Vibrations of a rotating membrane with unsteady rotations of the axis of rotation

A method and algorithm are developed for numerical calculation of the vibrations of a rotating circular membrane with a rigid central insert. The vibrations are caused by plane rotation of the rotation axis with a variable angular velocity. A system of differential equations is obtained to describe the motion of the membrane in relation to the stress-strain state caused by the rotation. Calculated results are presented for the case when the angular velocity of the membrane is constant, while the angular velocity of the rotation axis changes over time in accordance with a piecewise-linear law.Translated from Problemy Prochnosti, No. 2, pp. 55–60, February, 1990.