Studying the effects of lumped end mass on vibrations of a Timoshenko beam using a wave-based approach

Abstract

Mast antenna structures and robot arms are often modeled as beams with lumped end masses. In this paper, bending vibrations in beams with lumped masses at boundaries are studied based on the advanced Timoshenko theory. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves that propagate along a uniform waveguide (such as a beam element) and are reflected and/or transmitted at discontinuities (such as boundaries and lumped mass attachments). The reflection relation corresponding to a bending incident vibration wave at the end mass is derived, which is assembled with propagation and reflection relations at classical boundaries to obtain the modes of vibrations. The effects of lumped end mass on vibrations of a Timoshenko beam are studied in detail.