| 一类含有分数阶导数的参数激励振动问题 |
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| 引用本文： | 葛志新,陈咸奖,陈松林.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. |
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| 作者姓名： | 葛志新 陈咸奖 陈松林 |
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| 作者单位： | 1.安徽工业大学 数理学院, 安徽马鞍山 243002;
2.安徽工业大学 商学院, 安徽马鞍山 243002 |
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| 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。
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| 关 键 词： | 多重尺度 分数阶导数 参数激励 过渡曲线 |
A Class of Parametric Excitation Vibration Problem with Fractional Derivative |
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| GE Zhixin,CHEN Xianjiang,CHEN Songlin.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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| Authors: | GE Zhixin CHEN Xianjiang CHEN Songlin |
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| Affiliation: | 1.School of Mathematics ＆ Physics,Anhui University of Technoloy,Maanshan 243002,China;
2.School of Economics,Anhui University of Technology,Ma’anshan 243002,China |
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| 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. |
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| Keywords: | multiple scalesfractional derivativeparametric excitationtransition curve |
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