Identification of systems containing nonlinear stiffnesses using backbone curves

Abstract This paper presents a method for the dynamic identification of structures containing discrete nonlinear stiffnesses. The approach requires the structure to be excited at a single resonant frequency, enabling measurements to be made in regimes of large displacements where nonlinearities are more likely to be significant. Measured resonant decay data is used to estimate the system backbone curves. Linear natural frequencies and nonlinear parameters are identified using these backbone curves assuming a form for the nonlinear behaviour. Numerical and experimental examples, inspired by an aerospace industry test case study, are considered to illustrate how the method can be applied. Results from these models demonstrate that the method can successfully deliver nonlinear models able to predict the response of the test structure nonlinear dynamics.

[1]  Alexander F. Vakakis,et al.  Normal modes and localization in nonlinear systems , 1996 .

[2]  G. Kerschen,et al.  Dynamic testing of nonlinear vibrating structures using nonlinear normal modes , 2011 .

[3]  Gaëtan Kerschen,et al.  Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure , 2005 .

[4]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[5]  A. Nayfeh.  The Method of Normal Forms: NAYFEH:NORMAL FORMS 2/E O-BK , 2011 .

[6]  Richard H. Rand,et al.  A direct method for non-linear normal modes , 1974 .

[7]  Michael Feldman,et al.  Identification of weakly nonlinearities in multiple coupled oscillators , 2007 .

[8]  Cyril Touzé,et al.  Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes , 2004 .

[9]  David J. Wagg,et al.  Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator , 2014 .

[10]  Jonathan E. Cooper,et al.  NORMAL-MODE FORCE APPROPRIATION—THEORY AND APPLICATION , 1999 .

[11]  Gaëtan Kerschen,et al.  Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration , 2011 .

[12]  David J. Wagg,et al.  Applying the method of normal forms to second-order nonlinear vibration problems , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  Jonathan E. Cooper,et al.  Identification of backbone curves of nonlinear systems from resonance decay responses , 2015 .

[14]  Claude-Henri Lamarque,et al.  Analysis of non-linear dynamical systems by the normal form theory , 1991 .

[15]  Jonathan E. Cooper,et al.  Identification of multi-degree of freedom non-linear systems using an extended modal space model , 2009 .

[16]  Jonathan E. Cooper,et al.  Identification of a Nonlinear Wing Structure Using an Extended Modal Model , 2009 .

[17]  Michael Feldman,et al.  Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method 'Freevib' , 1994 .

[18]  R. M. Rosenberg,et al.  The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .

[19]  Cyril Touzé,et al.  Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures , 2004 .

[20]  Jonathan E. Cooper,et al.  Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method , 2004 .

[21]  G. Tomlinson,et al.  Nonlinearity in Structural Dynamics: Detection, Identification and Modelling , 2000 .

[22]  S. Billings.  Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains , 2013 .

[23]  Ali H. Nayfeh,et al.  The Method of Normal Forms , 2011 .

[24]  Ali H. Nayfeh,et al.  On Direct Methods for Constructing Nonlinear Normal Modes of Continuous Systems , 1995 .

[25]  Gaëtan Kerschen,et al.  THEORETICAL AND EXPERIMENTAL IDENTIFICATION OF A NON-LINEAR BEAM , 2001 .

[26]  P. L. Green.  Bayesian system identification of a nonlinear dynamical system using a novel variant of Simulated Annealing , 2015 .

[27]  J. Hensman,et al.  Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference , 2012 .

[28]  Christophe Pierre,et al.  Normal Modes for Non-Linear Vibratory Systems , 1993 .

[29]  S. A. Neild,et al.  Out-of-unison resonance in weakly nonlinear coupled oscillators , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.