Gravitational effects and mode interactions of vertical cantilever beams

Abstract

As a basic structure and a fundamental vibration issue, the vibration of cantilever structures has been thoroughly studied, and there are some generally accepted conclusions, for example, internal resonance does not take place in the transverse vibration of a basic cantilever beam. In this study, by including 3:1 internal resonance caused by gravity, mode interactions of hanging cantilever beams are firstly presented in the primary and secondary external resonance. The second mode can be easily and remarkably stimulated in the primary resonance, while the first mode response can also be generated in the secondary resonance. Besides, internal resonance complicates the dynamic characteristics of mode responses, such as ring-like and other strange response shapes, and further influences the mode interactions in the primary resonance. Furthermore, with non-strict internal resonance and large excitation amplitude, the chaotic motion can be achieved in the secondary resonance, which may not occur in the primary resonance. In summary, the research in this paper shows that, although it is a fundamental subject of vibration, there are still some unknown phenomena in the vibration of cantilever beams. Understanding these phenomena will undoubtedly help design engineering systems and control structural vibration.