{"title":"Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress","authors":"Yuri Mikhlin, Konstantin V. Avramov","doi":"10.1115/1.4063593","DOIUrl":null,"url":null,"abstract":"Abstract This paper contains review of the theory and applications of nonlinear normal modes, which are developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers of the same authors (Mikhlin Y.V., Avramov K.V.: Nonlinear normal modes for vibrating mechanical systems. Review of Theoretical Developments. Appl. Mech. Rev. 63, 060802 (2010); Avramov, K.V., Mikhlin, Yu.V.: Review of applications of nonlinear normal modes for vibrating mechanical systems. Appl. Mech. Rev. 65, 020801 (2013)). The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal forms theory for nonlinear modes construction; nonlinear modes in finite degrees of freedom systems; resonances and bifurcations; reduced-order modelling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":null,"pages":null},"PeriodicalIF":12.2000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mechanics Reviews","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4063593","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper contains review of the theory and applications of nonlinear normal modes, which are developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers of the same authors (Mikhlin Y.V., Avramov K.V.: Nonlinear normal modes for vibrating mechanical systems. Review of Theoretical Developments. Appl. Mech. Rev. 63, 060802 (2010); Avramov, K.V., Mikhlin, Yu.V.: Review of applications of nonlinear normal modes for vibrating mechanical systems. Appl. Mech. Rev. 65, 020801 (2013)). The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal forms theory for nonlinear modes construction; nonlinear modes in finite degrees of freedom systems; resonances and bifurcations; reduced-order modelling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.
期刊介绍:
Applied Mechanics Reviews (AMR) is an international review journal that serves as a premier venue for dissemination of material across all subdisciplines of applied mechanics and engineering science, including fluid and solid mechanics, heat transfer, dynamics and vibration, and applications.AMR provides an archival repository for state-of-the-art and retrospective survey articles and reviews of research areas and curricular developments. The journal invites commentary on research and education policy in different countries. The journal also invites original tutorial and educational material in applied mechanics targeting non-specialist audiences, including undergraduate and K-12 students.