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Nonlinear model updating by means of identified nonlinear normal modes

Modal parameters are the most common features used for linear model updating. Although the modal analysis theory does not hold for nonlinear dynamic systems, its popularity encouraged researchers to come up with an equivalent version of normal modes for nonlinear systems, i.e., nonlinear normal modes (NNMs). A nonlinear system vibrates in NNMs when all masses have periodic motions of the same period, and at any time, the position of all the masses is uniquely defined by the position of any one of them. This paper investigates the feasibility of nonlinear model updating by minimizing the difference between the model-predicted and measured/identified nonlinear normal modes. A two degree-of-freedom mass-spring system with three linear springs and a cubic nonlinear spring is considered as the case study. The energy-dependent natural frequency and NNM of the first vibration mode of the system are identified at three different levels of energy. The stiffness parameters of the system are estimated by minimizing an objective function which is defined as the discrepancy between model-predicted natural frequency and NNM of the first mode, and their identified counterparts at the three measured energy levels. Performance of the proposed updating approach is evaluated at different levels of noise and different levels of modeling errors (i.e., nonlinear model classes).

Author(s):

Mingming Song    
Tufts University
United States

Ludovic Renson    
University of Liege
Belgium

Jean-Philippe Noël    
University of Liege
Belgium

Babak Moaveni    
Tufts University
United States

Gaetan Kerschen    
University of Liege
Belgium