分数阶半主动颗粒阻尼隔振系统动力学特性分析

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (21) : 194-200.

论文

薛程1，夏兆旺1,2，卢志伟1，鞠福瑜1，茅凯杰3

作者信息 +

Dynamic characteristics analysis of vibration isolation system with fractional-order semi-active particle damper

XUE Cheng, XIA Zhaowang1,2, LU Zhiwei1, JU Fuyu1, MAO Kaijie3

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文章历史 +

摘要

针对半主动颗粒阻尼器建立其分数阶模型，通过试验及参数识别确定了分数阶参数与实际物理量之间的定量关系。试验结果表明：分数阶系数与颗粒填充率之间满足线性关系，而分数阶阶次与外圈电流满足三次多项式关系。随后，研究了一类含分数阶半主动颗粒阻尼器的单自由度隔振系统，通过平均法求解了其解析解，并基于Grünwald-Letnikov分数阶定义得到其离散化数值解；对比表明解析解和数值解具有良好的一致性。最后，分析了分数阶参数对隔振系统稳态响应的影响规律，研究结果表明：随着分数阶阶次的增大或是分数阶系数的减小，系统稳态响应幅值逐渐减小；通过观察幅频响应曲线可知阶次值的变化会引发“频移”现象，同时推导出了分数阶系统的最优阶次值为1.47。

Abstract

This article established a fractional-order model for semi-active particle damper and the relationship between fractional-order parameters and its actual physical parameters is identified by experiments. The experimental results show that the fractional-order coefficient has a linear relation with particle filling rates and the fractional order has a cubic polynomial relation with the coil current. Then, this article researched a SDOF vibration isolation system including fractional-order semi-active particle damper, whose analytical solution is obtained by averaging method and numerical solution is got based on Grünwald-Letnikov Fractional-order definition. The comparison between the analytical solution and the numerical solution shows that they have a great consistency. Finally, this article discussed the influences of fractional parameters on the steady-state response amplitude of the system. The results found that with the increase of fractional order or the decrease of fractional-order coefficient, the steady-state response amplitude of the system would show a downward trend. The change of fractional order will lead the natural frequency to change and the optimal value of fractional order is 1.47.
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导出引用

薛程1，夏兆旺1,2，卢志伟1，鞠福瑜1，茅凯杰3. 分数阶半主动颗粒阻尼隔振系统动力学特性分析[J]. 振动与冲击, 2021, 40(21): 194-200

XUE Cheng, XIA Zhaowang1,2, LU Zhiwei1, JU Fuyu1, MAO Kaijie3. Dynamic characteristics analysis of vibration isolation system with fractional-order semi-active particle damper[J]. Journal of Vibration and Shock, 2021, 40(21): 194-200

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