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山东大学学报 (工学版) ›› 2018, Vol. 48 ›› Issue (4): 78-87.doi: 10.6040/j.issn.1672-3961.0.2017.373

• 机器学习与数据挖掘 • 上一篇    下一篇

变质量弹性梁结构动力学特性

马驰骋1,2,郭宗和1,刘灿昌1,代祥俊1,张希农2,毛伯永2   

  1. 1. 山东理工大学交通与车辆工程学院, 山东 淄博 255000;2. 西安交通大学机械结构强度与振动国家重点试验室, 陕西 西安 710049
  • 收稿日期:2017-07-26 出版日期:2018-08-20 发布日期:2017-07-26
  • 作者简介:马驰骋(1989— ),男,山东潍坊人,讲师,博士,主要研究方向为结构动力学响应分析及振动控制.E-mail:machch@sdut.edu.cn
  • 基金资助:
    机械结构强度与振动国家重点实验室开放基金资助项目(SV2016-KF-07);山东省自然科学基金资助项目(ZR2016AL06,2016ZRB0179SF)

Dynamics charactersitics of flexible beams undergoing time varying mass

MA Chicheng1,2, GUO Zonghe1, LIU Canchang1, DAI Xiangjun1, ZHANG Xinong2, MAO Boyong2   

  1. 1. College of Transportation and Vehicles Engineering, Shandong University of Technology, Zibo 255000, Shandong, China;
    2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
  • Received:2017-07-26 Online:2018-08-20 Published:2017-07-26

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摘要： 以变质量弹性梁结构为力学模型,利用模态叠加法推导系统的运动方程,分析质量变化引起的非结构阻尼对系统振动的影响,使用自适应Newmark法求解系统的振动响应。设计变质量-弹性梁结构动力学测试试验,通过控制液体的流入流出实现系统质量的变化。采用时频分析技术处理时变系统的非平稳响应信号,在时频域上更全面得到了系统的振动特性。数值仿真和试验结果一致,说明建模以及试验设计的有效性。研究表明:系统质量减小会引起一个非结构负阻尼,对系统的振动影响非常显著,在机械臂等高精度结构设计时,不能忽略该非结构阻尼对系统振动特性的影响。

关键词: 变质量系统, 时变结构, 自适应Newmark法, 时频特性, 试验

Abstract: In terms of an elastic beam with a time varying mass, the oscillation equations were derived using mode superposition method, and the influences of the nonstructural damping induced by the changing mass were investigated. The differential equations were solved by self-adaptive Newmark method, then a relative confirmatory experiment was designed, while the change of the mass was realized by controlling the flow of water. The vibration signals were processed using time-frequency analysis toolkit, which showed more features of the time varying mass system in the time-frequency domain. The comparison of experimental results and numerical results demonstrated the feasibility of the proposed approach and the experimental test. The study showed that the nonstructural negative damping induced by the decreasing mass affected the motions significantly, which could not be neglected in the dynamic design of high precision structures as large-scale flexible robotic manipulators.

Key words: variable mass system, time varying structure, self-adaptive Newmark method, time frequency analysis, experiment

中图分类号: 

