Stability Analysis of a Deep Cantilever Beam with Laterally Distributed Follower Force

Abstract

The static and dynamic stability analysis of a beam subjected to a laterally distributed follower force is presented. The effect of the uniformly distributed follower force is considered in the work and energy terms, and the equations of motion are obtained using the extended Hamilton’s principle. Applying Galerkin’s technique, the resulting equations are transformed into a general eigenvalue problem. The effects of several physical parameters, such as mass centroid offset, radius of gyration of the cantilever, fundamental frequencies ratio, and magnitude of the distributed follower force, are investigated. Numerical results reveal that the load increment may cause either static or dynamic instability types.