Nonlinearities in mechanical systems demand extensive efforts both in modeling their dynamics and identification of their parameters. In this paper an identification approach is proposed for nonlinear multi-degree-of-freedom systems when there is a single nonlinear element in the system and its location is known. The proposed method is an extension of the frequency response function (FRF) sensitivity method used in the linear systems. The method uses measured nonlinear FRFs and employs a reduced order model for sensitivity calculations. Numerical and experimental case studies are used to verify the accuracy of the proposed method.
AdamsDEAllemangRJ (2000) A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback. Mechanical Systems and Signal Processing, 14: 637–656.
2.
AhmadianHZamaniA (2009) Identification of nonlinear boundary effects using nonlinear normal modes. Mechanical Systems and Signal Processing, 23: 2008–2018.
3.
AhmadianHJalaliHPourahmadianF (2010) Nonlinear model identification of a frictional contact support. Mechanical Systems and Signal Processing, 24: 2844–2854.
4.
ArslanOAykanMOzguvenHN (2011) Parametric identification of structural nonlinearities from measured frequency response data. Mechanical Systems and Signal Processing, 25: 1112–1125.
5.
CarrellaAEwinsDJ (2011) Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions. Mechanical Systems and Signal Processing, 25: 1011–1027.
6.
CrawleyEFAubertAC (1986) Identification of nonlinear structural elements by force-state mapping. AIAA Journal, 24: 155–162.
7.
Crawley EF and O'Donnell (1986) Identification of nonlinear system parameters in joints using the force-state mapping technique. In: 27th Structures, Structural Dynamics and Materials Conference, San Antonio, TX, 19–21 May, pp.659–667.
8.
FeldmanM (1994a) Nonlinear system vibration analysis using the Hilbert transform-I. Free vibration analysis method ‘FREEVIB’. Mechanical Systems and Signal Processing, 8: 119–127.
9.
FeldmanM (1994b) Nonlinear system vibration analysis using the Hilbert transform-I. Forced vibration analysis method ‘FORCEVIB’. Mechanical Systems and Signal Processing, 8: 309–318.
10.
FriswellMIMottersheadJE (1995) Finite Element Model Updating in Structural Dynamics, London: Kluwer Academic Publishers.
11.
GelbAVander VeldeWE (1968) Multiple-Input Describing Functions and Nonlinear System Design, New York: McGraw-Hill.
12.
Gifford SJ (1989) Volterra series analysis of nonlinear structures. PhD thesis, Heriot-Watt University, UK.
13.
Grafe H (1998) Model updating of large structural dynamic models using measured response functions. PhD thesis, Imperial college of Science Technology and Medicine, UK.
14.
HemezFMDoeblingSW (2001) Review and assessment of model updating for nonlinear, transient dynamics. Mechanical Systems and Signal Processing, 15: 45–74.
15.
IwanWD (1973) A generalization of the concept of equivalent linearization. International Journal of Non-Linear Mechanics, 8: 279–287.
16.
JalaliHAhmadianHPurahmadianF (2011) Identification of micro-vibro-impacts at boundary condition of a nonlinear beam. Mechanical Systems and Signal Processing, 25: 1073–1085.
17.
KerschenGGolinvalJC (2004) A model updating strategy of non-linear vibrating structures. International Journal of Numerical Methods in Engineering, 60: 2147–2164.
18.
KerschenGWordenKVakakisAF (2006) Past, present and future of nonlinear system identification in structural dynamics. Mechanical Systems and Signal Processing, 20: 505–592.
19.
MasriSFCaugheyTK (1979) A non-parametric identification technique for nonlinear dynamic problems. Journal of Applied Mechanics, 46: 433–447.
20.
MasriSFSassiHCaugheyTK (1982) A nonparametric identification of nearly arbitrary nonlinear systems. Journal of Applied Mechanics, 49: 619–628.
21.
MeyerSWeilandMLinkM (2003) Modeling and updating of local non-linearities using frequency response residuals. Mechanical Systems and Signal Processing, 17: 219–226.
22.
MottersheadJELinkMFriswellMI (2011) The sensitivity method in finite element model updating: a tutorial. Mechanical Systems and Signal Processing, 25: 2275–2296.
23.
OzerMBOzguvenHNRoystonTJ (2009) Identification of structural non-linearities using describing functions and the Sherman–Morrison method. Mechanical Systems and Signal Processing, 23: 30–44.
24.
Perinpanayagam S, Robb D, Ewins DJ, et al. (2004) Non-linearities in an aero-engine structure: from test to design. In: Proceedings of the International Conference on Modal Analysis, Noise and Vibration Engineering, Leuven, Belgium, 20–22 September, pp.3167–3182.
25.
RiceHJFitzpatrickJA (1988) A generalized technique for spectral analysis of non-linear systems. Mechanical Systems and Signal Processing, 2: 195–207.
26.
RichardsCMSinghR (1998) Identification of multi-degree-of-freedom non-linear systems under random excitations by the reverse-path spectral method. Journal of Sound and Vibration, 213: 673–708.
27.
SchetzenM (1980) The Volterra and Wiener Theories of Nonlinear Systems, New York: Wiley.
28.
StorerDMTomlinsonGR (1993) Recent developments in the measurements and interpretation of higher order functions from nonlinear structures. Mechanical Systems and Signal Processing, 7: 173–189.
29.
TaylorGJBrownRG (1960) Analysis and Design of Feedback Control Systems, New York: McGraw-Hill.
30.
TikhonovANArseninVY (1977) Solutions of Ill-posed Problems, New York: John Wiley.
