  Google Scholar 

  134. S. Fahey, A.H. Nayfeh, Experimental nonlinear identification of a single structural mode, Proceedings of the 16th International Modal Analysis Conference, Orlando, 737–745, 1998.

    Google Scholar 

  135. T.A. Doughty, P. Davies, A.K. Bajaj, A comparison of three techniques using steady state data to identify non-linear modal behavior of an externally excited cantilever beam, Journal of Sound and Vibration 249 (2002), 785–813.

    Article  Google Scholar 

  136. J.C. Golinval, M. Link, COST action F3 Structural Dynamics (1997–2001) — An European co-operation in the field of science and technology, Mechanical Systems and Signal Processing 17 (2003a), 3–7.

    Article  Google Scholar 

  137. J. Piranda, R. Fillod, E. Foltete, Modal identification of non-linear structures, Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 1998.

    Google Scholar 

  138. D. Göge, U. Fullekrug, M. Link, L. Gaul, A strategy for the identification and characterisation of non-linearities within modal survey testing, Proceedings of the 22nd International Modal Analysis Conference, Dearborn, 2004.

    Google Scholar 

  139. W. Szemplinska-Stupnicka, The modified single mode method in the investigations of the resonant vibrations of nonlinear systems, Journal of Sound and Vibration 65 (1979), 475–489.

    Article  Google Scholar 

  140. W. Szemplinska-Stupnicka, Nonlinear normal modes and generalized Ritz method in the problems of vibrations of nonlinear elastic continuous systems, International Journal of Non-Linear Mechanics 18 (1983), 149–165.

    Article  MATH  MathSciNet  Google Scholar 

  141. L. Jezequel, Extension des métnodes de synthèse modale au cas non linéaire, Revue-francaise-de-Mecanique 3 (1987), 159–172.

    Google Scholar 

  142. S. Setio, H.D. Setio, L. Jezequel, Modal analysis of non-linear multidegree-of-freedom systems, International Journal of Analytical and Experimental Modal Analysis 7 (1992a), 75–93.

    Google Scholar 

  143. S. Setio, H.D. Setio, L. Jezequel, A method of nonlinear modal identification from frequency-response tests, Journal of Sound and Vibration 158 (1992b), 497–515.

    Article  MATH  Google Scholar 

  144. Y.H. Chong, M. Imregun, Development and application of a nonlinear modal analysis technique for multi-degree-of-freedom systems, Journal of Vibration and Control 7 (2001), 167–179.

    Article  MATH  Google Scholar 

  145. C. Gibert, F. Thouverez, L. Jezequel, Non-linear modal analysis applied to an industrial structure, Proceedings of the 17th International Modal Analysis Conference, Kissiee, 87–93, 1999.

    Google Scholar 

  146. C. Gibert, Fitting measured frequency response using non-linear modes, Mechanical Systems and Signal Processing 17 (2003), 211–218.

    Article  Google Scholar 

  147. L. Huang, W.D. Iwan, Modal identification of nonlinear systems using successive approximation model, Proceedings of the 15th International Modal Analysis Conference, Orlando, 1997.

    Google Scholar 

  148. E. Pesheck, N. Boivin, C. Pierre, S.W. Shaw, Nonlinear modal analysis of structural systems using multi-mode invariant manifolds, Nonlinear Dynamics 25 (2001a), 183–205.

    Article  MATH  MathSciNet  Google Scholar 

  149. J.R. Wright, M.F. Platten, J.E. Cooper, M. Sarmast, Identification of multi-degree-of-freedom weakly non-linear systems using a model based in modal space, Proceedings of the International Conference on Structural System Identification, Kassel, 49–68, 2001.

    Google Scholar 

  150. R. Williams, J. Crowley, H. Void, The multivariate mode indicator function in modal analysis, Proceedings of the 4-th Internation Modal Analysis Conference, Los Angeles, 1986.

    Google Scholar 

  151. J.R. Wright, J.E. Cooper, M. Desforges, Normal mode force appropriation — Theory and application, Mechanical Systems and Signal Processing 13 (1999), 217–240.

    Article  Google Scholar 

  152. P. Atkins, J.R. Wright, K. Worden, An extension of force appropriation to the identification of non-linear multi-degree-of-freedom systems, Journal of Sound and Vibration 237 (2000), 23–43.

