弹性连接旋转柔性梁动力学分析

黄意新; 田浩; 赵阳

doi:10.6052/0459-1879-16-083

弹性连接旋转柔性梁动力学分析

doi: 10.6052/0459-1879-16-083

哈尔滨工业大学航天学院, 哈尔滨 150001

基金项目: 国家重点基础研究发展计划(973 计划) 资助项目(2013CB733004).

详细信息

通讯作者:
赵阳,教授,主要研究方向:复杂航天器系统动力学.E-mail:yangzhao@hit.edu.cn

中图分类号: O313;O326
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出版历程
- 收稿日期: 2016-03-30
- 修回日期: 2016-05-13
- 刊出日期: 2016-07-18

DYNAMIC ANALYSIS OF A ROTATING FLEXIBLE BEAM WITH ELASTIC BOUNDARY CONDITIONS

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

摘要

摘要: 采用Chebyshev 谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究. 基于Gauss-Lobatto 节点与Chebyshev 多项式方法对柔性梁变形场进行离散，通过投影矩阵法施加固定及弹性连接边界条件. 利用Chebyshev 谱方法获得了系统固有频率和模态振型数值解，通过与有限元方法及加权残余法的比较，验证了方法的有效性. 分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响. 研究发现：由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致，将出现频率转向与振型转换现象；随着弹性连接刚度、角速度比率及系统径长比的增大，低阶弯曲模态频率增大并超过高阶拉伸模态频率，随着梁的长细比的增大，低阶拉伸模态频率增大并超过高阶弯曲模态频率.
- 旋转柔性梁 /
- Chebyshev 谱方法 /
- 刚柔耦合 /
- 频率转向 /
- 动力学特性
Abstract: The dynamic characteristics of a flexible beam rotating in a plane with elastic boundary condition are investigated by the Chebyshev spectral method. The discrete equations of motion are obtained based on Gauss-Lobatto sampling and Chebyshev polynomials. Employing projection matrices, fixed and elastic boundary conditions are incorporated in the same form. Numerical solutions of natural frequencies and mode shapes are gained by Chebyshev spectral method and compared with the results of finite element and weighted residual methods to verify its correctness. The effects of various parameters, such as connection sti ness, angular velocity, hub radius ratio and slenderness ratio of the beam, on the vibration of the beam are analyzed. The results show that there is a veering phenomenon of natural frequencies loci accompanied by exchanges of the corresponding mode shape,due to the difference in sensitivity to system parameters between bending mode and strength mode. With the increasing of connection sti ness, angular velocity and hub radius ratio, a lower bending mode frequency will surpass its adjacent higher strength mode frequency. Similarly, strength mode frequencies will also surpass their adjacent higher bending mode frequencies with the increasing of slenderness ratio of the beam.
- rotating flexible beam /
- Chebyshev spectral method /
- rigid-flexible coupling /
- frequency veering /
- dynamic characteristics

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参考文献(41)

1 蔡国平, 洪嘉振. 旋转运动柔性梁的假设模态方法研究. 力学学报, 2005, 37(1): 48-56 (Cai Guoping, Hong Jiazhen. Assumed mode method of a rotating flexible beam. Acta Mechanica Sinica, 2005, 37(1): 48-56 (in Chinese))

2 赵婕, 于开平, 学忠. 末端带有刚体的旋转梁运动稳定性分析. 力学学报, 2013, 45(4): 606-613 (Zhao Jie, Yu Kaiping, Xue Zhong. The motion stability analysis of a rotating beam with a rigid body on its end. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(4): 606-613 (in Chinese))

3 赵迪, 尚新春. 含裂纹旋转叶片结构的振动特征分析. 武汉大学学报(工学版), 2011, 44(4): 487-491 (Zhao Di, Shang Xinchun. Analysis of vibration characteristic of rotating blade with cracks. Engineering Journal of Wuhan University, 2011, 44(4): 487-491 (in Chinese))

4 董兴建, 孟光, 蔡国平等. 旋转柔性梁的动力学建模及分析. 振动工程学报, 2006, 19(4): 488-493 (Dong Xingjian, Meng Guang, Cai Guoping, et al. Dynamic modeling and analysis of a rotating flexible beam. Journal of Vibration Engineering, 2006, 19(4): 488-493 (in Chinese))

5 Kane TR, Ryan R, Banerjee AK. Dynamics of a cantilever beam attached to a moving base. Journal of Guidance Control & Dynamics, 1987, 10(2): 139-151.

