Dynamic response of a constrained axially loaded beam

Abstract:
A dynamic beam system loaded harmonically in the axial direction and constrained in the transverse direction is modelled using different theoretical descriptions. Results from an experimental set-up are compared to calculations using Bernoulli as well as Timoshenko beam theories. Some results from investigations of this beam system unveiling its chaotic nature have earlier been presented, but here the refining of Timoshenko theory is done in order to get a better understanding of the influence of the impacts on the beam motion. The free motion of the beam is described as a finite sum of modes, while at impact an infinite number of modes is considered, albeit approximately. These ideas were also used for the Bernoulli beam, but modifications will be made here to account for the modal equations of fourth order in time for the Timoshenko beam. The investigation is complemented with new experiments.