Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms

Abstract

For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [ Li & Chen, 2007 ] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly.