北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (7): 1337-1348.doi: 10.13700/j.bh.1001-5965.2018.0643

• 论文 • 上一篇    下一篇

基于非线性模态的复杂系统动力学特性分析方法

黄行蓉1, 刘久周2, 李琳3   

  1. 1. 北京航空航天大学 中法工程师学院, 北京 100083;
    2. 中国运载火箭技术研究院, 北京 100076;
    3. 北京航空航天大学 能源与动力工程学院, 北京 100083
  • 收稿日期:2018-11-07 出版日期:2019-07-20 发布日期:2019-07-25
  • 通讯作者: 李琳 E-mail:feililin@buaa.edu.cn
  • 作者简介:黄行蓉 女,博士,讲师。主要研究方向:流固耦合动力学、非线性结构动力学及振动控制;刘久周 男,博士,工程师。主要研究方向:非线性系统动力学、高速飞行器热防护设计;李琳 女,博士,教授。主要研究方向:叶盘结构流致振动、智能结构动力学及振动控制。

Dynamic characteristics analysis method of complex systems based on nonlinear mode

HUANG Xingrong1, LIU Jiuzhou2, LI Lin3   

  1. 1. L'école Centrale de Pékin, Beihang University, Beijing 100083, China;
    2. China Academy of Launch Vehicle Technology, Beijing 100076, China;
    3. School of Energy and Power Engineering, Beihang University, Beijing 100083, China
  • Received:2018-11-07 Online:2019-07-20 Published:2019-07-25

摘要: 针对非线性问题计算方法复杂和计算时间冗长一直是动力学领域的难点问题,给出了一套简单、准确、高效的非线性模态分析方法,对于常见的非线性系统(如杜芬系统、干摩擦系统和非线性材料等)均适用,具有一般性。首先,给出所提方法的基本理论与分析流程;然后,以杜芬系统为例阐述了其在非线性实模态域的应用,以干摩擦系统为例描述了其在非线性复模态域的应用,以压电系统为例展示了其在多场耦合域的应用;最后,给出了基于该理论对大型复杂非线性系统求解时的减缩方法。所提方法的核心在于建立非线性模态参数关于模态幅值的变化规律,不仅将系统的稳态响应求解问题简化为一维代数问题,极大地简化了数值计算过程,而且有助于分析、理解系统的非线性动力学行为。将所提方法与模态综合法结合,可用于高效求解大型复杂非线性系统动力学特性。

关键词: 非线性模态分析, 模态综合, 杜芬, 干摩擦, 非线性材料, 减缩模型

Abstract: Nonlinear problem has always been an obstacle in dynamic analysis domain due to its complexity and high computational cost. This paper aims to present a simple, accurate and efficient nonlinear modal analysis method which can be applied to some common nonlinear systems, including Duffing system, dry friction, nonlinear material and so on. The kernel technique of this numerical method lies in establishing the variation law of the nonlinear modal parameters in function of modal amplitude:on the one hand, the steady-state problem is simplified into one-dimensional algebraic nonlinear problem, resulting in a significant simplification in numerical computation; on the other hand, the analysis of nonlinear modal parameters in function of modal amplitude provides a modal overview for the comprehension of system's nonlinear dynamic behavior. Following a description of the theoretical aspects and numerical simulation process of this method, it has been proven to be efficient in analyzing a Duffing system with real nonlinear mode, a dry friction system with complex nonlinear mode and a multi-physics system integrating piezoelectric material. A reduction method based on the proposed strategy is then presented, which is simple in mathematical form and efficient in numerical computations for analyzing large complex nonlinear systems. It has significant advantages in computational efficiency when combined with the mode synthesis method to solve the dynamic behavior of large complex nonlinear systems.

Key words: nonlinear modal analysis, mode synthesis, Duffing, dry friction, nonlinear material, reduced model

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