On the Stability of Elastic Systems Subjected to Nonconservative Forces

Free motions of a linear elastic, nondissipative, two-degree-of-freedom system, subjected to a static nonconservative loading, are analyzed with the aim of studying the connection between the two instability mechanisms (termed divergence and flutter by analogy to aeroelastic phenomena) known to be possible for such systems. An independent parameter is introduced to reflect the ratio of the conservative and nonconservative components of the loading. Depending on the value of this parameter, instability is found to occur for compressive loadings by divergence (static buckling), flutter, or by both (at different loads) with multiple stable and unstable ranges of the load. In the latter case either type of instability may be the first to occur with increasing load. For a range of the parameter, divergence (only) is found to occur for tensile loads. Regardless of the non-conservativeness of the system, the critical loads for divergence can always be determined by the (static) Euler method. The critical loads for flutter (occurring only in nonconservative systems) can be determined, of course, by the kinetic method alone.