Free vibration of rubber band slider system on air cushion track
HE Songlin1, HUANG Yan2
1.School of Mechanical and Electrical Engineering, Kunming University, Kunming 650214, China；
2.School of Physical Science and Technology, Kunming University, Kunming 650214, China
Abstract：Free vibration tests of rubber band slider system was conducted on air cushion track to measure the system’s vibration period and logarithmic decrement. The large difference between theoretical analysis and test results showed that the free vibration of rubber band slider system can’t be treated as viscous damping vibration of a harmonic oscillator. Then, a free vibration model of oscillator containing fractional derivative was proposed. The second order ordinary differential equation with fractional derivative term was solved using the numerical method and the average one. It was found that the theoretical analysis results of this model are consistent with the test ones to reveal it is feasible to describe mechanical properties of rubber band using elastic coefficient, viscoelasticity and viscoelastic coefficient.
何松林1,黄焱2. 气垫导轨上橡皮筋滑块系统自由振动研究[J]. 振动与冲击, 2021, 40(3): 279-283.
HE Songlin1, HUANG Yan2. Free vibration of rubber band slider system on air cushion track. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(3): 279-283.
[1]张启宵,贺占蜀,邵丽娜.橡胶材料力学性能试验方法研究[J].汽车电器,2019(05):62-64.
ZHANG Qi-xiao， HE Zhan-shu， SHAO Li-na. Study on Test Method of Mechanical Properties of Rubber Material [J]. Auto Electric Parts. 2019(05):62-64.
[2]王强,齐晓杰,王云龙,杨兆,王国田,吕德刚.车辆轮胎冰雪路面摩擦特性与橡胶材料物理力学性能的相关性研究[J].武汉理工大学学报(交通科学与工程版),2018,42(04):574-578.
Wang Qiang Qi Xiaojie Wang Yunlong etal.Relevance Study Between Friction characteristics of Vehicle Tires on Ice-snow Roads and Physical
[3]徐超. 粘弹性阻尼器微振减振机理及试验研究[D].东南大学,2018.
Xu Chao. Micro-Vibration Damping Mechanism and Experiment study pm the viscoelastic Damper.[D]. Southeast University, 2018.
[4]初红艳,许康健,黄为,蔡力钢.橡胶材料生热及其对力学性能的影响[J].北京工业大学学报,2017,43(11):1635-1640.
CHU Hongyang, XU Kangjiang, HUANG Wei etl. Heat-Generating of Rubber and Its Influence on Mechanical Properties [J]. Journal of Beijing University of Technology. 2017,43(11):1635-1640.
[5]赵国营. 天然橡胶材料基础拉伸实验研究[D].青岛科技大学,2016.
Zhao GuoYin. STUDY ON TENSILE TEST OF NATURAL RUBBER MATERIAL [D]. Qingdao University of science and technology, 2016.
[6]方庆红. 纤维增强橡胶在不同温度条件下的力学性能研究[D].东北大学,2006.
Fang Qing Hong. Study on Mechanical Characteristics of Fiber-Reinforced Rubber at Different Temperatures. [D]. Northeastern University, 2006.
[7]刘延柱，陈立群. 非线性振动[M].北京：高等教育出版社，2001.
LIU Yanzhu, CHEN Liqun. Nonlinear vibrations [M]. Beijing: Higher Education Press,.2001.
[8] Heymans N. Fractional calculus description of non-linear viscoelastic behavior of polymers. Nonlinear Dyn, 2004, 38(1-4): 221—231
[9]陈文，孙洪广，李西成等. 力学与工程问题的分数阶导数建模[M].北京：科学出版社，2010.
CHEN Wen, SHAN Hongguang, LI Xicheng,et al.Fractional derivative modeling of mechanical and engineering problems[M].Beijing: Science Press, 2010.
[10]吴强，黄建华.分数阶微积分[M].北京：清华大学出版社，2016.
WUQiang, HUANGJian-hua.Fractional calculus[M]. Beijing: Tsinghua university press, 2016.
[11]杨建华.分数阶系统的分岔与共振[M].北京：科学出版社，2017.
Yang Jianhua. Bifurcation and Resonance in Fractional-order systems.[M].Beijing: Science Press, 2017.
[12]申永军,杨绍普,邢海军.含分数阶微分的线性单自由度振子的动力学分析[J].物理学报,2012,61(11):158-163.
SHEN Yongjun, YANG Shaopu, XING Haijun. Dynamical analysis of linear single degree of freedom oscillator with fractional order derivative. [J].Acta phys. Sin.2012,61(11):158-163.
