Refined Beam Elements for the Free Vibration Analysis of Stepped Shafts With and Without Transition Area

Abstract

Investigation of the free vibration of stepped shafts with and without transition area is presented in this paper. The refined one-dimensional beam theories are chosen to be used based on the Carrera Unified Formulation (CUF) in the present work. According to CUF, Taylor-type expansion is employed to describe the displacement field over cross section of shafts. With the implementation of Hamilton’s principle, the governing differential equations and the related mass matrix, the stiffness matrix and the load vector are obtained. To obtain the numerical solutions, the finite method is adopted in this paper. The accuracy and reliability of the present model are demonstrated by comparing with classical beam model (Timoshenko beam model) and a solid model generated in the commercial software ANSYS. Meanwhile, the influences of step ratio, step location, boundary conditions and the slope of generatrix attached to the transition area on vibration characteristics are studied.