On the forced vibration of simply supported rotating cylindrical shells

Abstract

The free and forced vibrations of rotating simply supported cylindrical shells are investigated. The equations of motion, which take into account the effects of initial tensions, are derived from Hamilton’s principle. The effects of rotation on the natural frequencies are first reviewed. Next, a new approach is developed for solving the general forced vibration response problem of rotating cylindrical shells. The solution in its final form is characterized by generalized coordinates. The orthogonality of trigonometric functions allows one to separate the solution such that the generalized coordinates associated with different rotational modes form a set of second-order differential equations and can be solved for independently. The solution is further simplified for the cases where flexural vibration predominates. An inverted problem, where the cylinder is stationary and the load is rotating around it, is solved too for comparison. Finally, analytical solutions to the constant point load, and to the harmonic point load in the radial direction, are obtained using the developed method. The influence of rotation on the forced vibration is then illustrated.