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Dynamic motion of whirling rods with Coriolis effect

机译：具有科里奥利效应的旋转棒的动态运动

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Longitudinal vibrations coupled with transverse vibrations of whirling rods are investigated. It is known that longitudinal and transverse vibrations are governed by second and fourth order differential equations, respectively. Due to the Coriolis effect, a system of equations that governs the longitudinal and transverse displacements will be constructed by coupling these two equations together. Solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the whirling rod. Exact and approximate solutions are obtained from the proposed governing equations, where the approximate solutions on displacements and natural frequencies are acquired by neglecting the Coriolis effect. A proposed numerical scheme known as complete function collocation method is implemented to solve the governing equations coupled with longitudinal and transverse displacements. The approximate results on both longitudinal and transverse natural frequencies show that natural frequencies are decreasing while the angular velocity of the rod is increasing. Exact and numerical results on both longitudinal and transverse natural frequencies show that there are no predictable trends whether natural frequencies are increasing or decreasing while the angular velocity of the rod is increasing.
机译：研究了旋转杆的纵向振动和横向振动。已知纵向和横向振动分别由二阶和四阶微分方程控制。由于科里奥利效应，通过将这两个方程耦合在一起，可以构建一个控制纵向和横向位移的方程组。方程的解假设振动的小振荡叠加在回旋杆的稳态上。从提出的控制方程中可以得到精确解和近似解，而忽略科里奥利效应可以得到位移和固有频率的近似解。为了解决与纵向和横向位移耦合的控制方程，提出了一种称为完整函数配置方法的数值方案。纵向和横向固有频率的近似结果表明，固有频率在减小，而杆的角速度在增加。纵向和横向固有频率的精确和数值结果表明，当杆的角速度增大时，固有频率是增加还是减小，没有可预测的趋势。

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