  • O329
[1] 杨来伍,梅凤翔.变质量系统动力学[M].北京:北京理工大学出版社,1989.
[2] 孙焕纯,宋亚新,张典仁.变质量变阻尼变刚度结构系统的动力响应[J].计算结构力学及其应用,1996,13(2):127-137. SUN Huanchun, SONG Yaxin, ZHANG Dianya. A method for analyzing the dynamic response of a structural system with variable mass damping and stiffness[J]. Computational Structural Mechanics and Applications, 1996, 13(2): 127-137.
[3] 陈占清,缪协兴,荆武兴.变质量挠性体动力学普遍方程(1)[J].湘潭大学自然科学学报,2001,23(4):56-59. CHEN Zhanqing, MIAO Xiexing, JING Wuxing. Universal dynamic equations for flexiable body with variable mass(I)[J]. Natural Science Journal of Xiangtan University, 2001, 23(4): 56-59.
[4] 缪协兴,陈占清,荆武兴.变质量挠性体动力学普遍方程(二)[J].哈尔滨工业大学学报,2001,33(6):736-739. MIAO Xiexing, CHEN Zhanqing, JING Wuxing. Universal dynamic equations for flexiable body with variable mass(II)[J]. Journal of Harbin Engineering University, 2001, 33(6): 736-739.
[5] 张耀良,朱卫兵.变质量非完整系统Hamilton正则方程的积分因子和守恒定理[J].哈尔滨工程大学学报,2002, 23(4):118-121. ZHANG Yaoliang, ZHU Weibing. Integrating factors and conservation theorems for Hamilton's canonicals equations of motion of variable mass nonholonomic nonconservative dynamical systems[J]. Journal of Harbin Engineering University, 2002, 23(4):118-121.
[6] 朱岩,王树林.一类变质量振动系统的近似求解[J].振动与冲击,2008,27(11):160-162,167,206. ZHU Yan, WANG Shulin. Analytical solution for vibration system with time varying mass[J]. Journal of vibration and shock, 2008, 27(11): 160-162,167,206.
[7] KALYONCU M, BOTSALI F M. Vibration analysis of an elastic robot manipulator with prismatic joint and a time-varying end mass[J]. Arabian Journal for Science and Engineering, 2004, 29(1): 27-38.
[8] NHLEKO S. Free vibration states of an oscillator with a linear time-varying mass[J]. Journal of Vibration and Acoustics, 2009, 131(5): 051011-1-8.
[9] MACIEJEWSKI I, MEYER L, KRZYZYNSKI T. The vibration damping effectiveness of an active seat suspension system and its robustness to varying mass loading[J]. Journal of Sound and Vibration, 2010, 329(19): 3898-3914.
[10] CVETICANIN L. Van der Pol oscillator with time variable parameters[J]. Acta Mechanica, 2013, 224(5): 945.
[11] CVETICANIN L. Dynamics of bodies with time-variable mass[M]. Cham(ZG), Switzerland:Springer International Publishing, 2016.
[12] RICHARDS J A. Analysis of periodically time-varying systems[M]. Springer-Verlag Berlin Heidelberg:Springer Science & Business Media, 2012.
[13] VAN HORSSEN W T, PISCHANSKYY O V, DUBBELDAM J L A. On the forced vibrations of an oscillator with a periodically time-varying mass[J]. Journal of Sound and Vibration, 2010, 329(6): 721-732.
[14] PISCHANSKYY O V, VAN HORSSEN W T. On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass[J]. Journal of Sound and Vibration, 2012, 331(8): 1887-1897.
[15] ABRAMIAN A K, VAN HORSSEN W T, VAKULENKO S A. Nonlinear vibrations of a beam with time-varying rigidity and mass[J]. Nonlinear Dynamics, 2013, 71(1-2): 291-312.
[16] 王宇楠,邢誉峰.变质量梁的自适应Newmark法[J]. 北京航空航天大学学报, 2014, 40(6):829-833. WANG Yunan, XING Yufeng. Self-adaptive Newmark method of variable-mass beam dynamic system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(6): 829-833.
[17] ZHAO Rui, YU Kaiping. Hamilton's law of variable mass system and time finite element formulations for time-varying structures based on the law[J]. International Journal for Numerical Methods in Engineering, 2014, 99(10): 711-736.
[18] MAZENC F, MALISOFF M, NICULESCU S I. Reduction model approach for linear time-varying systems with delays[J]. IEEE Transactions on Automatic Control, 2014, 59(8): 2068-2082.
[19] 杜妍辰,高雷,周燕瑜,等.变质量振动系统的求解与分析[J].上海理工大学学报,2015,37(5):462-466. DU Yanchen, GAO Lei, ZHOU Yanyu, et al. Solution and analysis of vibration system with variable mass[J]. Journal of University of Shanghai for Science and Technology. 2015, 37(5): 462-466.
[20] 于开平.变质量航天器结构动响应分析[M]. 西安:中国力学大会,2013:119-119.
[21] FLORES J, SOLOVEY G, GILL S. Variable mass oscillator[J]. American Journal of Physics, 2003, 71(7): 721-725.
[22] 舒俊成.变质量SD振子动力学分析与试验研究[D].哈尔滨:哈尔滨工业大学,2016. SHU Juncheng. Dynamical analysis and experiment of variable mass SD oscillator[D]. Harbin: Harbin Institute of Technology, 2016.
[23] BARTKOWIAK T, GRABSKI J K, KOŁODZIEJ J A. Numerical and experimental investigations of the dynamics of a variable mass pendulum[J]. Proceedings of the Institution of Mechanical Engineers:Part C: Journal of Mechanical Engineering Science, 2016, 230(12): 2124-2132.
[24] 科恩L.时-频分析:理论与应用[M].白居宪,译.西安:西安交通大学出版社,1998.
[25] 李小彭,姚红良,任朝晖,等.时频分析在质量慢变碰摩转子系统中的应用[J].机械制造,2005,43(10):20-22. LI Xiaopeng, YAO Hongliang, REN Chaohui, et al. Application of time frequency analysis for a slow-varying rotor system with rubbing fault[J]. Machinery, 2005, 43(10): 20-22.
[26] 马驰骋,张希农,柳征勇,等.变质量贮箱类流固耦合系统的振动响应及时频特性分析[J].振动与冲击,2014,33(21):166-171. MA Chicheng, ZHANG Xinong, LIU Zhengyong, et al. Dynamic responses and time-frequency feature analysis for a fluid-structure coupling system with avariable mass tank[J]. Journal of Vibration and Shock, 2014, 33(21): 166-17.
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