NON-LINEAR BEAM OSCILLATIONS EXCITED BY LATERAL FORCE AT COMBINATION RESONANCE

Non-linear oscillations of a beam subjected to a periodic force at a combination resonance are considered. Using the Galerkin method, a partial differential equation of oscillations is reduced to a system of ordinary differential equations with a small parameter. A system of three autonomous differential equations is derived, the multiple scales method being used. Qualitative properties of trajectories are analyzed. The Naimark-Sacker bifurcations at the combination resonance are analyzed by the center manifold method. Almost-periodic oscillations of a beam arise due to these bifurcations. These oscillations are investigated qualitatively and numerically.