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Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

机译：粘弹性管道输送流体分数动态模型的非线性振动分析

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Highlights•A new non-linear, fractional dynamic model of the viscoelastic pipe is established.•Analytical solutions of the fractional model are derived using the method of multiple scales.•The amplitude predicted by the fractional model is much larger than that predicted by the previous model.•With the fractional order increase, the nonlinear frequency increases at first and then diminishes.•The fractional order can change the variation trend of the amplitude versus the fluid velocity.AbstractThe nonlinear free vibration of a fractional dynamic model for the viscoelastic pipe conveying fluid is studied in this paper. The dynamic equations of coupled planar motion for the pipe are derived by employing the Euler beam theory and the generalized Hamilton principle when we consider both the fractional material model and the geometric non-linearity. Then the equations are simplified into a new nonlinear, fractional order dynamic model governing transverse vibration of the pipe in small but limited stretching issues. The method of multiple scales is directly applied for the analysis and simulation of the nonlinear vibration. Numerical results show the influence of the factional order, the mass ratio, the fluid velocity and the nonlinear coefficient on the nonlinear amplitudes and frequencies of the viscoelastic pipe. It is noticeable that the amplitudes of the fluid-conveying pipe constituted by the fractional viscoelastic material model display much higher than those predicted by the previous models.
机译： 突出显示 • 建立了新的粘弹性管道非线性分数动态模型。 • 分数模型的解析解是使用多尺度方法得出的。 • 分数模型预测的幅度比先前模型预测的幅度大得多。 • 随着分数阶的增加，非线性频率首先增大，然后减小。 • 分数顺序可以更改变化振幅与流体速度的趋势。 摘要 < ce：simple-para id =“ spara0007” view =“ all”>研究了粘弹性管道输送流体的分数动态模型的非线性自由振动。当考虑分数材料模型和几何非线性时，采用欧拉梁理论和广义汉密尔顿原理推导了管道耦合平面运动的动力学方程。然后，将方程简化为一个新的非线性，分数阶动力学模型，该模型控制在较小但受限制的拉伸问题中管道的横向振动。多尺度法直接用于非线性振动的分析与仿真。数值结果表明，分形顺序，质量比，流体速度和非线性系数对粘弹性管道的非线性振幅和频率有影响。值得注意的是，由分数粘弹性材料模型构成的流体输送管的振幅显示出远高于先前模型所预测的振幅。

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