Vibration analysis of rotating composite beams using polynomial based dimensional reduction method

• A dimensional reduction method based on polynomials and Rayleigh-Ritz method is presented.
• Simple polynomial series are employed to derive the necessary cross sectional warpings.
• Natural frequencies of rotating and non-rotating beams are obtained for isotropic, laminated composite beams and thin-walled composite box beams.
• The procedure eliminates non-straightforward process of mesh generation on beam section.

Free vibration analysis of rotating composite beams with arbitrary cross section is presented. The analysis is based on dimensional reduction method. Contrary to most of the previous studies, which finite element is used to analyze the cross section, the present study examines a simple polynomial based sectional analysis. The three-dimensional (3D) elasticity problem of the composite beam is decomposed into a two-dimensional (2D) cross section analysis and a one-dimensional (1D) beam analysis. In 2D cross-sectional problem in-plane and out-of-plane warpings are calculated by minimizing the energy functional with respect to warping functions. Simple polynomial series are employed to derive the necessary warping functions analytically. Cross sectional properties are determined as a fully populated 4×4 stiffness matrix. Based on a 1D beam potential and kinetic energy, natural frequencies of rotating and non-rotating beams are obtained. The presented approach is applied to isotropic, laminated composite beams as well as thin-walled composite box beams. The effects of fiber angle and rotational speed are investigated for flap and lag bending vibration. The accuracy of the results is validated in comparison with other theories, 3D FEM and experimental data. This procedure, which gives accurate predictions, eliminates the costly use of 3D finite element analysis.