Modeling and dynamic characteristics of spinning Rayleigh beams
Modeling and dynamic characteristics of spinning Rayleigh beams
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DOI：
10.1016/j.ijmecsci.2013.01.029
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发表时间：
2013-03
影响因子：
7.3
通讯作者：
P. Pai;Xin Qian;Xing-wen Du
中科院分区：
文献类型：
--
作者：
P. Pai;Xin Qian;Xing-wen Du
本文推导了旋转瑞利梁的线性和非线性模型，并研究了具有六组不同边界条件的向下垂直旋转瑞利梁的动态特性。推导表明，由于在推导中非线性项的使用不一致，许多文献报告中都缺少由离心力引起的重要线性项，但该项对于旋转梁的正确建模和分析是必不可少的。使用解析和有限元方法详细研究了旋转惯量、旋转速度、科里奥利力和离心力、细长度和重力对向前和向后涡动速度、涡动振型和临界速度的影响。数值结果表明，当旋转速度增加时，每个正向涡动速度增加到其临界速度，并且相应的反向涡动速度减小。每个正向旋动速度均高于相应的反向旋动速度，并且当旋动速度和模态数增加以及长细比减小时，差异增大。对于具有六组不同边界条件中任意一组的旋转瑞利光束，存在无限（而不是像一些报告所说的有限）前向临界速度和无限后向临界速度。此外，重力会增加向下旋转的均匀光束的向前和向后旋转速度，但只有当它是很长的细光束时，这种增加才显着。
This paper derives linear and nonlinear models of spinning Rayleigh beams and investigates dynamic characteristics of downward vertical spinning Rayleigh beams with six different sets of boundary conditions. The derivations show that an important linear term due to centrifugal forces is missing in many reports in the literature because of inconsistent use of nonlinear terms in the derivation, but this term is indispensible for correct modeling and analysis of spinning beams. The influences of rotary inertia, spinning speed, Coriolis and centrifugal forces, slenderness, and gravity on forward and backward whirling speeds, whirling mode shapes, and critical speeds are investigated in detail using analytical and finite-element methods. Numerical results show that each forward whirling speed increases up to its critical speed and the corresponding backward whirling speed decreases when the spinning speed increases. Each forward whirling speed is higher than the corresponding backward whirling speed, and the difference increases when the spinning speed and the mode number increase and the slenderness ratio decreases. For a spinning Rayleigh beam with any of the six different sets of boundary conditions, there are infinite (instead of finite, as some reports said) forward critical speeds and infinite backward critical speeds. Moreover, gravity increases the forward and backward whirling speeds of a downward spinning uniform beam, but the increase is significant only if it is a very long thin beam.