FINITE ELEMENT VIBRATION ANALYSIS OF NON-UNIFORM TIMOSHENKO BEAMS

摘要

During the past few years, a number of different finite elements for Timoshenko beams, which include shear deformation and rotary inertia effect, have been published. In this paper a beam element which has three nodes and two degrees of freedom per node is used for the analysis of free vibrations of non-uniform beams. The nodal degrees of freedom include the values of the lateral deflection and cross-sectional rotation. The element model is based on the differential equation of the beam in static equilibrium. The variation of the cross sectional area and the second moment of inertia of the area along the length of the beam are both represented by general formulae. Improved accuracy has been obtained more efficiently due to the use of higher order functions for approximating the variation of nodal variables. Comparison of results with analytical and numerical solutions appearing in the literature shows the accuracy and good rate of convergence of the element for tapered beams.