Dynamic model for the nonlinear hysteresis of metal rubber based on the fractional-order derivative

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (14) : 233-241.

CHANG Yujian1， TIAN Wowo1， CHEN Enli2， SHEN Yongjun2， XING Wuce2

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Abstract

The stress-strain characteristic of metal rubber components appears as a nonlinear hysteretic curve.Most of the existing dynamic models for metal rubber are described by multi-parameter and piecewise functions, increasing the complexity of the system.Making use of the fractional-order derivative which has been applied to the description of the memory characteristics of various materials and processes, a viscoelastic constitutive model for metal rubber with the fractional-order derivative was established through analyzing the composition of the elastic restoring force and the damping force of metal rubber.On this basis, a nonlinear dynamic system model for metal rubber was founded.The restoring force of a typical metal rubber vibration isolation system was analyzed through sinusoidal displacement loading experiments under various excitation amplitudes and frequencies.All the parameters of the model were identified by the curve fitting of the experimental data with the genetic algorithm.The functional relationships between the parameters of the system model and the amplitude and frequency were derived by a series of analysis.The results show that the nonlinear dynamic system model for metal rubber with a fractional order differential item can be described as continuous mathematical expressions，which can reflect the full metal rubber nonlinear system dynamic performance.The model involves less parameters and has a simpler structure compared to other existing metal rubber dynamics system models.The results provide a new way to the study of metal rubber dynamics systems.

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metal rubber / fractional-order derivative / nonlinear dynamics / hysteretic characteristic

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CHANG Yujian1， TIAN Wowo1， CHEN Enli2， SHEN Yongjun2， XING Wuce2. Dynamic model for the nonlinear hysteresis of metal rubber based on the fractional-order derivative[J]. Journal of Vibration and Shock, 2020, 39(14): 233-241

