a New Dynamic Finite Element (dfe) Formulation for Lateral Free Vibrations of 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 adopted, and the frequency dependent trigonometric shape functions are used to 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 frequencies of cantilevered beams, for a variety of configurations, are studied. The results are compared to those found by the Dynamic Stiffness Matrix and the classical Finite Elements Method, using “Hermite” beam elements. Much better convergency rates are found using the proposed DFE method.