NIXO-Based identification of the dominant terms in a nonlinear equation of motion of structures with geometric nonlinearity

Abstract

The objective of this publication is to propose a novel technique for black-box identification of structures with geometric nonlinearity. The technique is based on a recently introduced frequency-domain system identification method called Nonlinear Identification through eXtended Outputs (NIXO). The proposed algorithm first expresses the nonlinear part of modal equation of motion (EOM) as a general polynomial of high order, and then removes the terms which are determined to be irrelevant to the mechanical system’s response. This division into dominant and irrelevant nonlinear terms relies on the values of two novel indicators that are particular to NIXO. The heuristic presented here was observed to work well only when the tested structure is excited with various swept-sine input signals of different magnitudes (so that the system oscillates at sufficiently distinctive amplitudes in different experimental tests). The technique is first demonstrated on a noise-free numerical case study employing a reduced model of a curved beam. The results obtained are verified via comparing the true Nonlinear Normal Mode (NNM) to the one computed using the modal EOM pointed out by NIXO. Then the method is demonstrated on experimental measurements collected on a 3D-printed flat beam exhibiting significant natural frequency shifts, and the outcomes are verified by overlaying the identified NNMs on the swept-sine responses.