Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress

IF 12.2 1区 工程技术 Q1 MECHANICS Applied Mechanics Reviews Pub Date : 2023-09-30 DOI:10.1115/1.4063593
Yuri Mikhlin, Konstantin V. Avramov
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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.
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振动机械系统的非线性正态:10年的进展
本文综述了近十年来发展起来的非线性正态模态理论及其应用。这篇综述有200多篇参考文献。这是前两篇相同作者的综述论文(Mikhlin y.v., Avramov k.v.)的延续:振动机械系统的非线性正态模态。理论发展回顾。达成。动力机械。Rev. 63, 060802 (2010);Avramov, k.v., Mikhlin, Yu.V:非线性正态模态在振动机械系统中的应用综述。达成。动力机械。Rev. 65, 020801(2013))。处理了以下非线性正态模态的理论问题:基本概念和定义;范式理论在非线性模态构造中的应用有限自由度系统的非线性模态共振和分岔;降维模型;随机动力系统的非线性模态数值方法;使用非线性模态的机械系统辨识。本文讨论了该理论的以下应用问题:非线性模态的实验测量;连续系统的非线性模态;工程应用(航空航天工程,动力工程,分段线性系统和干摩擦结构);纳米结构和物理系统中的非线性模式;目标能量传递和吸收问题。
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来源期刊
CiteScore
28.20
自引率
0.70%
发文量
13
审稿时长
>12 weeks
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.
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