Free Vibration of a Spinning Spherical Shell

An analysis is presented for the free vibration of a spinning spherical shell. For this purpose, the governing equations and the boundary conditions of the shell are derived by applying Hamilton's principle to the strain and kinetic energies of the shell. The variables in the equations can be written as summation of the quasi-static components which are independent of time and the dynamic ones. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method. The method is applied to a spinning clamped-free spherical shell. The quasi-static and dynamic displacements and the frequency parameters are calculated numerically, and the effects of the spinning of the shell on the free vibration are studied.