    Article  Google Scholar 

  153. M.F. Plat ten, J.R. Wright, J.E. Cooper, M. Sarmast, Identification of multi-degree-of-freedom non-linear simulated and experimental systems, Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 1195–1202, 2002.

    Google Scholar 

  154. M.F. Plat ten, J.R. Wright, J.E. Cooper, Identification of a continuous structure with discrete non-linear components using an extended modal model, Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 2155–2168, 2004.

    Google Scholar 

  155. S. Bellizzi, P. Gullemain, R. Kronland-Martinet, Identification of coupled non-linear modes from free vibration using time-frequency representation, Journal of Sound and Vibration 243 (2001), 191–213.

    Article  Google Scholar 

  156. T.K. Hasselman, M.C. Anderson, W.G. Gan, Principal component analysis for nonlinear model correlation, updating and uncertainty evaluation, Proceedings of the 16th International Modal Analysis Conference, Santa Barbara, 644–651, 1998.

    Google Scholar 

  157. V. Lenaerts, G. Kerschen, J.C. Golinval, Proper orthogonal decomposition for model updating of non-linear mechanical systems, Mechanical Systems and Signal Processing 15 (2001), 31–43.

    Article  Google Scholar 

  158. V. Lenaerts, G. Kerschen, J.C. Golinval, Identification of a continuous structure with a geometrical non-linearity, part II: proper orthogonal decomposition, Journal of Sound and Vibration 262 (2003), 907–919.

    Article  Google Scholar 

  159. P. Argoul, T.P. Le, T.M. Nguyen, Continuous wavelet transform for parameter identification from free decay responses of nonlinear structures, Proceedings of the EUROMECH Colloquium 457 on Nonlinear Modes of Vibrating Systems, Fréjus, 73–78, 2004.

    Google Scholar 

  160. M.B. Priestley, Power spectral analysis of nonstationary processes, Journal of Sound and Vibration 6 (1967), 86–97.

    Article  Google Scholar 

  161. J.K. Haond, On the response of single and multidegree of freedom systems to nonstationary excitations, Journal of Sound and Vibration 7 (1968), 393–419.

    Article  Google Scholar 

  162. J.K. Haond, P.R. White, The analysis of non-stationary signals using time-frequency methods, Journal of Sound and Vibration 190 (1996), 419–447.

    Article  Google Scholar 

  163. K.C. Park, A. Robertson, K.F. Alvin, Identification of structural dynamic models using wavelet-generated impulse response data, Report CU-CAS-95-02, University of Colorado at Boulder, 1995.

    Google Scholar 

  164. M. Ruzzene, A. Fasana, L. Garibaldi, B. Piombo, Natural frequencies and dampings identification using wavelet transform: application to real data, Mechanical Systems and Signal Processing 11 (1997), 207–218.

    Article  Google Scholar 

  165. W.J. Staszewski, Identification of damping in mdof systems using time-scale decomposition, Journal of Sound and Vibration 203 (1997), 283–305.

    Article  Google Scholar 

  166. P. Argoul, T.P. Le, Continuous wavelet transform for modal identification using free decay response, Journal of Sound and Vibration 277 (2004), 73–100.

    Article  Google Scholar 

  167. M. Boltezar, J. Slavic, Enhancements to the continuous wavelet transform for damping identifications on short signals, Mechanical Systems and Signal Processing 18 (2004), 1065–1076.

    Article  Google Scholar 

  168. D. Spina, C. Valente, G.R. Tomlinson, A new procedure for detecting nonlinearity from transient data using Gab or transform, Nonlinear Dynamics 11 (1996), 235–254.

    Article  MathSciNet  Google Scholar 

  169. H. Franco, R.M.O. Pauletti, Analysis of nonlinear oscillations by gabor spectrograms, Nonlinear Dynamics 12 (1997), 215–236.

    Article  MATH  Google Scholar 

  170. W.J. Staszewski, Analysis of non-linear systems using wavelets, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science 214 (2000), 1339–1353.

    Article  Google Scholar 

  171. M. Feldman, S. Braun, Identification of non-linear system parameters via the instantaneous frequency: application of the Hilbert transform and Wigner-Ville technique, Proceedings of the 13th International Modal Analysis Conference, Nashville, 637–642, 1995.

    Google Scholar 

  172. L. Wang, J. Zhang, C. Wang, S. Hu, Time-frequency analysis of non-linear systems: the skeleton linear model and the skeleton curves, Journal of Vibration and Acoustics 125 (2003a), 170–177.