6 蔡国平, 洪嘉振. 中心刚体-柔性悬臂梁系统的动力特性研究. 航空学报, 2004, 25(3): 248-253 (Cai Guoping, Hong Jiazhen. Dynamic analysis of a flexible hub-beam system. Acta Aeronautica et Astronautica Sinica, 2004, 25(3): 248-253 (in Chinese))

7 刘锦阳, 李彬, 洪嘉振. 作大范围空间运动柔性梁的刚-柔耦合动力学. 力学学报, 2006, 38(2): 276-282 (Liu Jinyang, Li Bin, Hong Jiazhen. Rigid-flexible coupling dynamics of a flexible beam with three-dimensional large overall motion. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(2):276-282 (in Chinese))

8 杨辉, 洪嘉振, 余征跃. 动力刚化问题的实验研究. 力学学报, 2004, 36(1): 118-124 (Yang Hui, Hong Jiazhen, Yu Zhengyue. Experimental investigation on dynamic stiffening phenomenon. Acta Mechanica Sinica, 2004, 36(1): 118-124 (in Chinese))

9 和兴锁, 邓峰岩, 王睿. 具有大范围运动和非线性变形的空间柔性梁的精确动力学建模. 物理学报, 2010, 59(3):1428-1436 (He Xingsuo, Deng Fengyan, Wang Rui. Exact dynamic modeling of a spatial flexible beam with large overall motion and nonlinear deformation. Acta Physica Sinica, 2010, 59(3): 1428-1436 (in Chinese))

10 赵国威, 吴志刚. 应变能中耦合项对旋转悬臂梁振动频率的影响. 力学学报, 2015, 47(2): 362-366 (Zhao Guowei, Wu Zhigang. Effect of coupling terms in strain energy on frequency of a rotating cantilever beam. Chinese Journal of Theoretical and Applied Mechanics. 2015,47(2): 362-366 (in Chinese))

11 Li L, Zhu WD, Zhang DG, et al. A new dynamic model of a planar rotating hub-beam system based on a description using the slope angle and stretch strain of the beam. Journal of Sound & Vibration, 2015, 345: 214-232

12 陈思佳, 章定国, 洪嘉振. 大变形旋转柔性梁的一种高次刚柔耦合动力学模型. 力学学报, 2013, 45(2): 251-256 (Chen Sijia, Zhang Dingguo, Hong Jiazhen. A high-order rigid-flexible coupling model of a rotating flexible beam under larger deformation. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 251-256 (in Chinese))

13 Davide I, Lorenzo D. A fully consistent linearized model for vibration analysis of rotating beams in the framework of geometrically exact theory. Journal of Sound and Vibration, 2016,370: 351-371

14 李彬, 刘锦阳, 洪嘉振. 计及剪切变形的Timoshenko 梁的刚-柔耦合动力学. 计算力学学报, 2006, 23(4): 419-422 (Li Bin, Liu Jinyang, Hong Jiazhen. Coupling dynamics of Timoshenko beam with shear deformation. Chinese Journal of Computational Mechanics, 2006, 23(4): 419-422 (in Chinese))

15 李莉, 刘铸永, 洪嘉振. 中心刚体-柔性梁刚柔耦合动力学模型降阶研究. 动力学与控制学报, 2015, 13(1): 6-10 (Li Li, Liu Zhuyong, Hong Jiazhen. Model reduction of rigid-flexible coupling dynamics of hub-beam system. Journal of Dynamics and Control, 2015, 13(1): 6-10 (in Chinese))

