On the dynamic stability of elastic structures subjected to follower forces

Abstract. Within the framework of second-order theory, some classical stability problems, whose critical load corresponded to dynamic instability, were considered in paper [1]. The main focus was on systems with just one lumped mass. This idealization, together assumption negligible axial strain and adoption reduced a single Lagrangian coordinate. In this way, static methods could be applied derive analytical expression stiffness coefficient study stability, starting well-known example, namely, cantilever beam mass at free end subjected follower [2]. paper, new system is studied: straight-axis constant cross-sectional area stiffness, mass-free, hinged end, simply supported an intermediate point (with sliding plane parallel axis) other free, where present force applied. As examples shown [1], example first asymptote corresponds load, due divergence infinity. It that equal buckling auxiliary structure, which differs from original concentrated replaced by constraint blocks corresponding