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力学与实践 ›› 2017, Vol. 39 ›› Issue (2): 172-174.doi: 10.6052/1000-0879-16-306

• 应用研究 • 上一篇    下一篇

一类二自由度系统振动的黄金分割率

朱贝贝1, 孙兰宁2, 赵忠虎1,3   

  1. 1. 兰州大学土木工程与力学学院, 兰州 730000;
    2. 中航勘察设计研究院有限公司, 北京 100098;
    3. 亚利桑那大学工程学院, 美国图森 AZ85721
  • 收稿日期:2016-11-02 修回日期:2016-12-14 出版日期:2017-04-15 发布日期:2017-04-19
  • 通讯作者: 朱贝贝,硕士,主要从事岩石力学与结构力学等方面的研究工作.E-mail:zhubei1991@yeah.net;赵忠虎,博士,副教授,主要从事岩石力学与结构力学等方面的研究工作.E-mail:zhaozhh@lzu.edu.cn E-mail:zhubei1991@yeah.net;zhaozhh@lzu.edu.cn
  • 基金资助:

    中央高校基本科研业务费专项资金(LZUJBKY-2016-110)和国家留学基金(201606185039)项目资助.

THE GOLDEN SECTION RATIO OF A CLASS OF VIBRATION SYSTEM OF TWO DEGREES OF FREEDOM

ZHU Beibei1, SUN Lanning2, ZHAO Zhonghu1,3   

  1. 1. School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China;
    2. AVIC Institute of Geotechnical Engineering Co., Ltd., Beijing 100098, China;
    3. College of Engineering, University of Arizona, Tucson, AZ 85721, USA
  • Received:2016-11-02 Revised:2016-12-14 Online:2017-04-15 Published:2017-04-19

摘要:

作为数学史上一个重要的比例关系,黄金分割理论已在美学、建筑学甚至工程学中发挥了一定的作用. 为了研究一类二自由度系统振动的黄金分割效应,首先介绍了黄金分割的基本理论,然后分别分析了该类二自由度体系的自由振动特征,以及简谐载荷作用下受迫振动的共振机制. 结果表明,结构圆频率与层刚度和质量之比、两结构质点振幅之比都符合黄金分割率,结构在振动中具有和谐之美.

关键词:

结构动力学|黄金分割|二自由度|自由振动|受迫振动

Abstract:

As an important relation of the proportion in the history of mathematics, the golden section relation plays an important role in aesthetics, architecture, and even engineering. This paper studies the gold segmentation effect for a class of vibration system of two degrees of freedom. The free vibration characteristics, and the resonance mechanism of the forced vibration under harmonic loading are analyzed. It is shown that, the ratios of the structure circular frequency to the layer stiffness and mass, and that of the structural amplitudes at two points conform well with the golden section ratio. The structure shows the beauty of harmony in vibration.

Key words:

structural dynamics|golden section|two degrees of freedom|free vibration|forced vibration

中图分类号: 

  • O325