References

[1] DA Xu, BAO Hong-han, WAN Heng-he, et al. Research on compressive mechanical properties of metal rubber and its constitutive relation model [J]. Journal of Vibroengineering, 2018, 20(1): 332-344.
[2] ZHOU Yan-guo, QU Wen-zhong, Xiao Li, et al. A practical mathematical model for nonlinear hysteresis of metal rubber isolator [J]. Applied Mechanics and Materials, 2012, 105-107: 20-23.
[3] CAO Feng-li, BAI Hong-bai, LI Dong-wei, et al. A constitutive model of metal rubber for hysteresis characteristics based on a meso-mechanical method [J]. Rare Metal Materials and Engineering, 2016, 45(1): 1-6.
[4] 卢成壮, 李静媛, 周邦阳等. 金属橡胶的刚度特性和阻尼试验研究[J]. 振动与冲击, 2017, 36(8):203-208.
LU Cheng-zhuang, LI Jing-yuan, ZHOU Bang-yang, et al. An experimental study on stiffness characteristics and damping of metal rubber [J]. Journal of Vibration and Shock, 2017, 36(8): 203-208.
[5] 曹凤利, 白鸿柏, 李冬伟等. 金属橡胶非成形方向迟滞特性力学模型研究[J]. 机械工程学报, 2015, 51(2):84-89.
CAO Feng-li, BAI Hong-bai, LI Dong-wei, et al. Research on mechanical model of metal rubber for hysteresis characteristic in the non-forming direction [J]. Journal of Mechanical Engineering, 2015, 51(2): 84-89.
[6] 王凤鸣, 唐伟, 毛志俊等. 基于位移加载控制的金属橡胶弹性元件试验建模研究[J]. 新技术新工艺, 2010, 7:83-86.
WANG Feng-ming, TANG Wei, MAO Zhi-jun, et al. Test modeling research on mental rubber elastic element based on displacement control [J]. New Technology & New Process, 2010, 7: 83-86.
[7] 曹凤利, 白鸿柏, 任国全等. 金属橡胶恢复力的迟滞模型研究[J]. 中国机械工程, 2014, 25(3):311-314.
CAO Feng-li, BAI Hong-bai, REN Guo-quan, et al. Research on hysteresis model of restoring force of metal rubber [J]. China Mechanical Engineering, 2014, 25(3): 311-314.
[8] 李玉龙, 白鸿柏, 何忠波等. 金属橡胶非线性隔振器试验研究与参数分析[J]. 噪声与振动控制, 2015, 35(2):194-200.
LI Yu-long, BAI Hong-bai, HE Zhong-bo, et al. Experimental study and parameter analysis of nonlinear metal-rubber isolators [J]. Noise and Vibration Control, 2015, 35(2): 194-200.
[9] 李玉龙, 白鸿柏, 何忠波等. 变激励条件下金属橡胶非线性减振器试验研究[J], 北京理工大学学报, 2015, 35(3):221-225.
LI Yu-long, BAI Hong-bai, HE Zhong-bo, et al. Experimental research on nonlinear metal rubber isolator under different incentives [J]. Journal of Beijing University of Technology, 2015, 35(3): 221-225.
[10] 杨坤鹏, 樊文欣, 曹存存等. 金属橡胶材料的动态力学建模及参数辨识[J]. 机械科学与技术, 2017, 36(12):1830-1833.
YANG Kun-peng, FAN Wen-xin, CAO Cun-cun, et al. Dynamic mechanical modeling and parameter identification of metal rubber materials [J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(12): 1830-1833.
[11] 朱彬, 马艳红, 张大义等. 金属橡胶迟滞特性本构模型研究[J]. 物理学报, 2012, 61(7):474-481.
ZHU Bin, MA Yan-hong, ZHANG Da-yi, et al. Study on constitutive model of metal rubber hysteresis [J]. Acta Physica Sinica, 2012, 61(7): 474-481.
[12] 闫辉, 姜洪源, 刘文剑等. 具有迟滞非线性的金属橡胶隔振器参数识别研究[J]. 物理学报, 2009, 58(8):5238-5243.
YAN Hui, JIANG Hong-yuan, LIU Wen-jian, et al. Identification of parameters for metal rubber isolator with hysteretic nonlinearity characteristics [J]. Acta Physica Sinica, 2009, 58(8): 5238-5243.
[13] 邹广平, 张冰, 唱忠良等. 弹簧-金属丝网橡胶组合减振器迟滞力学模型及实验研究[J]. 力学学报, 2018, 50(5):1125-1134.
ZOU Guang-ping, ZHANG Bing, CHANG Zhong-liang, et al. Hysteresis mechanical model and experimental study of spring metal-net rubber combination damper [J]. Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1125-1134.
[14] 姜洪源, 敖宏瑞, 李瑰贤等. 金属橡胶隔振器动力学模型与分析[J]. 湖南科技大学学报：自然科学版, 2004, 19(3):23-27 .
JIANG Hong-yuan, AO Hong-rui, LI Gui-xian, et al. Modeling and analysisof dynamic characteristics of metal rubber isolator [J]. Journal of Hunan University of Science & Technology：Natural Science Edition, 2004, 19(3): 23-27.
[15] 李韶华, 杨绍普. 滞后非线性模型的研究进展[J]. 动力学与控制学报, 2006, 4(1):8-15.
LI Shao-hua, YANG Shao-pu. Advances in research of latent nonlinear models [J], Journal of Dynamics and Control, 2006, 4(1): 8-15.
[16] 白鸿柏, 郑坚, 张培林等. 2自由度滞迟振动系统简谐激励响应的等效线性化计算方法研究[J]. 机械工程学报, 2000, 36(11):90-93.
BAI Hong-bai, ZHENG Jian, ZHANG Pei-lin, et al. Equivalent linearization approximate method of response computation of a two degree of freedom hysteretic vibration system under sinusoidal excitation [J]. Journal of Mechanical Engineering, 2000, 36(11):90-93.
[17] 白鸿柏, 黄协清. 干摩擦振动系统响应计算方法研究[J]. 振动工程学报, 1998, 11(4):473-475.
BAI Hong-bai, HUANG Xie-qing. Study on response computation of dry friction damped vibration system [J]. Journal of Vibration Engineering, 1998, 11(4): 473-475.
