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Identification of Weakly Nonlinear Systems Using Describing Function Inversion

Abstract

In this paper describing functions inversion is used and the restoring force of a nonlinear element in a MDOF system is characterized. The describing functions can be obtained using linearized frequency response functions (FRFs). The response of the system to harmonic excitation forces at distinct frequencies close to the resonant frequency results in linearized FRFs. The nonlinear system can be approximated at each excitation frequency by an equivalent linear system. This approximation leads to calculation of the first-order describing functions. By having the experimental describing functions calculated and the system’s responses corresponding to the nonlinear element (measured or interpolated), nonlinear parameter identification can be performed. Two numerical and experimental case studies are provided to show the applicability of this method.

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Correspondence to H. Jalali.

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Jalali, H., Bonab, B.T. & Ahmadian, H. Identification of Weakly Nonlinear Systems Using Describing Function Inversion. Exp Mech 51, 739–747 (2011). https://doi.org/10.1007/s11340-010-9375-x

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Keywords

  • MDOF system
  • Nonlinearity identification
  • Describing functions