Structural Nonlinearity Identification Using Perturbed Eigen Problem and ITD Modal Analysis Method


Article Preview

Identification of nonlinear behavior in structural dynamics has been considered here, in this paper. Time domain output data of system are directly used to identify system through Ibrahim Time Domain (ITD) modal analysis method and perturbed eigen problem. Cubic stiffness and Jenkins element, as case studies, are employed to qualify the identification method. Results are compared with Harmonic Balance (HB) estimation of nonlinear dynamic stiffness. Results of ITD based identification are in good agreement with the HB estimation, for stiffness parts of nonlinear dynamic stiffness but for damping parts of nonlinear dynamic stiffness, method needs some additional improvements which are under investigation.



Edited by:

Amanda Wu




H. Kashani and A.S. Nobari, "Structural Nonlinearity Identification Using Perturbed Eigen Problem and ITD Modal Analysis Method", Applied Mechanics and Materials, Vol. 232, pp. 949-954, 2012

Online since:

November 2012




[1] G. Kaschen, K. Worden, A. F. Vakakis, J. C. Golinval, Past, Present and Future of Nonlinear System Identification in Structural Dynamics, Mechanical System and Signal Processing, 20(3), 505-592, (2006).


[2] C. Meskell, J. A. Fitzpatrick, H. J. Rice, Application of Force-State Mapping to a Nonlinear Fluid-Elastic System, Mechanical System and Signal Processing, 15, 75-85, (2001).


[3] F. Thouverez, L. Jezequel, Identification of NARMAX models on a Modal Base, J. Sound and Vibration, 89, 193-213, (1996).


[4] M. Feldman, Nonlinear System Vibration Analysis Using the Hilbert Transform-I. Forced Vibration Analysis Method 'FORCEVIB', Mechanical System and Signal Processing, 8, 309-318, (1994).


[5] V.N. Pilipchuk, C.M. Tan, Nonlinear System Identification Based on the Lie Series Solutions, Mechanical System and Signal Processing, 19, 71-86, (2005).


[6] R. M. Rosenberg, The Normal Modes of Nonlinear n-Degree-of-Freedom Systems, J. Applied Mechanics, 29, 7-14, (1962).

[7] V. Lenaerts, G. Kerschen, J. C. Golinval, Proper Orthogonal Decomposition for Model Updating of Nonlinear Mechanical Systems, Mechanical System and Signal Processing, 15, 31-43, (2001).


[8] A. Chatterjee, N. S. Vyas, Nonlinear Parameter Estimation in Multi-Degree-of-freedom Systems Using Multi-Input Volterra Series, Mechanical System and Signal Processing, 18, 457-489, (2004).


[9] M. R. Hajj, J. Fung, A. H. Nayfeh, S. Fahey, Damping Identification Using Perturbation Techniques and Higher-order Spectra, Nonlinear Dynamics, 23, 189-203, (2000).

[10] G. Kreschen, J. C. Golinval, Generation of Accurate Finite Element Models of Nonlinear Systems-Application to an Aeroplane-like Structure, Nonlinear Dynamics, 39, 129-142, (2005).


[11] D. E. Adams, R. J. Allemang, A Frequency Domain Method for Estimating the Parameters of a Nonlinear Structural Dynamic Model through Feedback, Mechanical System and Signal Processing, 14, 637-656, (2000).


[12] H. Kashani, A. S. Nobari, Identification of Dynamic Characteristics of nonlinear Joint Based on the Optimum Equivalent Linear Frequency Response Function, J. of Sound and Vibration, 329, 9, 1460-1479, (2010).


[13] S. R, Ibrahim, E. c. Mikulcik, A Time Domain Modal Vibration Test Technique, Shock Vibration Bull., 21-37, (1973).

[14] W. Zhou, D. Chelidze, Generalized Eigenvalue Decomposition in Time Domain Modal Parameter Identification, J. of Vibration and Acoustic, 130, 1, 761-769, (2006).