    Article  Google Scholar 

  173. W.J. Staszewski, Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform, Journal of Sound and Vibration 214 (1998), 639–658.

    Article  Google Scholar 

  174. L. Garibaldi, M. Ruzzene, A. Fasana, B. Piombo, Identification of non-linear damping mechanisms using the wavelet transform, Mecanique Industrielle et Materiaux 51 (1998), 92–94.

    Google Scholar 

  175. P. Argoul, T.P. Le, Instantaneous indicators of structural behaviour based on the continuous cauchy wavelet analysis, Mechanical Systems and Signal Processing 17 (2003), 243–250.

    Article  Google Scholar 

  176. V. Lenaerts, G. Kerschen, J.C. Golinval, M. Ruzzene, E. Giorcelli, Validation of two nonlinear system identification techniques using an experimental testbed, Shock and Vibration 11 (2004), 365–375.

    Google Scholar 

  177. Y. Kitada, Identification of nonlinear structural dynamic systems using wavelets, Journal of Engineering Mechanics 124 (1998), 1059–1066.

    Article  Google Scholar 

  178. R. Ghanem, F. Romeo, A wavelet-based approach for model and parameter identification of non-linear systems, International Journal of Non-Linear Mechanics 36 (2001), 835–859.

    Article  MATH  Google Scholar 

  179. S.L. Chen, K.C. Ho, Identification of nonlinear systems by Haar Wavelet, ASME International Mechanical Engineering Congress, Anaheim, 2004.

    Google Scholar 

  180. L. Wang, J. Zhang, C. Wang, S. Hu, Identification of nonlinear systems through time-frequency filtering technique, Journal of Vibration and Acoustics 125 (2003b), 199–204.

    Article  Google Scholar 

  181. G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals, and Systems 2 (1989), 303–314.

    Article  MATH  MathSciNet  Google Scholar 

  182. J. Sjöberg, Q. Zhang, L. Ljung, A. Beneviste, B. Delyon, P.Y. Glorennec, H. Hjalmarsson, A. Juditsky, Nonlinear black-box modelling in system identification: a unified overview, Automatica 31 (1995), 1691–1724.

    Article  MATH  Google Scholar 

  183. A. Juditsky, H. Hjalmarsson, A. Beneviste, B. Delyon, L. Ljung, J. Sjöberg, Q. Zhang, Nonlinear black-box models in system identification: mathematical foundations, Automatica 31 (1995), 1725–1750.

    Article  MATH  Google Scholar 

  184. S.R. Chu, R. Shoureshi, M. Tenorio, Neural networks for system identification, IEEE Control Systems Magazine 10 (1990), 36–43.

    Article  Google Scholar 

  185. K.S. Narendra, K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks 1 (1990), 4–27.

    Article  Google Scholar 

  186. S. Chen, S.A. Billings, C.F.N. Cowan, P.M. Grant, Nonlinear-systems identification using radial basis functions, International Journal of Systems Science 21 (1990b), 2513–2539.

    Article  MATH  Google Scholar 

  187. S.F. Masri, A.G. Chassiakos, T.K. Caughey, Structure-unknown non-linear dynamic systems: identification through neural networks, Smart Materials and Structures 1 (1992), 45–56.

    Article  Google Scholar 

  188. S.F. Masri, A.G. Chassiakos, T.K. Caughey, Identification of non-linear dynamic systems using neural networks, Journal of Applied Mechanics 60 (1993), 123–133.

    Article  Google Scholar 

  189. K. Worden, G.R. Tomlinson, Modelling and classification of nonlinear systems using neural networks — I Simulation, Mechanical Systems and Signal Processing 8 (1994a), 319–356.

    Article  Google Scholar 

  190. K. Worden, G.R. Tomlinson, W. Lim, G. Sauer, Modelling and classification of non-linear systems using neural networks — II A pre-liminary experiment, Mechanical Systems and Signal Processing 8 (1994b), 395–419.

    Article  Google Scholar 

  191. A.G. Chassiakos, S.F. Masri, Modelling unknown structural systems through the use of neural networks, Earthquake Engineering and Structural Dynamics 25 (1996), 117–128.

    Article  Google Scholar 

  192. E.B. Kosmatopoulos, A.W. Smyth, S.F. Masri, A.G. Chassiakos, Robust adaptive neural estimation of restoring forces in nonlinear structures, Journal of Applied Mechanics 68 (2001), 880–893.

