Free Vibration Analysis of Rotating Composite Beam Using Dimensional Reduction Method

Free vibration of a rotating composite beam with arbitrary cross section is presented. 3D elasticity problem of the composite beam is decomposed into a 2D cross sectional analysis and a 1D beam analysis across the beam length, using dimensional reduction method. In 2D cross section problem in and out of plane warpings are calculated by minimizing energy functional with respect to warping functions. In this paper, simple polynomial series are employed to derive warpings. Based on a 1D beam potential energy, natural frequencies for rotating and non-rotating beams are acquired. The effects of fiber angle and rotational speed are investigated for Flap and Lag bending vibration. This procedure, which gives accurate results, eliminates the costly use of 3D finite element tools.