Frequency‐Dependent Matrices for Tapered Beams

Abstract

Dynamic correction stiffness and mass matrices are derived in explicit form for a tapered beam element of any cross‐sectional shape. These matrices are derived using exact expressions for the required displacement functions. Variation of area and moment of inertia of cross section along the axis of the element is exactly represented by simple functions involving shape factors. Vibration analysis of an example tapered beam is performed using static and dynamic correction tapered beam element matrices, and uniform beam element matrices. The costs, and advantages and disadvantages of analyzing tapered beams using these matrices are considered.