Dynamic Stability Analysis of Geometrically Nonlinear Equilibrium Configurations of Cantilever Beams

摘要

Flexible structures which undergo very large deformations raise interesting questions about their stability. In this connection, the cantilever beam is a frequently considered problem due to its relative simplicity and practical importance. A number of approaches to this type of problem have been used, including perturbation series expansions about the equilibrium configuration and a static finite element approach with stability determined by the signs of the stiffness eigenvalues. Note that these works considered only planar structures. In the stability of both planar and non-planar equilibrium configurations of massless beams with large tip masses were determined by considering the signs of flexibility eigenvalues associated with the tip of the beam. The purpose of this work is to use fully nonlinear dynamic equations to investigate the behaviour of large, static deformations (due to dead loads at the tip) of flexible cantilever beams subjected to small perturbations about equilibrium configurations.