Spline Finite Point Method for Free Bending Vibration Analysis of Rotating Tapered Euler-Bernoulli Beams

Abstract

Based on the Euler-Bernoulli beam theory (EBT), a new model for free bending vibration problems of rotating tapered beams using spline finite point method (SFPM) was investigated. The beam was discretized by a set of uniformly scattered spline nodes along the beam axis direction instead of meshes, and the displacement field was approximated by the cubic B-spline interpolation functions. Both of the variations of cross-sectional dimension and the rotating centrifugally stiffened effect were considered in the proposed model, and the global stiffness and mass matrices of the structures were deduced based on the Hamilton principle. Computer programs were compiled to study the dynamic properties of rotating tapered beams. The finite element model (FEM) for the rotating tapered beams by using ANSYS was also built for validating the proposed model. The results show that the present results agree very well with the results of other reported literatures and the FEM, and the proposed model has the advantages of good computational accuracy, high modeling efficiency, simple boundary conditions, and convenience for compiling computer program. It is capable of studying the free bending vibration of rotating tapered beams with the variation of boundary conditions, taper ratios, cross-sectional types, rotating speeds, and hub radius. Both the taper ratios and rotating speeds have important roles on the dynamic properties of rotating tapered beams through parameter analysis.

Keywords: Euler-Bernoulli beam theory,  rotating tapered beam,  free bending vibration,  spline finite point method