Natural Frequencies of Rotating Uniform Beams with Coriolis Effects

Abstract

A Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration, due to the presence of gyroscopic, or Coriolis forces, is taken into consideration. The dynamic trigonometric shape functions of uncoupled bending and axial vibrations of an axially loaded uniform beam element are derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables, based on these dynamic shape functions, leads to a single frequency dependent stiffness matrix which is Hermitian and represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by two illustrative examples of vertical and radial beams where the influence of Coriolis forces on natural frequencies of the clamped-free rotating beams is demonstrated by numerical results.