基于分数阶导数的黏弹性悬架减振模型及其数值方法

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摘要为了准确掌握黏弹性悬架的动态响应，针对传统整数阶减振模型的不足，引入分数阶导数原理，构建了黏弹性材料FKV本构模型，建立了考虑几何参数的黏弹性悬架分数阶减振模型，利用Grumwald-Letnikov定义将模型中分数阶导数离散化，并转化为状态方程形式，依据矩阵函数理论推导出模型的数值解。以某型安装黏弹性悬架的履带车辆参数为例，分别建立了悬架的动态接触有限元模型和分数阶减振模型，获得了在翻越障碍工况下两种模型响应的对比解。结果表明：分数阶减振模型体现了黏弹性悬架响应具有全局相关性和记忆性，且历史作用渐近加强；黏弹性悬架有较好的缓冲减振性能；分数阶减振模型解与有限元方法计算结果有较好的一致性。旨为下一步的实车试验和实际应用提供理论参考。

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	李占龙1
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	孙大刚1
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	宋勇2
	刘付喜1
	赵树萍2

关键词 ：分数阶导数, 黏弹性悬架, 减振模型, 数值方法

Abstract：To obtain dynamic responses of viscoelastic suspension accurately, FKV constitutive model of viscoelastic materials was developed by employing fractional derivative. Vibration model of viscoelastic suspension considering geometric factor was also built based on FKV. Numerical solution was derived by employing Grumwald-Letnikov definition for fraction calculus and matrix function theory. For comparison, dynamic contact FEM was established based on a crawler vehicle installed viscoelastic suspension to compare with fractional method. Results show that fractional vibration control model can embody the nonlocal correlation and memory feature of viscoelastic suspension which exhibits excellent vibration control capability. The numerical result displays well agreement with that from FEM. The study provides essential theoretical references for the future in-situ test and practice application.

Key words： factional calculus viscoelastic suspension vibration control model numerical method

收稿日期: 2015-05-14 出版日期: 2016-08-15

引用本文:

李占龙1，2，孙大刚1,2，宋勇2，刘付喜1，赵树萍2. 基于分数阶导数的黏弹性悬架减振模型及其数值方法[J]. 振动与冲击, 2016, 35(16): 123-129.
LI Zhan-long1,2， SUN Da-gang1,2, LIU Fu-xi1, SONG Yong2, ZHAO Shu-pin2. Fractional calculus-based vibration suppression model and numerical method for viscoelastic suspension. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(16): 123-129.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I16/123

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