Dynamic Analysis of a Spinning Timoshenko Beam by the Differential Quadrature Method

Abstract

ThedynamiccharacteristicsofaspinningTimoshenkobeamareinvestigatedbyusingthedifferentialquadrature method (DQM). The beam is subject to any combination of free, simply supported, clamped, and elastically supported boundary conditions. The weighting matrices in the differential quadrature formulation are modie ed to incorporate classical boundary conditions of the beam, whereas boundary conditions of elastic supports are incorporated into the discretized equations. Numerical results of the spinning Timoshenko beam obtained by the DQM are compared with the exact solutions orresults obtained by the e nite element method. The results show the high accuracy and efe ciency of the differential quadrature method. Nomenclature A = cross-sectional area of beam [C b ] = damping matrix of elastic supports Cxx, Cyy = damping coefe cients E = Young’ s modulus G = shear modulus [G] = gyroscopic matrix I = transverse moment of inertia Jp = polar mass moment of inertia [K] = stiffness matrix [K b ] = stiffness matrix of elastic supports Kxx, Kyy = spring constants l