中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (6): 63-70.doi: 10.13471/j.cnki.acta.snus.2018.06.008

• 论文 • 上一篇    下一篇

非线性系统准周期振动的多时间尺度IHB法

张丹伟,刘济科,黄建亮   

  1. 中山大学工学院应用力学与工程系,广东 广州 510275
  • 收稿日期:2017-10-08 出版日期:2018-11-25 发布日期:2018-11-25
  • 通讯作者: 黄建亮(1977年生),男;研究方向:非线性振动;E-mail:huangjl@mail.sysu.edu.cn

The IHB method with multiple time scales for quasi-periodic motions of nonlinear systems

ZHANG Danwei, LIU Jike, HUANG Jianliang   

  1. Department of Applied Mechanics and Engineering, School of Engineering, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2017-10-08 Online:2018-11-25 Published:2018-11-25

摘要:

准周期运动是实际工程中较为广泛的一类振荡现象,也是从周期运动通往混沌的途径之一。利用增量谐波平衡法(incremental harmonic balance method, IHB),结合多时间尺度研究了非线性系统的准周期振动。在Duffing和van der Pol-Duffing两个算例方程中,由增量谐波平衡法得到了系统在多个频率不可公约的外激励作用下的准周期运动特性。同时,与数值法得到的结果进行对比,两者相吻合。算例说明了多时间尺度增量谐波平衡法能够解决非线性系统的准周期运动问题,为非线性振动领域的深入研究提供了一种有效的分析方法。

关键词: 非线性振动, 多时间尺度, IHB法, 准周期运动

Abstract:

Quasi-periodic motion is a kind of common phenomenon in practical engineering. It is also one of the ways from periodic motion to chaos. In this paper the incremental harmonic balance (IHB) method with multiple time scales is presented for the study of quasi-periodic motions of nonlinear systems. Two examples of Duffing and van der Pol-Duffing equations, quasi-periodic motions characteristics of the systems which subjected to the external multi-excitations are obtained. Moreover, the results obtained from the IHB method agree well with those from the numerical integration method using the fourth-order Runge-Kutta method. The numerical examples illustrate the IHB method with multiple time scales can be used to study quasi-period motions of nonlinear systems. It provides an effective method for the further study in nonlinear vibration field.

Key words: nonlinear vibration, multiple time scales, IHB method, quasi-periodic motion

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