The Instability of a Cantilever on an Elastic Foundation under the Influence of a Follower Force

The instability of a uniform cantilever compressed by a follower force at its free tip is investigated. The cantilever is supported on an elastic foundation and subjected to external viscous damping. The differential equation of lateral vibration of the cantilever is solved simply by Galerkin's method and the instability boundary is determined by applying Routh's criterion. It is found that the cantilever becomes unstable by flutter and that the critical force and the critical frequency depend on both damping coefficient and foundation modulus. Only with no damping is the critical force independent of foundation modulus, a phenomenon reported by other investigators.