一类含有分数阶导数的二自由度耦合系统  

A Class of 2-DOF Coupled Systems With Fractional-Order Derivatives

作　　者：葛志新[1] 陈咸奖 陈松林[1] GE Zhi-xin CHEN Xian-jiang CHEN Song-lin(School of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China School of Business, Anhui University of Technology, Maanshan, Anhui 243002, P.R. China)

机构地区：[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

出　　处：《应用数学和力学》2017年第11期1300-1308,共9页Applied Mathematics and Mechanics

基　　金：安徽省高校自然科学研究重点项目(KJ2016A084)

摘　　要：研究了一类含有小扰动具有分数阶导数的二自由度耦合振子的振动问题.首先对含有由Riemann-Liouville定义的分数阶导数的振动方程组构造渐近解,利用多重尺度法,得到振动问题的可解性条件.然后在可解性条件下,得到分数阶指数、系数及小参数对振动的影响,并求得渐近解.最后研究了该解的稳定性,发现定常解都是稳定的.The vibration problems of a class of 2-DOF coupled systems with fractional-order derivatives and small perturbations were studied. First,the asymptotic solutions of the vibration equations with Riemann-Liouville fractional-order derivatives were constructed. With the multi-scale method,the solvability conditions for the asymptotic solutions to the vibration problems were obtained. Then,under the solvability conditions for the solutions,the influences of the fractional-order derivatives,their coefficients and the small parameters on the vibration were discussed,and the asymptotic solutions were also given. Finally,the stability properties of the 1st-order approximate solutions were studied.It is found that all the steady-state solutions are stable.

关 键 词：多重尺度 分数阶导数 二自由度耦合系统 可解性条件 

分 类 号：O175.14[理学—数学]