北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (3): 500-507.doi: 10.13700/j.bh.1001-5965.2017.0196

• 论文 • 上一篇    下一篇

基于K-V阻尼模型的铁木辛柯梁振动响应分析

张夏阳, 祝明, 武哲   

  1. 北京航空航天大学航空科学与工程学院, 北京 100083
  • 收稿日期:2017-04-05 出版日期:2018-03-20 发布日期:2018-03-30
  • 通讯作者: 祝明 E-mail:zhumingbuaa@163.com
  • 作者简介:张夏阳男,博士研究生。主要研究方向:飞行器设计;祝明男,副教授,博士生导师。主要研究方向:飞行器设计;武哲男,教授,博士生导师。主要研究方向:飞行器设计。
  • 基金资助:
    国家重点研发计划(2016YFB1200100)

Response analysis of Timoshenko beam based on K-V damping model

ZHANG Xiayang, ZHU Ming, WU Zhe   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2017-04-05 Online:2018-03-20 Published:2018-03-30
  • Supported by:
    National Key R&D Program of China (2016YFB1200100)

摘要: 基于铁木辛柯梁理论,对两端固支梁在承受阶跃载荷和移动载荷下的响应进行了分析。借助K-V阻尼模型,研究了阻尼对系统动态性能的影响。为了进行理论求解,推导了比例阻尼的使用条件,继而运用实模态叠加法理论,最终导出了系统受载时响应的解析解。数值分析结果表明,该方法准确可靠,为其他数值算法,如拉普拉斯变换法,提供了横向对比的依据。有阻尼振动的分析表明系统在高阶模态具有过临界阻尼特性,在低阶模态为收敛振荡特性。阻尼对系统的响应有很大影响,尤其在大长细比时,甚至出现了振幅增大的情形。此外,在阶跃载荷的作用下,系统均呈现出了低频模态为主的响应特性。

关键词: 铁木辛柯梁, K-V阻尼, 实模态理论, 阶跃载荷, 移动载荷

Abstract: Based on Timoshenko beam theory, this paper has analyzed the dynamic properties when a clamped beam subjected to step load and moving load respectively. In addition, K-V damping model is considered to study the influence of damping on dynamic performance of the system. To acquire the theoretical solution, proportional damping utilization condition is derived, the real modal superposition method is applied, and eventually obtain the analytical responses when beam subjected to external loads. The numerical analysis results indicate that the solving process is accurate and reliable, providing a measurement reference to other methods, like Laplace transformation. The results of damping cases demonstrate that the high modes inherit over damping property, while in low modes present oscillation convergent characteristic. Sometimes, the damping can have significantly impact on the whole system, and for large slender ratios, the amplitude under moving load is even enlarged. Furthermore, the dynamic response subjected to step load is dominated by the low modes.

Key words: Timoshenko beam, K-V damping, real mode theory, step load, moving load

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