EFFECTS OF CORIOLIS ACCELERATION ON THE VIBRATIONS OF SPINNING STRUCTURES
Abstract
The vibration behavior of a rotating ring and a rotating cylindrical shell is investigated. The equations of motion for a rotating cylindrical shell are derived from Hamilton's principle. The initial tensions generated by the centrifugal forces due to rotation and internal pressure are taken into account in the equations of motion. The equations are first specialized for the rotating ring problem. Bifurcations of natural frequencies and traveling modes due to Coriolis acceleration are discussed for the free vibration. A modal expansion technique follows to yield the solution for the forced vibration, where the so-called generalized coordinates characterize the solution. The inextensional assumption further simplifies the solution such that closed form solutions are feasible for various loading conditions. The steady state response of the rotating ring to constant point load, distributed load, harmonic load, and periodic load, are obtained using the developed theory. A stationary ring subjected to traveling loads is also solved for so that the effect of the Coriolis component can be extracted through the comparison. The analysis is extented to a rotating cylindrical shell. Similar properties as for the rotating ring problem are obtained for a rotating shell as far as the natural response is concerned. The forced vibration of a rotating cylindrical shell, however, is characterized by six generalized coordinates as a set, two more than the rotating ring case. A similar simplification again reduces the number of independent generalized coordinates to be solved to two. Closed form solutions to various types of loading are hence obtained. Examples follow to demonstrate the developed theory. Similarly, corresponding traveling loads on a stationary shell case accompany each example to show the effect of Coriolis components on the steady state response.
Degree
Ph.D.
Subject Area
Mechanical engineering
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