一类含时间分数阶导数的膜振动方程近似解析解的研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (11) : 248-251.

论文

葛志新1,陈咸奖2

作者信息 +

Approximate analytical solution to a class of membrane vibration equations with time fractional derivatives

GE Zhixin1, CHEN Xianjiang2

Author information +

文章历史 +

摘要

研究一类含时间分数阶导数的膜振动方程,该方程边界正弦摄动变化。先对边界自变量应用泰勒级数展开,引入多重尺度到原方程及边界,利用Riemann-Liouville分数阶导数定义和性质得到关于小参数的零阶近似解。应用微分不等式理论证明了解的一致有效性。利用图形分析出各参数对解的影响。

Abstract

Here, a class of membrane vibration equation with time fractional derivative was studied.The equation boundary varied with sinusoidal perturbation.Taylor series was applied to expand the boundary independent variable, and then multi-scale were introduced to the original equation and boundary.By using the definition and properties of Riemann-Liouville fractional derivative, the approximate solution of the equation for the zero-order small parameter was obtained.Furthermore, the consistent effectiveness of the solution was proved by using the theory of differential inequalities.Finally, the influence of each parameter on the solution was analyzed using graphs.

导出引用

葛志新1,陈咸奖2. 一类含时间分数阶导数的膜振动方程近似解析解的研究[J]. 振动与冲击, 2021, 40(11): 248-251

GE Zhixin1, CHEN Xianjiang2. Approximate analytical solution to a class of membrane vibration equations with time fractional derivatives[J]. Journal of Vibration and Shock, 2021, 40(11): 248-251

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