Vibration of Tapered Beams

Abstract

Stiffness and consistent mass matrices for linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of the matrices. Variation of area and moment of inertia of the cross section along the axis of the element is exactly represented by simple functions involving shape factors. Numerical results of vibration of some tapered beams are obtained using the derived matrices and compared with the analytical solutions and the solutions based upon stepped representation of the beams using uniform beam elements. The significance of the severity of taper within beams upon solution accuracy and convergence characteristics is examined.