Non-conservative Instability Of A Timoshenko Beam Resting On Winkler Elastic Foundation

Abstract

The transfer matrix method is used to investigate the influence of a Winkler elastic foundation on the non-conservative instability of uniform Timoshenko beams. It is found that the critical flutter load for a cantilever Timoshenko beam subjected to an end-concentrated or linearly distributed tangential follower force will first decrease as the elastic foundation modulus is increased and, as the elastic foundation modulus increases beyond the corresponding critical value, which corresponds to the lowest critical flutter load, it will increase instead. It is also observed that when the elastic foundation modulus is large enough, the critical flutter load for a cantilever Timoshenko beam can be greater than that of a Bernoulli-Euler beam, and there exists a corresponding critical turning point for the critical flutter load. At this critical turning point, the instability mechanism changes. The instability mechanisms for a beam subjected to end concentrated and linearly distributed tangential follower force are different.