力学与实践 ›› 2021, Vol. 43 ›› Issue (2): 252-255.DOI: 10.6052/1000-0879-20-430

• 教育研究 • 上一篇    下一篇

关于对模态概念的理解

陈立群1)()   

  1. 上海大学力学与工程科学学院力学系,上海 200444
  • 收稿日期:2020-10-09 出版日期:2021-04-20 发布日期:2021-04-20
  • 通讯作者: 陈立群
  • 作者简介:1)陈立群,教授,主要研究方向为振动控制和非线性动力学。E-mail: lqchen@shu.edu.cn

ON THE CONCEPT OF MODES

CHEN Liqun1)()   

  1. Department of Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China
  • Received:2020-10-09 Online:2021-04-20 Published:2021-04-20
  • Contact: CHEN Liqun

摘要:

通过分析模态的性质并与复模态和非线性模态比较以加强对模态概念的理解。固有模态的基本性质是模态振动的同频性、对初始条件的不变性、模态的正交性和系统响应的叠加性。复模态仍具有模态振动的同频性,但没有对初始条件的不变性,正交性和叠加性仅在状态空间中成立。非线性模态仅保留了同频性或不变性,不具有正交性和叠加性。

关键词: 教学, 模态, 复模态, 非线性模态, 振动

Abstract:

In order to better understand the concept of modes, the characteristics of modes are analyzed and compared with those of complex modes or nonlinear modes. The connotation of a mode includes the synchronicity of the modal vibrations, the invariance to the initial conditions, the orthogonality among modes, and the superposition of the modal vibrations into the response. A complex mode concerns with the synchronicity but not the invariance, while the orthogonality and the superposition hold only in the state space. A nonlinear mode concerns both with the synchronicity and the invariance, but not the orthogonality nor the superposition.

Key words: teaching, mode, complex mode, nonlinear mode, vibration

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