{"title":"分析具有接触非线性的系统的非线性法向模态的混合连续框架","authors":"Shih-Chun Huang, Meng-Hsuan Tien","doi":"10.1115/1.4064272","DOIUrl":null,"url":null,"abstract":"\n The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Hybrid Continuation Framework for Analyzing Nonlinear Normal Modes of Systems With Contact Nonlinearity\",\"authors\":\"Shih-Chun Huang, Meng-Hsuan Tien\",\"doi\":\"10.1115/1.4064272\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-05-13\",\"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/10.1115/1.4064272\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4064272","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}
A Hybrid Continuation Framework for Analyzing Nonlinear Normal Modes of Systems With Contact Nonlinearity
The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.
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.