C0-continuous isoparametric Timoshenko beam element for rotating

Abstract

This paper presents a C0-continuous isoparametric finite element for free vibration analysis of a rotating, tapered Timoshenko beam mounted on the periphery of a rotating rigid hub, at a setting angle with the plane of rotation. The finite element has three nodes and two degrees of freedom per node and employs modified shape functions for rotational displacement associated with the shear strain energy to avoid shear locking. To obtain a finite element equation of the generalized eigenvalue problem, Hamilton’s principle is applied to kinetic and potential energy expressions of a rotating Timoshenko beam with non-zero setting angle. The numerical solutions for various situations including variations of rotational speed, taper ratio, slenderness ratio, hub radius and setting angle are compared with other numerical results available in the literature whenever possible. The results show that the new 3-noded isoparametric element yields accurate results when compared to other numerical ones.