STABILITY AND BIFURCATION-ANALYSIS OF THE NONLINEAR DAMPED LEIPHOLZ COLUMN

An analysis of stability and self-excited vibrations of the non-linear damped Leipholz column is presented in this paper. The theory of bifurcations is used. Geometric nonlinearity corresponding to moderate deflections is considered, and the presence of both external and internal damping is assumed. The near-critical behaviour of the system under both tension and compression loads is studied, including construction of the periodic vibration and analysis of stability of the corresponding limit cycle. It is shown that, when geometrically non-linear, the Leipholz column under tension always exhibits a supercritical Hopf bifurcation in which a stable limit cycle occurs and develops. When compressive follower forces are considered, flutter can occur either as a supercritical bifurcation into a stable limit cycle if the internal damping is slight, or a subcritical bifurcation into an orbitally unstable limit cycle existing in the stable region of equilibrium when the internal damping is sufficiently high. A catastrophic loss of equilibrium stability is then not excluded. © 1992.