Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses

Identifying dynamical system models from measurements is a central challenge in the structural dynamics community. Nonlinear system identification, in particular, is of great challenge since there are combinatorically many possible model structures which requires expert knowledge for constructing an appropriate model. Furthermore, traditional nonlinear system identification methods require a steady excitation input that is not always available in many practical applications. Recently, a technique referred to as the sparse identification of nonlinear dynamics (SINDy) algorithm was developed for discovering mathematical models of general nonlinear systems. The SINDy method is able to find a generalized linear state-space model for the autonomous nonlinear system by analyzing the collected response data. In this work, the SINDy method is adapted and combined with the shooting method and numerical continuation technique to form a system identification platform that is capable of predicting the nonlinear modal properties of mechanical oscillators. The proposed platform is able to predict the nonlinear normal modes (NNMs) of these systems by processing the noised data of their free vibration response. Also, the NNMs and internal resonance of the nonlinear systems at a high energy level can be captured using the proposed technique by processing the response data at a lower energy level. The proposed method is numerically demonstrated on a two degree of freedom mechanical oscillator. Furthermore, the effects of measurement error and excitation condition on the NNMs prediction are investigated. The NNM prediction platform presented in this paper is applicable to a variety of nonlinear systems.