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.
P. Ibanez, Identification of dynamic parameters of linear and nonlinear structural models from experimental data, Nuclear Engineering and Design 25 (1973), 30-41.
S.F. Masri, T.K. Caughey, A nonparametric identification technique for nonlinear dynamic problems, Journal of Applied Mechanics 46 (1979), 433-447.
T.K. Caughey, Response of Van der Pol’s oscillator to random excitations, Journal of Applied Mechanics 26 (1959), 345-348.
T.K. Caughey, Random excitation of a system with bilinear hysteresis, Journal of Applied Mechanics 27 (1960), 649-652.
I.E. Kazakov, Approximate probabilistic analysis of the accuracy of operation of essentially nonlinear systems, Automatika i Telemekhanika 17 (1956), 423-450.
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.
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.
J.B. Roberts, P.D. Spanos, Random Vibrations and Statistical Linearization, Wiley, New York, 1990.
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.
O. Fillatre, Identification of weakly nonlinear dynamic systems by means of random excitations, La Recherche Aéerospatiale 3 (1992), 11-22.
H.J. Rice, Identification of weakly non-linear systems using equivalent linearization, Journal of Sound and Vibration 185 (1995), 473-481.
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.
S.H. Crandall, Les vibrations forcées dans les systèmes non-linéaires, Colloques Internationaux du CNRS, Marseille, 1963.
R. Bouc, The power spectral density of response for a strongly nonlinear random oscillator, Journal of Sound and Vibration 175 (1994), 317-331.
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.
C. Soize, Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: prediction and identification procedures, Probabilistic Engineering Mechanics 10 (1995), 143-152.
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.
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.
S. Bellizzi, M. Defilippi, Non-linear mechanical systems identification using linear systems with random parameters, Mechanical Systems and Signal Processing 17 (2003), 203-210.
K. Yasuda, S. Kawamura, K. Watanabe, Identification of nonlinearmulti-degree-of-freedom systems (presentation of an identification technique), JSME International Journal Series 3 31(1988a), 8-14.
K. Yasuda, S. Kawamura, K. Watanabe, Identification of nonlinear multi-degree-of-freedom systems (identification under noisy measurements), JSME International Journal Series 3 31 (1988b), 302-309.
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.
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.
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.
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.
E.F. Crawley, A.C. Aubert, Identification of nonlinear structural elements by force-state mapping, AIAA Journal 24 (1986), 155-162.
S.F. Masri, H. Sassi, T.K. Caughey, A nonparametric identification of nearly arbitrary nonlinear systems, Journal of Applied Mechanics 49 (1982), 619-628.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
H.R. Lo, J.K. Haond, Identification of a class of nonlinear systems, Preprint Institute of Sound and Vibration Research, Southampton, 1988.
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.
K. Shin, J.K. Haond, Force-state mapping method of a chaotic dynamical system, Journal of Sound and Vibration 218 (1998b), 405-418.
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.
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.
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.
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.
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.
S. Duym, J. Schoukens, P. Guillaume, A local restoring force surface method, International Journal of Analytical and Experimental Modal Analysis 11 (1996b), 116-132.
S. Duym, J. Schoukens, Selection of an optimal force-state map, Mechanical Systems and Signal Processing 10 (1996c), 683-695.
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.
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.
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.
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.
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.
G.E.P. Box, G.M. Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco, 1970.
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.
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.
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.
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.
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.
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.
E. Bedrosian, S.O. Rice, The output properties of systems driven by harmonic and Gaussian inputs, Proceedings IEEE5 9 (1971), 1688-1707.
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.
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.
F. Thouverez, L. Jezequel, Identification of models on a modal base, Journal of Sound and Vibration 189 (1996), 193-213.
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.
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.
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.
M. Feldman, Non-linear free vibration identification via the Hilbert transform, Journal of Sound and Vibration 208 (1997), 475-489.
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.
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.
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.
J.N. Yang, S. Lin, Hilbert-Huang based approach for structural damage detection, Journal of Engineering Mechanics 130 (2004b), 85-95.
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.
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.
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.
J.W. Liang, B.F. Feeny, Identifying Coulomb and viscous friction from free-vibration decrements, Nonlinear Dynamics 16 (1998), 337-347.
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.
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.
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.
K. Yasuda, K. Kamiya, Experimental identification technique of non-linear beams in time domain, Nonlinear Dynamics 18 (1999),185-202.
