您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（工学版）》

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

PDF (PC)

488

PDF (Mobile)

8

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.
[1] 刘欣,杨锋苓. 柔性Rushton桨的振动特性[J]. 山东大学学报 (工学版), 2020, 50(5): 50-55.
[2] 徐振,李德明,王彬,詹谷益,张世杰. 硬岩隧道纯钢纤维混凝土管片应用[J]. 山东大学学报 (工学版), 2020, 50(5): 44-49.
[3] 吕国仁,葛建东,肖海涛. 水泥土搅拌桩沿海软基处理[J]. 山东大学学报 (工学版), 2020, 50(3): 73-81.
[4] 孙连勇,时刚,崔新壮,周明祥,王永军,纪方,闫小东. 饱和地基中单排孔近场隔振的现场试验与数值分析[J]. 山东大学学报 (工学版), 2020, 50(3): 88-97.
[5] 谢雅娟,虞松,李邦祥,徐翔,朱维申. 含裂隙水预制平面裂隙的启裂理论与试验验证[J]. 山东大学学报 (工学版), 2019, 49(4): 36-43.
[6] 刘杰,王者超,张宇鹏,孙华阳. 岩石粗糙裂隙大范围雷诺数条件下渗流特性[J]. 山东大学学报 (工学版), 2019, 49(4): 70-77, 85.
[7] 江健宏,杨振宇,陈奇,孟庆宇,张宏博. 预应力对拉式挡土墙受力特征模型试验研究[J]. 山东大学学报 (工学版), 2019, 49(4): 61-69.
[8] 董震,杨永鲁,熊国栋,赖艳华,吕明新. 用于降低接触热阻的复合黏结材料的制备优化[J]. 山东大学学报(工学版), 2017, 47(3): 143-150.
[9] 陈方明,胡泉光,宁光忠. 三轴应力条件下粉砂质泥岩分级松弛特性[J]. 山东大学学报(工学版), 2017, 47(3): 125-129.
[10] 陈玉成,孙强,苗强,白书战,李国祥. 混合动力汽车动力总成试验台设计与开发[J]. 山东大学学报(工学版), 2017, 47(1): 119-124.
[11] 万利,王春河,王琦,李术才,邵行,江贝,孙会彬,秦乾. 超大断面隧道软弱围岩控制机制及应用[J]. 山东大学学报(工学版), 2017, 47(1): 59-67.
[12] 郑林彬,王建明,何讯超. 2024铝合金喷丸粗糙度试验与数值模拟[J]. 山东大学学报(工学版), 2017, 47(1): 84-89.
[13] 彭元诚,董旭,梁娜,邓振全. 北盘江新型空腹式连续刚构桥角隅节点模型试验研究[J]. 山东大学学报(工学版), 2016, 46(6): 113-119.
[14] 张露晨,李树忱,李术才,廖麒凯. 硅灰粉煤灰对喷射混凝土性能影响[J]. 山东大学学报(工学版), 2016, 46(5): 102-109.
[15] 雷正保,廖卓,刘助春. 交叉缠绕式柔性护栏端部锚固优化设计[J]. 山东大学学报(工学版), 2016, 46(3): 93-98.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 王素玉,艾兴,赵军,李作丽,刘增文 . 高速立铣3Cr2Mo模具钢切削力建模及预测[J]. 山东大学学报(工学版), 2006, 36(1): 1 -5 .
[2] 王波,王宁生 . 机电装配体拆卸序列的自动生成及组合优化[J]. 山东大学学报(工学版), 2006, 36(2): 52 -57 .
[3] 孔祥臻,刘延俊,王勇,赵秀华 . 气动比例阀的死区补偿与仿真[J]. 山东大学学报(工学版), 2006, 36(1): 99 -102 .
[4] 秦通,孙丰荣*,王丽梅,王庆浩,李新彩. 基于极大圆盘引导的形状插值实现三维表面重建[J]. 山东大学学报(工学版), 2010, 40(3): 1 -5 .
[5] 李士进,王声特,黄乐平. 基于正反向异质性的遥感图像变化检测[J]. 山东大学学报(工学版), 2018, 48(3): 1 -9 .
[6] 李芳佳, 高尚策, 唐政, 石井雅博, 山下和也. 基于元胞自动化模型的三维雪花晶体近似模式的产生（英文）[J]. 山东大学学报(工学版), 2009, 39(1): 102 -105 .
[7] 孔维涛,张庆范,张承慧 . 基于DSP的空间矢量脉宽调制(SVPWM)的实现[J]. 山东大学学报(工学版), 2008, 38(3): 81 -84 .
[8] 朱向彩,栾云才,徐健 . 基于VB及FTA的城市交通评价系统[J]. 山东大学学报(工学版), 2007, 37(4): 89 -92 .
[9] 于海波,李宇,余恬,雷虹 . W波段折叠波导慢波系统的尺寸对其冷特性的影响[J]. 山东大学学报(工学版), 2008, 38(3): 90 -94 .
[10] 李善评,赵玉晓,乔鹏,冯正志 . 好氧颗粒污泥的培养及基质降解和污泥生长动力学分析[J]. 山东大学学报(工学版), 2008, 38(3): 95 -98 .
版权所有 © 2018 《山东大学学报(工学版)》编辑部　
地址: 济南市山大南路27号（250100）　 电话: 0531-88366735　 E-mail: xbgxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发