    Article  MATH  Google Scholar 

  193. J.S. Pei, A.W. Smyth, E.B. Kosmatopoulos, Analysis and modification of / Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems, Journal of Sound and Vibration 275 (2004), 693–718.

    Article  Google Scholar 

  194. R. Le Riche, D. Gualandris, J.J. Thomas, F.M. Hemez, Neural identification of non-linear dynamic structures, Journal of Sound and Vibration 248 (2001), 247–265.

    Article  Google Scholar 

  195. Y. Song, C.J. Hartwigsen, D.M. McFarland, A.F. Vakakis, L.A. Bergman, Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements, Journal of Sound and Vibration 273 (2004), 249–276.

    Article  Google Scholar 

  196. Y.C. Liang, D.P. Feng, J.E. Cooper, Identification of restoring forces in non-linear vibration systems using fuzzy adaptive neural networks, Journal of Sound and Vibration 242 (2001), 47–58.

    Article  Google Scholar 

  197. Y. Fan, C.J. Li, Non-linear system identification using lumped parameter models with embedded feedforward neural networks, Mechanical Systems and Signal Processing 16 (2002), 357–372.

    Article  Google Scholar 

  198. S. Saadat, G.D. Buckner, T. Furukawa, M.N. Noori, An intelligent parameter varying (IPV) approach for non-linear system identification of base excited structures, International Journal of Non-Linear Mechanics 39 (2004), 993–1004.

    Article  MATH  Google Scholar 

  199. M. Peifer, J. Tier, H.U. Voss, Nonparametric identification of nonlinear oscillating systems, Journal of Sound and Vibration 267 (2003), 1157–1167.

    Article  Google Scholar 

  200. G.P. Liu, S.A. Billings, V. Kadirkamanathan, Nonlinear system identification using wavelet networks, International Journal of Systems Science 31 (2000), 1531–1541.

    Article  MATH  Google Scholar 

  201. R. Babuska, H. Verbruggen, Neuro-fuzzy methods for nonlinear system identification, Annual Reviews in Control 27 (2003), 73–85.

    Article  Google Scholar 

  202. O. Zienkiewicz, The Finite Element Method. McGraw-Hill, London, 1977.

    MATH  Google Scholar 

  203. A. Berman, E.J. Nagy, Theory of incomplete models of dynamic structures, AIAA Journal 9 (1971), 1481–1487.

    Article  Google Scholar 

  204. M. Baruch, Optimization procedure to correct stiffness and flexibility matrices using vibration test, AIAA Journal 16 (1978), 1208–1210.

    Article  MATH  Google Scholar 

  205. H.G. Natke, Einfuhrung in Theorie und Praxis der Zeitreihen und Modalanalyse, Vieweg Verlag, Braunschweig/Wiesbaden 1992.

    Google Scholar 

  206. M.I. Friswell, J.E. Mottershead, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, London, 1995.

    MATH  Google Scholar 

  207. M. Link, Updating of Analytical Models — Basic Procedures and Extensions in Modal Analysis & Testing, J.M.M. Silva and N.M.M. Maia, editors, Kluwer Academic Publishers, Dordrecht, 1999.

    Google Scholar 

  208. R. Schmidt, Updating non-linear components, Mechanical Systems and Signal Processing 8 (1994), 679–690.

    Article  Google Scholar 

  209. R.K. Kapania, S. Park, Parametric identification of nonlinear struc-tural dynamic systems using time finite element method, AIAA Journal 35 (1997), 719–726.

    Article  MATH  Google Scholar 

  210. K.D. Dippery, S.W. Smith, An optimal control approach to nonlinear system identification, Proceedings of the 16th International Modal Analysis Conference, Santa Barbara, 637–643, 1998.

    Google Scholar 

  211. A. Kyprianou, Non-linear Parameter Estimation of Dynamic Models using Differential Evolution: Application to Hysteretic Systems and Hydraulic Engine Mounts, Ph.D. Thesis, University of Sheffield, 1999.

    Google Scholar 

  212. A. Kyprianou, K. Worden, M. Panet, Identification of hysteretic systems using the differential evolution algorithm, Journal of Sound and Vibration 248 (2001), 289–314.

    Article  Google Scholar 

  213. S. Meyer, M. Link, Modelling local non-linear behaviour — Simultaneous updating of linear and non-linear parameters using frequency response residuals, Proceedings of International Conference on Structural Dynamics Modelling, Funchal, 2002.