M. Schetzen, The and Wiener Theories of Nonlinear Systems. John Wiley & Sons, New York, 1980.
F. Thouverez, L. Jezequel, Identification of a localized non-linearity, International Journal of Non-Linear Mechanics 33 (1998), 935-945.
S.J. Gifford, Series Analysis of Nonlinear Structures, Ph.D. Thesis, Department of Mechanical Engineering, Heriot-Watt University, 1989.
D.M. Storer, Dynamic Analysis of Nonlinear Structures Using Higher Order Frequency Response Functions, Ph.D. Thesis, Department of Engineering, University of Manchester, 1991.
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.
A.A. Khan, N.S. Vyas, Non-linear parameter using and Wiener theories, Journal of Sound and Vibration 221 (1999), 805-821.
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.
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.
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.
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.
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.
I. Tawfiq, T. Vinh, Nonlinear behaviour of structures using the seriessignal processing and testing methods, Nonlinear Dynamics 37 (2004), 129-149.
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.
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.
J.B. Roberts, M. Vasta, Parametric identification of systems with non-Gaussian excitation using measured response spectra, Probabilistic Engineering Mechanics 15 (2000a), 59-71.
J.B. Roberts, M. Vasta, Energy-based stochastic estimation for non-linear oscillators with random excitation, Journal of Applied Mechanics 67 (2000b), 763-771.
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.
A. Swami, G.B. Giannakis, G. Zhou, Bibliography on higher-order statistics, Signal Processing 60 (1997), 65-126.
K. Yasuda, K. Kamiya, Identification of a nonlinear beam (proposition of an identification technique), JSME International Journal Series 3 33 (1990), 535-540.
K. Yasuda, K. Kamiya, Experimental identification technique of vibrating structures with geometrical nonlinearity, Journal of Applied Mechanics 64 (1997), 275-280.
C.M. Yuan, B.F. Feeny, Parametric identification of chaotic systems, Journal of Vibration and Control 4 (1998), 405-426.
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.
Y. Liang, B.F. Feeny, Parametric identification of chaotic base-excited double pendulum experiment, ASME International Mechanical Engineering Congress, Anaheim, 2004b.
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.
M. Thothadrai, F.C. Moon, Nonlinear system identification of systems with periodic limit-cycle response, Nonlinear Dynamics 39 (2005).
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.
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.
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.
J. S. Bendat, Nonlinear System Analysis and Identification from Random Data, John Wiley & Sons, New York, 1990.
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.
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.
B.A. Zeldin, P.D. Spanos, Spectral identification of nonlinear structures, Journal of Engineering Mechanics 124 (1998), 728-733.
J.S. Bendat, Spectral techniques for nonlinear system analysis and identification, Shock and Vibration 1 (1993), 21-31.
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.
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.
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.
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.
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.
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.
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.
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.
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.
L. Garibaldi, Application of the conditioned reverse path method, Mechanical Systems and Signal Processing 17 (2003), 227-236.
S. Marchesiello, Application of the conditioned reverse path method, Mechanical Systems and Signal Processing 17 (2003), 183-188.
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.
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.
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.
J.A. Vazquez Feijoo, K. Worden, R. Stanway, System identification using associated linear equations, Mechanical Systems and Signal Processing 18 (2004), 431-455.
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.
R.W. Krauss, A.H. Nayfeh, Experimental nonlinear identification of a single mode of a tranversely excited beam, Nonlinear Dynamics 18 (1999), 69-87.
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.
A.H. Nayfeh, Parametric identification of nonlinear dynamic systems, Computers and Structures 20 (1985), 487-493.
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.
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.
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.
J. Piranda, R. Fillod, E. Foltete, Modal identification of non-linear structures, Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 1998.
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.
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.
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.
L. Jezequel, Extension des métnodes de synthèse modale au cas non linéaire, Revue-francaise-de-Mecanique 3 (1987), 159-172.
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.
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.
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.
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.
C. Gibert, Fitting measured frequency response using non-linear modes, Mechanical Systems and Signal Processing 17 (2003), 211-218.
L. Huang, W.D. Iwan, Modal identification of nonlinear systems using successive approximation model, Proceedings of the 15th International Modal Analysis Conference, Orlando, 1997.
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.
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.
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.
J.R. Wright, J.E. Cooper, M. Desforges, Normal mode force appropriation — Theory and application, Mechanical Systems and Signal Processing 13 (1999), 217-240.
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.
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.
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.
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.
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.
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.
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.
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.
