A new Dynamic Finite Element (DFE) formulation for lateral free vibrationsof Euler-Bernoulli spinning beams using trigonometric shape functions

This paper presents a new Dynamic Finite Element (DFE) formulation for the vibrational analysis of spinning beams. A non-dimensional formulation is ad opted, and the frequency dependent trigonometric shape functions are used t o find a simple frequency dependent element stiffness matrix which has both mass and stiffness properties. An appropriate bisection method, based on a Sturm sequence root counting technique, is used and the flexural natural f requencies of cantilevered beams, for a variety of configurations, are stud ied. The results are compared to those found by the Dynamic Stiffness Matix and the classical Finite Elements Method, using "Hermite" beam elements. M uch better convergency Fates are found using the proposed DFE method. (C) 1 999 Academic Press.