摘要
利用分数阶导数算子-∞βt研究线性分数阶振动系统在谐波激励下的稳态响应。采用复指数函数形式的谐波激励，利用待定函数法得到与激励同频率的稳态响应，以及幅频关系和相频关系。讨论了分数阶导数项对刚度和阻尼的影响。
The steady-state response of the linear fractional vibration system with the harmonic excitation is considered by using the fractional derivative operator-∞βt. The harmonic excitation is adopted in the form of the complex exponential function, and the steady-state response with the same frequency as the excitation, the amplitude-frequency relation, and the phase-frequency relation are obtained by using the method of undetermined functions. The effect of the fractional derivative term on the stiffness and damping is discussed.
出处
《应用数学与计算数学学报》
2015年第2期240-247,共8页
Communication on Applied Mathematics and Computation
基金
上海市自然科学基金资助项目(14ZR1440800)
上海市教育委员会科研创新基金资助项目(14ZZ161)
关键词
分数阶微积分
分数阶振动
响应
激励
fractional calculus
fractional vibration
response
excitation
