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

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (11) : 248-251.

GE Zhixin1, CHEN Xianjiang2

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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.

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multi-scale / time fractional derivative / differential inequality

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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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