Non-Conservative Instability of Non-uniform Beams Resting on an Elastic Foundation

Abstract The influence of a Winkler elastic foundation and the slenderness ratio on the non-conservative instability of cantilever non-uniform beams of rectangular cross-section with constant height and linearly varied breadth (T1), constant breadth and linearly varied height (T2) and double taper (T3), subjected to an end concentrated follower force is investigated. It is found that without the elastic foundation the critical flutter load of the non-uniform beam decreases as the taper ratio of the beam is increased. However, when the elastic foundation modulus is greater than a critical value, the critical flutter load of the taper beams is always greater than that of uniform beams. Within the domain considered, when the taper ratio of the beam lies in a certain range, several critical turning points, including a jump phenomenon, may exist for the critical flutter load. The jump mechanism and the influence of the elastic foundation modulus and the slenderness ratio on the jump phenomenon of Timoshenko beams is explored.