Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load

Abstract The resonance of a rotating cylindrical shell due to the action of harmonic moving loads is investigated. Instabilities caused by rotation are found for the n = 1 free vibration modes, which correspond to synchronous whirl and in which the shell vibrates as a flexural beam. A general modal expansion method in which in-plane membrane effects are neglected is adopted to solve for, analytically, the forced response of the shell to harmonic traveling loading. The closed form solution is then specialized for various cases so that the individual and combined effects of rotation, moving load speed and harmonic frequency on the resonance are looked into. It is first discovered that, according to the theory, no resonance situation would occur for a stationary constant point load case. Two critical driving frequencies associated with each mn are then obtained for a stationary harmonic load case, where m is the axial half-wave number and n is the circumferential wavenumber. The resonance expressions for the case of a moving constant load, after normalization, come out the same as those for the case of a stationary harmonic load. This means that the moving load imposes effects similar to those of a harmonic force. The simultaneous presence of the load speed and harmonic frequency, however, bifurcates the resonant frequencies. The bifurcations of resonant frequencies due to rotation, moving load speed, and harmonic frequency are then explained and discussed from various viewpoints.

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