Non-conservative instability of a timoshenko beam subjected to a partially tangential follower force

The governing differential equations and boundary conditions for the non-conservative instability of a Timoshenko beam subjected to an end partial tangential follower force are derived via Hamilton’s principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The characteristic equation is expressed in terms of four linear independent fundamental solutions of the system. The influences of the tangency coefficient, the slenderness ratio and the elastically restrained boundary conditions on the elastic instability and the critical load of a Timoshenko beam are investigated. The boundary curves for the flutter and divergence instability of clamped–elastically restrained beams are determined.