一类含有分数阶导数的参数激励振动问题

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (4) : 88-92.

论文

一类含有分数阶导数的参数激励振动问题

葛志新1 , 陈咸奖2, 陈松林1

作者信息 +

A Class of Parametric Excitation Vibration Problem with Fractional Derivative

GE Zhixin1,CHEN Xianjiang2,CHEN Songlin1

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文章历史 +

摘要

研究了一类具有分数阶导数阻尼的参数激励振动问题. 首先对含有由 Riemann-Liouville 定义的分数阶导数的Mathieu振动方程构造渐近解,利用多重尺度法,在激励参数取不同值的情况下,求得渐近解, 得到分数阶指数对解的影响.

Abstract

A class of parametric excitation vibration problems with fractional derivative damping was studied. First of all,the asymptotic solution of the Mathieu vibration equation of the fractional derivative defined by the Riemann-Liouville was structured. In the case of different values of excitation parameters,asymptotic solutions were obtained by the method of multiple scales. The influence of fractional order index on the asymptotic solution was obtained.

导出引用

葛志新1,陈咸奖2, 陈松林1. 一类含有分数阶导数的参数激励振动问题[J]. 振动与冲击, 2017, 36(4): 88-92

GE Zhixin1,CHEN Xianjiang2,CHEN Songlin1. A Class of Parametric Excitation Vibration Problem with Fractional Derivative[J]. Journal of Vibration and Shock, 2017, 36(4): 88-92

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