Abstract
Free vibrations are analyzed for a rotating uniform circular cylindrical shell capped by an uniform circular plate without a hole at one end. First, the basic equations for the steady rotation of a circular cylindrical shell and a circular plate are derived. Then considering the effect of initial tensions due to the steady rotation, the equations of motion and boundary conditions for vibrations of the circular cylindrical shell and for in-plane and out-of-plane vibrations of the circular plate are derived. This is realized by using the stationary conditions of each Lagrangian of vibrations. Each equation of motion is solved exactly by using power series expansions. The natural conditions of continuity between the circular cylindrical shell and circular plate are obtained from the stationary conditions of Lagrangian by considering the geometrical conditions of continuity at connecting points. In the numerical calculations, natural frequencies and mode shapes of the rotating circular cylindrical shell with one end clamped and the other end capped by a circular plate without a hole are presented showing their variations with rotating angular velocity, circumferential wavenumber and other parameters
