{"title":"Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses","authors":"Shih-Chun Huang, Hao-Wen Chen, Meng-Hsuan Tien","doi":"10.1115/1.4056949","DOIUrl":null,"url":null,"abstract":"\n 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.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"66 5 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4056949","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.