Beam stability on an elastic foundation subjected to distributed follower force

Abstract

Problems related to the stability and behavior of a cantilevered beam with a tip mass on an elastic foundation and subjected to a distributed follower force are addressed. The stability of a beam partially attached to an elastic foundation is also considered. The dynamic stability of a beam subjected to a distributed follower force is formulated by using finite element method to get a general eigenvalue problem. The influence of the modulus on the elastic foundation and the ratio of the cantilevered beam’s mass to the tip mass on the critical flutter are investigated. Finally, the stability of the cantilevered beam is found to depend on both the modulus of the elastic foundation and the ratio of the cantilevered beam’s mass to the tip mass.