Vibration analysis of tapered rotating composite beams using the hierarchical finite element
A hierarchical finite element model is presented for the flapwise bending vibration analysis of a tapered rotating multi-layered composite beam. The shear and rotary inertia effects are considered based on the higher shear deformation theory to derive the stiffness and mass matrices of a tapered-twisted rotating and composite beam element. Certain non-composite beams for which comparative results are available in the literature are used to illustrate the application of the proposed technique. Dimensionless parameters are identified from the equations of motion and the combined effects of the dimensionless parameters on the modal characteristics of the rotating composite beams are investigated through numerical studies. The results indicate that, comparedwith the conventional finite element method, the hierarchical finite element has the advantage of using fewer elements to obtain a better accuracy in the calculation of the vibration characteristics of rotating beams such as natural frequencies and mode shapes.