[18] 李冬伟, 白鸿柏, 杨建春等. 金属橡胶动力学建模及参数识别[J]. 振动与冲击, 2005, 24(6):57-60.
LI Dong-wei, BAI Hong-bai, YANG Jian-chun, et al. Dynamic modeling and parameter recognition of metal rubber [J]. Journal of Vibration and Shock, 2005, 24(6): 57-60.
[19] 周艳国, 屈文忠. 金属橡胶非线性动力学特性建模方法研究[J]. 噪声与振动控制, 2013, 33(1):31-36.
ZHOU Yan-guo, QU Wen-zhong. Several practical approaches for nonlinear dynamic modeling of metal rubber [J]. Noise and vibration control, 2013, 33(1): 31-36.
[20] 王东志. 金属橡胶阻尼器滞回性能及其动态模型研究[D]. 黑龙江: 哈尔滨工业大学, 2014
WNAG Dong-zhi. Metal rubber damper hysteresis and dynamic model research [D]. Heilongjiang: Harbin Polytechnic Institute, 2014.
[21] YANG Shao-pu, LI Shao-hua, Gordaninejad F, et al. A hysteresis model for magneto-rheological damper [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2005, 6(2): 139-144.
[22] 王亚杰, 赵亚哥白, 任小龙等. 金属橡胶的本构关系研究[J]. 山西建筑, 2019, 45(4):29-31.
WANG Ya-jie, ZHAO Ya-ge-bai, Ren Xiao-long, et al. Study on the constitutive relationship of metal rubber [J]. Shanxi Architecture, 2019, 45(4): 29-31.
[23] 肖坤, 白鸿柏, 薛新等. 高温管路包覆金属橡胶耗能特性及参数识别[J]. 兵器材料科学与工程, 2019, 42(1):11-17.
XIAO Kun, BAI Hong-bai, XUE Xin, et al. Energy dissipation characteristics and parameter identification of metal rubber coated pipe in high temperature environment [J]. Weapons Materials Science and Engineering, 2019, 42(1): 11-17.
[24] 白鸿柏, 路纯红, 曹凤利等. 金属橡胶材料及工程应用[M]. 北京: 科学出版社, 2014
BAI Hong-bai, LU Chun-hong, CAO Feng-li, et al. Metal rubber material and its engineering application [M], Beijing: Science Press. 2014.
[25] 赵国伟, 李德勇, 陈勇. 金属橡胶隔振系统动刚度及减振效能分析[J]. 振动与冲击, 2014, 33(22):193-197.
ZHAO Guo-wei, LI De-yong, CHEN Yong. Dynamic stiffness and vibration reduction efficiency of metal rubber [J]. Journal of vibration and shock, 2014, 33(22): 193-197 .
[26] 李冬伟, 毛志俊, 谭人仁. 一种金属橡胶元件建模方法研究[J]. 军械工程学院学报, 2005, 17(2):64-66.
LI Dong-wei, MAO Zhi-jun, TAN Ren-ren, Research on a new method for modeling of metal rubber [J]. Journal of Ordnance Engineering College, 2005, 33(2): 64-66.
[27] 孙海忠, 张卫. 分数算子描述的粘弹性材料的本构关系研究[J]. 材料科学与工程学报, 2006, 24(6):926-930.
SUN Hai-zhong, ZHANG Wei. Study on constitutive relation of viscoelastic material described by fractional operator [J]. Journal of Materials Science and Engineering, 2006, (6): 926-930.
[28] 李宇明, 彭威, 白鸿柏等. 金属橡胶材料宏观和细观力学模型[J]. 机械工程学报, 2005, 41(9):38-41.
LI Yu-ming, PENG wei, BAI Hong-bai, et al. Mechanical modol of metal rubber material in macro and micro level [J]. Chinese Journal of Mechanical Engineering, 2005, 41(9): 38-41.
[29] CAO Feng-li, BAI Hong-bai, HE Zhong-bo, et al. A hysteresis restoring force model of disc-shaped metal rubber isolation component [J]. Applied Mechanics and Materials, 2013, 271-272: 186-189.
[30] 白鸿柏, 张培林, 郑坚等. 迟滞振动系统及其工程应用[M]. 北京: 科学出版社, 2002.
BAI Hong bai, ZHANG Pei-lin, ZHENG jian, et al. Hysteresis vibration system and engineering application [M]. Beijing: Science Press, 2002.
[31] SHEN Yong-jun, WEN Shao-fang, LI Xiang-hong. Dynamical analysis of fractional–order nonlinear oscillator by incremental harmonic balance method [J], Nonlinear Dynamics, 2016, 85(3): 1457-1467.
[32] WEN Shao-fang, SHEN Yong-jun, YANG Shao-pu, et al. Dynamical response of Mathieu-Duffingoscillator with fractional-order delayed feedback [J]. Chaos, Solitons and Fractals, 2017, 94: 54-62.
[33] SHEN Yong-jun, WEN Shao-fang, YANG Shao-pu. Analytical threshold for chaos in a Duffing oscillator with delayed feedbacks [J]. International Journal of Non-linear Mechanics, 2018, 98: 173-179.
[34] WEN Shao-fang, SHEN Yong-jun, LI Xiang-hong, et al. Dynamical analysis offractional-order Mathieu equation [J]. Journal of Vibroengineering, 2015, 17(5): 2696-2709.
[35] 温少芳. 分数阶参激系统的动力学与控制研究[D]. 河北: 石家庄铁道大学, 2018.
WEN Shao-fang. Study on dynamics and control of fractional order parameter excitation system [D]. Hebei: Shijiazhuang tiedao university, 2018.
[36] CAO Feng-li, BAI Hong-bai, He Zhongbo, et al. A hysteresis restoring force model of disc-shaped metal rubber isolation component [J]. Applied Mechanics and Materials, 2013, 271-272: 186-189.
[37] SHEN Yong-jun, YANG Shao-pu, XING Hai-jun. Primary resonance of Duffing oscillator with fractional-order derivative [J]. Commun Nonlinear Sci Number Simulat. 2012, 17(7): 3092-3100.