M.B. Priestley, Power spectral analysis of nonstationary processes, Journal of Sound and Vibration 6 (1967), 86-97.
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.
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.
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.
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.
W.J. Staszewski, Identification of damping in mdof systems using time-scale decomposition, Journal of Sound and Vibration 203 (1997), 283-305.
P. Argoul, T.P. Le, Continuous wavelet transform for modal identification using free decay response, Journal of Sound and Vibration 277 (2004), 73-100.
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.
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.
H. Franco, R.M.O. Pauletti, Analysis of nonlinear oscillations by gabor spectrograms, Nonlinear Dynamics 12 (1997), 215-236.
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.
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.
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.
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.
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.
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.
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.
Y. Kitada, Identification of nonlinear structural dynamic systems using wavelets, Journal of Engineering Mechanics 124 (1998), 1059-1066.
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.
S.L. Chen, K.C. Ho, Identification of nonlinear systems by Haar Wavelet, ASME International Mechanical Engineering Congress, Anaheim, 2004.
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.
G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals, and Systems 2 (1989), 303-314.
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.
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.
S.R. Chu, R. Shoureshi, M. Tenorio, Neural networks for system identification, IEEE Control Systems Magazine 10 (1990), 36-43.
K.S. Narendra, K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks 1 (1990), 4-27.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
M. Peifer, J. Tier, H.U. Voss, Nonparametric identification of nonlinear oscillating systems, Journal of Sound and Vibration 267 (2003), 1157-1167.
G.P. Liu, S.A. Billings, V. Kadirkamanathan, Nonlinear system identification using wavelet networks, International Journal of Systems Science 31 (2000), 1531-1541.
R. Babuska, H. Verbruggen, Neuro-fuzzy methods for nonlinear system identification, Annual Reviews in Control 27 (2003), 73-85.
O. Zienkiewicz, The Finite Element Method. McGraw-Hill, London, 1977.
A. Berman, E.J. Nagy, Theory of incomplete models of dynamic structures, AIAA Journal 9 (1971), 1481-1487.
M. Baruch, Optimization procedure to correct stiffness and flexibility matrices using vibration test, AIAA Journal 16 (1978), 1208-1210.
H.G. Natke, Einfuhrung in Theorie und Praxis der Zeitreihen und Modalanalyse, Vieweg Verlag, Braunschweig/Wiesbaden 1992.
M.I. Friswell, J.E. Mottershead, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, London, 1995.
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.
R. Schmidt, Updating non-linear components, Mechanical Systems and Signal Processing 8 (1994), 679-690.
R.K. Kapania, S. Park, Parametric identification of nonlinear struc-tural dynamic systems using time finite element method, AIAA Journal 35 (1997), 719-726.
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.
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.
A. Kyprianou, K. Worden, M. Panet, Identification of hysteretic systems using the differential evolution algorithm, Journal of Sound and Vibration 248 (2001), 289-314.
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.
K.V. Yuen, J.L. Beck, Updating properties of nonlinear dynamical systems with uncertain input, Journal of Engineering Mechanics 129 (2003), 9-20.
D.R. Mulville, Pyroshock Test Criteria, NASA Technical Standard, Report NASA-S-7003, 1999.
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.
X. Ma, A.F. Vakakis, Karhunen-Loève decomposition of the transient dynamics of a multibay truss, AIAA Journal 37 (1999), 939-946.
G. Kerschen, On the Model Validation in Non-linear Structural Dynamics, Ph.D. Thesis, University of Liège, 2003c.
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.
D.C Zierman, T. Hasselman, M. Anderson, Approximation and cal-ibration of nonlinear structural dynamics, Nonlinear Dynamics 39 (2005).
J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures, Wiley Inter science, New York, 3rd edition, 2000.
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.
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.
R.M. Rosenberg, Normal modes of nonlinear dual-mode systems, Journal of Applied Mechanics 27 (1960), 263-268.
R.M. Rosenberg, The normal modes of nonlinear n-degree-of-freedom systems, Journal of Applied Mechanics 29 (1962), 7-14.
R.M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom, Advances in Applied Mechanics 9 (1966), 155-242.
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.
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.
S.W. Shaw, C. Pierre, Normal modes for non-linear vibratory systems, Journal of Sound and Vibration 164 (1993), 85-124.
S.W. Shaw, C. Pierre, Normal modes of vibration for non-linear continuous systems, Journal of Sound and Vibration 169 (1994), 319-347.
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.