{"title":"Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics","authors":"G. Cassoni, A. Zanoni, A. Tamer, P. Masarati","doi":"10.1115/1.4056591","DOIUrl":null,"url":null,"abstract":"\n The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"450 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-01-03","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/10.1115/1.4056591","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
The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.
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.