Session: VIB-08-01: Nonlinear Systems & Phenomena

Paper Number: 97516

97516 - Predicting Modal Properties of Nonlinear Oscillators by Measuring Free Vibration Response 

The exploitation of nonlinear structures is becoming a critical issue in the structural dynamics community since the nonlinear systems provide rich dynamic features that can be utilized to enhance the performance of engineered systems. In order to characterize the dynamic features of these systems, nonlinear system identification has been an active research area over the past decades and hence a broad array of methods has been developed. Linearization methods, in particular, have been widely employed to obtain approximate models of nonlinear structures since most structural designs in industry still rely on linear techniques. However, these methods cannot capture nonlinear phenomena such as jumps and modal interactions, and they are usually valid only for a unique set of excitation parameters. In order to enhance the robustness of system identification, a variety of nonlinear system identification methods that are built off of processing time-domain data or frequency-domain data have been proposed.

Recently, a time-domain nonlinear system identification algorithm referred to as the sparse identification of nonlinear dynamics (SINDy) method was developed for constructing nonlinear models of dynamical systems. The SINDy method utilizes the fact that most dynamical systems only have a few active nonlinear terms in the space of possible functions. Thus, the system parameters can be estimated by applying sparse regression techniques, such as the sequential thresholded least-squares algorithm, to process collected data of time-domain response. The SINDy method transforms the nonlinear system to a generalized linear model in which nonlinear parameters are reserved, and hence the nonlinear features of the system can be successfully predicted. Furthermore, the SINDy method is able to recover the governing equation of the system by processing the data of free vibration response since the method is applicable to autonomous dynamical systems.

In this work, the SINDy method is combined with a couple of numerical methods to predict the nonlinear modal properties of mechanical oscillators. First, the effectiveness of SINDy on constructing the governing equation of nonlinear oscillator is numerically investigated. The effect of measurement noise on the system identification is discussed. Second, The SINDy method is combined with the shooting method and arc length continuation technique to predict the nonlinear normal modes (NNMs) of the oscillator. The NNMs predicted by the combined method are compared with the exact NNMs to investigate the capability of the proposed technique. Also, the effect of vibration energy level on the NNM prediction is investigated in this work. Finally, the effect of the condition of initial excitation on the system identification is discussed. A guideline of choosing better initial conditions for generating appropriate data of vibration response will be proposed.

Presenting Author: Shih-Chun Huang National Tsing Hua University (Hsinchu, Taiwan)

Presenting Author Biography: Shih-Chun Huang is a master's student in the Department of Power Mechanical Engineering at the National Hsing Hua University in Taiwan. Huang's research is focusing on the development of computational tools for structural dynamics and nonlinear vibration.

Authors:

Shih-Chun Huang National Tsing Hua University (Hsinchu, Taiwan)
Hao-Wen Chen National Tsing Hua University (Hsinchu, Taiwan)
Meng-Hsuan Tien National Tsing Hua University (Hsinchu, Taiwan)