Dynamic Stability of Pretwisted Cantilever Beams Subjected to Distributed Follower Force

摘要

The dynamic stability analysis of a pretwisted cantilever beam subjected to a distributed follower force is investigated. The spatial form of the follower force is chosen to cover a wide range of possible forms of distributed, nonconservative loads acting on a pretwisted cantilever beam such as lateral, axial tangential, or a combination of both types. The effect of the distributed follower force is taken into account by the work and energy terms, and Hamilton's principle is used to derive the equations of motion. The partial differential equations of motion are transformed into a general eigenvalue problem by using the finite-element method. The effects of several physical parameters, such as the magnitude and setting angles of the follower force, the pretwist angle of the cantilever, geometrical parameters, and the fundamental frequency ratio, are studied. Numerical results show that the pretwist angle and setting angle of the follower force affect the dynamic instability of the cantilever.