Bifurcation control for a parametrically excited cantilever beam by linear feedback

Abstract

In this article, we propose a bifurcation control method for a parametrically excited cantilever beam by linear feedback. Quadratic damping plays a dominant role in the nonlinear response of the parametrically excited cantilever beam, and two transcritical bifurcations can exist in the frequency–response curve. In the relatively high-amplitude excitation or in sweeping the excitation amplitude, there are two saddle-node bifurcations in addition to the transcritical bifurcations. The discontinuous bifurcation as a saddle-node bifurcation induces jumping phenomena in the sweeps of the excitation amplitude and the excitation frequency. In this article, we focus on the case of the excitation amplitude sweep and propose a control method to avoid the jumping phenomena by bifurcation control, i.e. by shifting the bifurcation set based on the linear feedback. The validity of the control method is experimentally confirmed using a simple apparatus.