Vibration Analysis of Vertical Rotating Thick Shells Subjected to the Gravity

In this paper, vibration analysis of vertical rotating thick shells is investigated. The gravity is modeled as a variable axial force. Using Hamilton s principle and based on first order shear deformation theory (FSDT), the set of governing equations and boundary conditions are derived. Considering trigonometric functions in circumferential direction and using differential quadrature method (DQM) in longitudinal direction, a semi-analytical solution is presented and forward and backward frequencies are obtained. Convergence, accuracy and versatility of the proposed solution are investigated and variation of forward and backward frequencies versus angular velocity of spin (Campbell diagrams), ratio of dimensions and gravity are investigated for various boundary conditions.