Contribution to the free vibration problem of a free‐free beam with large end masses

Abstract

Free vibration of an Euler‐Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.

Mechanical Modeling and General Analytical Solution for the Dynamic Buckling of Plane Structures Using a Beam-Column Element with Varying End Restraints

“…A number of studies have been performed over the last few decades to analyse the dynamic stability in beam structures, for example [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Based on the model proposed by Kausel [45], Aristizabal-Ochoa [46] proposed a more elaborate model by adding to each end of the mechanical model two translational springs acting in parallel with the translational behavior of the beam-column element.…”