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首页> 外文期刊>Applied Mathematical Modelling >Nonlinear vibration and stability analysis of the curved microtube conveying fluid as a model of the micro coriolis flowmeters based on strain gradient theory
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Nonlinear vibration and stability analysis of the curved microtube conveying fluid as a model of the micro coriolis flowmeters based on strain gradient theory

机译：基于应变梯度理论的微科里奥利流量计模型的弯曲微管输送流体的非线性振动和稳定性分析

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摘要

Micro coriolis flowmeters are extensively used in fluidic micro circuits and are of great interest to many researchers. Straight and curved coriolis flowmeters are common types of coriolis flowmeters. Therefore in the present work, the out-of- plane vibration and stability of curved micro tubes are investigated to study the dynamic behavior of curved coriolis flowmeters. The Hamilton principle is applied to derive a novel governing equation based on strain gradient theory for the curved micro tube conveying fluid. Lagrangian nonlinear strain is adopted to take into account the geometric nonlinearity and analyze hardening behavior as a result of the cubic nonlinear terms. Linear stability analysis is carried out to investigate the possibility of linear instabilities. Afterwards, the first nonlinear out-of-plane natural frequency is plotted versus fluid velocity to determine the influence of nonlinear terms and hardening behavior on stability of the system. The influence of the length scale parameter is studied by comparison of the results for classical, coupled stress and strain gradient theory. Finally the phase difference between two points at upstream and downstream is plotted versus fluid velocity. Linear relation between the phase difference and fluid velocity is noticed, thus the curved coriolis flowmeter can be calibrated to measure flow rate by measuring the phase difference between two points.
机译：微型科里奥利流量计广泛用于流体微回路中，许多研究人员对此非常感兴趣。直线和弯曲科里奥利流量计是科里奥利流量计的常见类型。因此，在当前工作中，研究了弯曲微管的平面外振动和稳定性，以研究弯曲科里奥利流量计的动态性能。应用汉密尔顿原理，基于应变梯度理论，为弯曲的微管输送流体推导了一个新的控制方程。采用拉格朗日非线性应变来考虑几何非线性，并根据三次非线性项分析硬化行为。进行线性稳定性分析以研究线性不稳定性的可能性。然后，绘制第一个非线性平面外固有频率与流体速度的关系曲线，以确定非线性项和硬化行为对系统稳定性的影响。通过比较经典，耦合应力和应变梯度理论的结果，研究了长度尺度参数的影响。最后，将上游和下游两点之间的相位差与流体速度作图。由于注意到了相位差和流体速度之间的线性关系，因此可以通过测量两点之间的相位差来校准弯曲的科里奥利流量计来测量流量。

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