    Google Scholar 

  214. K.V. Yuen, J.L. Beck, Updating properties of nonlinear dynamical systems with uncertain input, Journal of Engineering Mechanics 129 (2003), 9–20.

    Article  Google Scholar 

  215. D.R. Mulville, Pyroshock Test Criteria, NASA Technical Standard, Report NASA-S-7003, 1999.

    Google Scholar 

  216. S. Doebling, F.M. Hemez, W. Rhee, Statistical model updating and validation applied to nonlinear transient structural dynamics, Proceedings of the European COST F3 Conference on System Identification & Structural Health Monitoring, Madrid, 409-418, 2000.

    Google Scholar 

  217. X. Ma, A.F. Vakakis, Karhunen-Loève decomposition of the transient dynamics of a multibay truss, AIAA Journal 37 (1999), 939–946.

    Article  Google Scholar 

  218. G. Kerschen, On the Model Validation in Non-linear Structural Dynamics, Ph.D. Thesis, University of Liège, 2003c.

    Google Scholar 

  219. G. Kerschen, J.C. Golinval, A model updating strategy of non-linear vibrating structures, International Journal for Numerical Methods in Engineering 60 (2004a), 2147–2164.

    Article  MATH  Google Scholar 

  220. M.A. Kramer, Nonlinear principal component analysis using aut©as-sociative neural networks, A.I.Ch.E. Journal 37 (1991), 233–243.

    Google Scholar 

  221. D.C Zierman, T. Hasselman, M. Anderson, Approximation and cal-ibration of nonlinear structural dynamics, Nonlinear Dynamics 39 (2005).

    Google Scholar 

  222. J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures, Wiley Inter science, New York, 3rd edition, 2000.

    MATH  Google Scholar 

  223. S. Naylor, M.F. Platten, J.R. Wright, J.E. Cooper, Identification of multi-degree-of-freedom systems with nonproportional damping using the resonant decay method, Journal of Vibration and Acoustics 126 (2004), 298–306.

    Article  Google Scholar 

  224. G. Kerschen, M. Peeters, J.C. Golinval, A.F. Vakakis, Nonlinear nor-mal modes, Part I: A useful framework for the structural dynamicist, Mechanical Systems and Signal Processing 23 (2009), 170–194.

    Article  Google Scholar 

  225. R.M. Rosenberg, Normal modes of nonlinear dual-mode systems, Journal of Applied Mechanics 27 (1960), 263–268.

    MATH  Google Scholar 

  226. R.M. Rosenberg, The normal modes of nonlinear n-degree-of-freedom systems, Journal of Applied Mechanics 29 (1962), 7–14.

    MATH  Google Scholar 

  227. R.M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom, Advances in Applied Mechanics 9 (1966), 155–242.

    Article  Google Scholar 

  228. A.F. Vakakis, L.I. Manevitch, Y.V. Mikhlin, V.N. Pilipchuk, A.A. Zevin, Normal Modes and Localization in Nonlinear Systems, John Wiley & Sons, New York, 1996.

    Book  MATH  Google Scholar 

  229. A.F. Vakakis, Non-linear normal modes and their applications in vi-bration theory: an overview, Mechanical Systems and Signal Process-ing 11 (1997), 3–22.

    Article  Google Scholar 

  230. S.W. Shaw, C. Pierre, Normal modes for non-linear vibratory systems, Journal of Sound and Vibration 164 (1993), 85–124.

    Article  MATH  MathSciNet  Google Scholar 

  231. S.W. Shaw, C. Pierre, Normal modes of vibration for non-linear continuous systems, Journal of Sound and Vibration 169 (1994), 319–347.

    Article  MATH  MathSciNet  Google Scholar 

  232. T.K. Caughey, A.F. Vakakis, J.M. Sivo, Analytical study of similar normal modes and their bifurcations in a class of strongly nonlinear systems, International Journal of Non-Linear Mechanics 25 (1990), 521–533.

    Article  MathSciNet  Google Scholar 

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Kerschen, G. (2010). Advanced Strategies for Nonlinear System Identification. In: Vakakis, A.F. (eds) Advanced Nonlinear Strategies for Vibration Mitigation and System Identification. CISM International Centre for Mechanical Sciences, vol 518. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0205-3_3

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