16 章孝顺, 章定国, 陈思佳等. 基于绝对节点坐标法的大变形柔性梁几种动力学模型. 物理学报, 2016, 65(9): 0945001 (Zhang Xiaoshun, Zhang Dingguo, Chen Sijia, et al. Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation. Acta Physica Sinica, 2016, 65(9): 0945001 (in Chinese))

17 洪嘉振, 刘铸永. 刚柔耦合动力学的建模方法. 上海交通大学学报, 2008(11): 1922-1926 (Hong Jiazhen, Liu Zhuyong. Modeling methods of rigid-flexible coupling dynamics. Journal of Shanghai Jiaotong University, 2008(11): 1922-1926 (in Chinese))

18 刘又午, 阎绍泽, 张大钧. 计及动力刚化的柔体动力学. 中国机械工程, 1997(4): 81-84 (Liu Youwe, Yan Shaoze, Zhang Dajun. Dynamics of flexible bodies considering the dynamic stiffening term. China Mechanical Engineering, 1997(4): 81-84 (in Chinese))

19 阎绍泽, 季林红, 范晋伟等. 柔性机械系统动力学的变形耦合方法. 机械工程学报, 2001, 37(8): 1-4 (Yan Shaoze, Ji Linhong. Deformation-coupling modeling method for dynamics of flexible mechanical systems. Chinese Journal of Mechanical Engineering, 2001, 37(8): 1-4 (in Chinese))

20 范纪华, 章定国, 洪嘉振. 基于Bezier 插值方法的作大范围旋转运动锥形悬臂梁动力学研究. 动力学与控制学报, 2012, 10(4): 347-354 (Fan Jihua, Zhang Dingguo, Hong Jiazhen. Dynamic analysis of a rotating tapered cantilever beam based on Bezier curve interpolation. Journal of Dynamics and Control, 2012, 10(4): 347-354 (in Chinese))

21 范纪华, 章定国. 旋转柔性悬臂梁动力学的Bezier 插值离散方法研究. 物理学报, 2014, 63(15): 154501 (Fan Jihua, Zhang Dingguo. Bezier interpolation method for the dynamics of rotating flexible cantilever beam. Acta Physica Sinica, 2014, 63(15): 154501 (in Chinese))

22 范纪华, 章定国. 旋转悬臂梁动力学的B 样条插值方法. 机械工程学报, 2012, 48(23): 59-64 (Fan Jihua, Zhang Dingguo. B-spline interpolation method for the dynamics of rotating cantilever beam. Journal of Mechanical Engineering, 2012, 48(23): 59-64 (in Chinese))

23 杜超凡, 章定国, 洪嘉振. 径向基点插值法在旋转柔性梁动力学中的应用. 力学学报, 2015, 47(2): 279-288 (Du Chaofan, Zhang Dingguo, Hong Jiazhen. A meshfree method based on radial point interpolation method for the dynamic analysis of rotating flexible beams. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288 (in Chinese))

24 杜超凡, 章定国. 基于无网格点插值法的旋转悬臂梁的动力学分析. 物理学报, 2015, 64(3): 34501 (Du Chaofan, Zhang Dingguo. A meshfree method based on point interpolation for dynamic analysis of rotating cantilever beams. Acta Physica Sinica, 2015, 64(3): 34501 (in Chinese))

25 Cheng JL, Xu H, Yan AZ. Frequency analysis of a rotating cantilever beam using assumed mode method with coupling effect. Mechanics Based Design of Structures & Machines, 2006, 34(1): 25-47

26 朱由锋, 任勇生. 基于有限差分法的水平旋转梁自由振动解析. 振动与冲击, 2012, 31(14): 43-46 (Zhu Youfeng, Ren Yongsheng. Free vibration analysis of horizontal spinning beams by using finite difference method. Journal of Vibration and Shock, 2012, 31(14): 43-46 (in Chinese))

