Dynamic Stability of an Elastic Beam Subjected to Axial Fluid Forces Considered to be Follower Forces

Abstract

The stability of nonconservative system of a beam is investigated when an elastic beam is subjected to follower forces. The mathematical formulations for a conservative system and a nonconservative system are established regarding to a uniform cantilever subjected to a concentrated force and a uniform distributed force axially. The displacement of a uniform cantilever is assumed to be obtained by superposing the modal functions which are normal modes in a vacuum, and is estimated by applying the Galerkin method. Changing the forces, the eigenvalue analysis is performed, and the root locus is calculated for the stability analysis. And, the relationships between forces and frequencies for the undamped system and the damped system of the uniform cantilever subjected to a concentrated force and a uniform force are investigated. When the system is subjected to a conservative force, the divergence phenomenon is confirmed to appear first. On the other hand, when the system is subjected to a nonconservative force such as follower force, the flutter phenomenon is confirmed to appear first although the critical force becomes high. And, by changing the structural damping, the destabilized effect due to the structural damping is confirmed when an elastic beam is subjected to follower forces. Moreover, the dynamic behaviors of the higher modes, and the stability of a simply supported beam and a free-free beam are also studied.