Elastic stability continues to be a subject of considerable interest due to the increasing demands of lightweight structures. It is well known that structures may lose stability through divergence or flutter and the nature of the instability depends on the type of loading. A structure may lose stability through divergence when the loading is conservative but may lose stability through divergence or flutter when the loading is non-conservative. In this work, we investigate stability transitions in structures due to: damping in the presence of non-conservative loading, terminal dynamic moment with and without intermediate support, and external flow with dynamic moment. The role of damping on non-conservative systems, which was first investigated by Ziegler, is revisited here. It is shown that increasing the level of damping can cause an unstable non-conservative system to become stable, then unstable, then stable again at the same value of the non-conservative load. This sequence of stability transitions, which has not been reported in the literature, is found to exist for several non-conservative systems, including articulated linkages with follower end forces and fluid-conveying pipes. The stability transitions were investigated by applying the Routh-Hurwitz criterion twice: once for the characteristic polynomial and the second time for the polynomial that guarantees the existence of a second-order auxiliary polynomial in the Routh array. Nonconservative loading in elastic structures has previously been limited to follower forces and forces generated by a fluid jet exiting a fluid-conveying pipe. A new type of non-conservative loading is introduced here in the form of a terminal dynamic moment. The terminal moment is dynamic in the sense that it is proportional to the slope or curvature of a point along the structure. Irrespective of whether the moment is slope-dependent or curvature-dependent, stability is lost in a beam through divergence when the constant of proportionality is positive, and through flutter when the constant of proportionality is negative. Some of the theoretical investigations are supported by experiments with a cantilever beam. In non-conservative systems, the introduction of an intermediate support is known to result in stability transitions between flutter and divergence. This result was confirmed for the new type of non-conservative loading, namely, the terminal dynamic moment. For a cantilever beam with terminal dynamic moment, a rich set of stability transitions were observed for the first time. This includes multiple stability transitions between divergence and flutter and between different modes of flutter. In some cases, the transitions are accompanied by an abrupt change in the critical load, which is commonly referred to as the 03000300jump phenomenon" in the literature. External flow is known to result in non-conservative loading and, therefore, stability transitions are investigated in a hinged beam in external flow. A dynamic moment, proportional to the curvature of the beam at some point along its length, is applied at the hinge. The combined effect of non-conservative loading due to both dynamic moment and external flow is investigated with the objective of developing a mechanism for energy harvesting from flow fields.
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