27 Kee YJ, Shin SJ. Structural dynamic modeling for rotating blades using three dimensional finite elements. Journal of Mechanical Science and Technology, 2015, 29(4): 1607-1618

28 Kim H, Hong HY, Chung J. Dynamic model for free vibration and response analysis of rotating beams. Journal of Sound & Vibration, 2013, 332(22): 5917-5928

29 蒋丽忠, 洪嘉振. 大范围运动对弹性梁振动频率及模态的影响. 振动与冲击, 1999, 18(2): 12-16 (Jiang Lizhong, Hong Jiazhen. The frequency and mode of elastic beams in large overall motion. Journal of Vibration and Shock, 1999, 18(2): 12-16 (in Chinese))

30 杨辉, 洪嘉振, 余征跃. 一类刚-柔耦合系统的模态特性与实验研究. 宇航学报, 2002, 23(2): 67-72 (Yang Hui, Hong Jiazhen, Yu Zhengyue. Vibration analysis and experiment investigation for a typical rigid-flexible coupling system. Journal of Astronautics, 2002, 23(2): 67-72 (in Chinese))

31 杨辉, 洪嘉振, 余征跃. 柔性多体系统动力学实验研究综述. 力学进展, 2004, 34(2): 171-181 (Yang Hui, Hong Jiazhen, Yu Zhengyue. Survey of experiments for dynamics of flexible multibody system. Advances in Mechanics, 2004, 34(2): 171-181 (in Chinese))

32 方建士, 黎亮, 章定国等. 基于刚柔耦合动力学的旋转悬臂梁的频率转向与振型转换特性. 机械工程学报, 2015, 51(17): 59-65 (Fang Jianshi, Li Liang, Zhang Dingguo, et al. Frequency veering and mode shape interaction properties of a rotating cantilever beam based on rigid-flexible coupling dynamics. Journal of Mechanical Engineering, 2015, 51(17): 59-65 (in Chinese))

33 Zhao Z, Liu C, Ma W. Characteristics of steady vibration in a rotating hub–beam system. Journal of Sound & Vibration, 2016, 363: 571-583

34 宋春明, 王明洋, 王德荣. 柔性动边界梁的弹塑性动力响应分析. 工程力学, 2008, 25(12): 42-47 (Song Chun-ming, Wang Mingyang, Wang Derong. Analysis of elastic-plastic dynamic responses of beams with flexible supports. Engineering Mechanics, 2008, 25(12): 42-47 (in Chinese))

35 Sarvestan V, Mirdamadi HR, Ghayour M, et al. Spectral finite element for vibration analysis of cracked viscoelastic Euler–Bernoulli beam subjected to moving load. Acta Mechanica, 2015, 226(12): 1-22

36 Cheng Y, Yu Z, Wu X, et al. Vibration analysis of a cracked rotating tapered beam using the p-version finite element method. Finite Elements in Analysis & Design, 2011, 47(7): 825-834

37 江凡, 薛冬新, 宋希庚. 裂纹悬臂梁的扭转弹簧模型及其实验验证. 振动、测试与诊断, 2004, 24(2): 143-145 (Jiang Fan, Xue Dongxin, Song Xigeng. Analysis and experiments of cracked cantilever beam using torsional spring model. Journal of Vibration, Measurement & Diagnosis, 2004, 24(2): 143-162 (in Chinese))

38 Yagci B, Filiz S, Romero LL, et al. A spectral-Tchebychev technique for solving linear and nonlinear beam equations. Journal of Sound & Vibration, 2007, 321(s1-2): 375-404

39 Romero L, Filiz S, Ozdoganlar OB. An analytical model for microendmill Dynamics. Journal of Control & Vibration, 2008, 14(8): 1125-1150

40 Huang CL, Lin WY, Hsiao KM. Free vibration analysis of rotating Euler beams at high angular velocity. Computers & Structures, 2010, 88(17): 991-1001

41 Chung J, Yoo HH. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound & Vibration, 2002, 249(1): 147-164

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