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。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。
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. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.
出处
《振动与冲击》
EI
CSCD
北大核心
2017年第4期88-92,共5页
Journal of Vibration and Shock
基金
安徽省高校自然科学研究重点项目(KJ2016A084)
关键词
多重尺度
分数阶导数
参数激励
过渡曲线
multiple scales
fractional derivative
parametric excitation
transition curve