Journal of Shandong University(Engineering Science) ›› 2018, Vol. 48 ›› Issue (4): 78-87.doi: 10.6040/j.issn.1672-3961.0.2017.373

Previous Articles     Next Articles

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

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

CLC Number: 

  • 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.
[1] Xin LIU,Fengling YANG. Vibration characteristics of flexible-blade Rushton impeller [J]. Journal of Shandong University(Engineering Science), 2020, 50(5): 50-55.
[2] Guoren LÜ,Jiandong GE,Haitao XIAO. Treatment of coastal soft foundation with cement-soil mixing pile [J]. Journal of Shandong University(Engineering Science), 2020, 50(3): 73-81.
[3] Jie LIU,Zhechao WANG,Yupeng ZHANG,Huayang SUN. Flow characteristics of rough rock fractures under wide range of Reynolds numbers [J]. Journal of Shandong University(Engineering Science), 2019, 49(4): 70-77, 85.
[4] Yajuan XIE,Song YU,Bangxiang LI,Xiang XU,Weishen ZHU. Crack initiation theory and experimental verification of pre-existing plane cracks with seepage pressure [J]. Journal of Shandong University(Engineering Science), 2019, 49(4): 36-43.
[5] DONG Zhen, YANG Yonglu, XIONG Guodong, LAI Yanhua, LYU Mingxin. Preparation and optimization of compound bonded material used in reducing the contact thermal resistance [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 143-150.
[6] WAN Li, WANG Chunhe, WANG Qi, LI Shucai, SHAO Xing, JIANG Bei, SUN Huibin, QIN Qian. The control mechanism for super section tunnel on weak surrounding rock and its application [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(1): 59-67.
[7] . Experiment and numerical simulation for surface roughness of 2024 aluminum alloy treated by shot peening [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(1): 84-89.
[8] PENG Yuancheng, DONG Xu, LIANG Na, DENG Zhenquan. Model test of the Beipan River's new open-web continuous rigid frame bridge corner node [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(6): 113-119.
[9] ZHANG Luchen, LI Shuchen, LI Shucai, LIAO Qikai. Effect on the performance of shotcrete mixed with silica fume and fly ash [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(5): 102-109.
[10] MA Zongzheng, SHAO Fengxiang, WANG Xinli, YANG Anjie. Thermoelectric generator system based on engine exhaust gas [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(2): 122-127.
[11] LUO Yanhua, SHE Shijie, CAO Weiguo, PAN Feng. Effects of reaction conditions on the size distribution of iron phosphate [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2015, 45(1): 82-87.
[12] ZHANG Tao, HAN Jitian, YAN Suying, YU Zeting, ZHOU Ran. The analysis and testing of thermal performance on solar evacuated tube [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2014, 44(4): 76-83.
[13] LIAN Gen-kuan1, TIAN Mao-cheng2, LENG Xue-li2. Fouling properties of a vibration pipe under the condition of constant heat flux [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2012, 42(2): 97-101.
[14] CUI Nai-xin, ZHAO Fang-fang, LIANG Bing, GAI Di. Experiment on internal particle size distribution law of a waste dump [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2012, 42(2): 52-57.
[15] WANG Gang1, 2, JIANG Yu-jing2, LI Shucai3. Rapid feedback analysis method for underground caverns during constructing [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2011, 41(4): 133-136.
Full text



[1] WANG Su-yu,<\sup>,AI Xing<\sup>,ZHAO Jun<\sup>,LI Zuo-li<\sup>,LIU Zeng-wen<\sup> . Milling force prediction model for highspeed end milling 3Cr2Mo steel[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(1): 1 -5 .
[2] WANG Bo,WANG Ning-sheng . Automatic generation and combinatory optimization of disassembly sequence for mechanical-electric assembly[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 52 -57 .
[3] KONG Xiang-zhen,LIU Yan-jun,WANG Yong,ZHAO Xiu-hua . Compensation and simulation for the deadband of the pneumatic proportional valve[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(1): 99 -102 .
[4] QIN Tong, SUN Fengrong*, WANG Limei, WANG Qinghao, LI Xincai. 3D surface reconstruction using the shape based interpolation guided by maximal discs[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 1 -5 .
[5] LI Shijin, WANG Shengte, HUANG Leping. Change detection with remote sensing images based on forward-backward heterogenicity[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(3): 1 -9 .
[6] LI Fangjia, GAO Shangce, TANG Zheng*, Ishii Masahiro, Yamashita Kazuya. 3D similar pattern generation of snow crystals with cellular automata[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 102 -105 .
[7] KONG Wei-tao,ZHANG Qing-fan,ZHANG Cheng-hui . DSP based implementation of the space vector pulse width modulation[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2008, 38(3): 81 -84 .
[8] ZHU Xiang-cai,LUAN Yun-cai,XU Jian . An urban traffic evaluation system based on VB and FTA[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2007, 37(4): 89 -92 .
[9] YU Hai-bo,LI Yu,YU Tian,LEI Hong . Influence of the dimensions of W-band folded waveguide slow-wave system on its cold characteristics[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2008, 38(3): 90 -94 .
[10] LI Shan-ping,ZHAO Yu-xiao,QIAO Peng,FENG Zheng-zhi . Cultivation of aerobic granular sludge and the kinetics of substrate degradation and biomass growth[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2008, 38(3): 95 -98 .