The existence of regions of divergence instability for nonconservative systems under follower forces

Abstract

In this investigation, the existence of regions of divergence instability for an elastically restrained column under a follower compressive force at its end, is discussed. Necessary and sufficient conditions for the existence of regions of divergence instability are established. The boundary between flutter and divergence instability passes always through a double critical point, where the first and second static (buckling) eigenmodes coincide. The eigenvalues (buckling loads) of nonself-adjoint problems of this type are positive and distinct for the entire region of divergence instability, except at its boundary, where the first and second eigenvalues coincide. At this boundary, where the buckling mechanism changes from divergence to flutter and vice-versa, a sudden increase in the critical load occurs with the flutter load always being higher than the corresponding divergence load.