Dynamic response of spinning tapered Timoshenko beams using modal reduction

A method for dynamic response analysis of spinning tapered Timoshenko beams utilizing the finite element method is developed. The equations of motion are derived to include the effects of Coriolis forces, shear deformation, rotary inertia, hub radius, taper ratios and angular setting of the beam. Modal transformations from the space of nodal coordinates to the space of modal coordinates are invoked to alleviate the problem of large dimensionality resulting from the finite element discretization. Both planar and complex modal transformations are presented and applied. The reduced order modal form of equations of motion is computer generated, integrated forward in time, and the system dynamic response is evaluated. Numerical results and comparisons with the full order model (FOM) are presented to demonstrate the accuracy of the reduced order model (ROM).