应变能中耦合项对旋转悬臂梁振动频率的影响

赵国威; 吴志刚

doi:10.6052/0459-1879-14-207

应变能中耦合项对旋转悬臂梁振动频率的影响

doi: 10.6052/0459-1879-14-207

赵国威¹,
吴志刚^1,2, ,

1.
大连理工大学, 工业装备结构分析国家重点实验室, 大连116024
2. 大连理工大学, 航空航天学院, 大连116024

基金项目: 国家自然科学基金资助项目(11072044)、高等学校博士学科点专项科研基金(20110041130001) 和教育部新世纪优秀人才支持计划(NCET-11-0054) 资助项目.

详细信息

通讯作者:
吴志刚,教授,主要研究方向:飞行器动力学与控制.E-mail:wuzhg@dlut.edu.cn

中图分类号: O327
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- 被引次数: 0
出版历程
- 收稿日期: 2014-09-18
- 修回日期: 2014-10-31
- 刊出日期: 2015-03-18

EFFECTS OF COUPLING TERMS IN STRAIN ENERGY ON FREQUENCY OF A ROTATING CANTILEVER BEAM

Zhao Guowei¹,
Wu Zhigang^{1,2
, ,}

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

Funds: The project was supported by the National Natural Science Foundation of China (11072044), the Research Fund for the Doctoral Program of Higher Education (20110041130001), and the Program for New Century Excellent Talents in University (NCET-11-0054).

摘要

摘要: 大范围运动悬臂梁的动力学建模问题对动力学特性分析及控制系统设计具有极其重要的作用. 当前研究多采用一次近似模型,其忽略了由轴向和横向变形所产生的应变能中的耦合项,然而这些项对动力学特性会产生影响. 通过讨论应变能的选取方式,计入了应变能中的耦合项;利用哈密尔顿原理建立结构的耦合振动模型;再借助瑞利—里兹法,以无大范围运动时的振型函数作为基本解组,得到了结构振动广义特征方程并求解. 通过数值算例对比分析,指出考虑应变能耦合项得到的频率与不考虑应变能耦合项得到的频率存在明显差别.
- 悬臂梁 /
- 刚柔耦合 /
- 浮动坐标系 /
- 瑞利—里兹法
Abstract: Dynamic modeling of a rotating cantilever beam is very important for dynamic characteristics analysis and controller design. In literature, the coupling terms between axial and transverse deformation in strain energy are ignored in first order approximate model. However, as shown by this paper, these terms have a significant impact on the dynamic characteristics. By discussing how to select the strain energy, this paper takes into account the coupling terms. Based on Hamilton's principle, the coupling vibration equations of the rotating cantilever beam are obtained. Using Rayleigh- Ritz method, the bending mode shapes of the beam without rotational motion are selected as basic functions to derive characteristic equation. A numerical example is presented to show that the evident difference of bending frequencies between the models with and without the coupling terms in strain energy.
- cantilever beam /
- rigid-flexible coupling /
- floating reference frame /
- Rayleigh—Ritz method

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参考文献(12)

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