Dynamic characteristics of spinning Rayleigh beams

This paper derives the motion equations of the spinningRayleigh beam under gravitation using the extended Hamilton principle andinvestigates the dynamic characteristics of spinning Rayleigh beam under ahinged-hinged boundary condition. The present equations show that animportant gyroscopic term induced by centrifugal force is missing in similarequations in the literature, but this term is indispensable in the modelingand analysis of spinning beams. The influences of rotary inertia, spinningspeed, gyroscopic effects, slenderness ratio on whirling frequencies,whirling modes and critical speeds are investigated in detail usinganalytical and numerical methods. The results show that the forward whirlingspeed increases up to the critical speed, and then decreases with thespinning speed; the corresponding backward whirling speed decreases thespinning speed. Each forward whirling speed is higher than the correspondingbackward whirling speed. For a spinning Rayleigh beam, there areinfinite-dimensional forward and backward critical speeds.