Two-to-one internal resonance in bending-torsion modes of an L-shaped cantilever structure

This paper presents an experimental study on the vibrations of an L-shaped cantilever undergoing in-plane and out-of-plane motions in the presence of an internal resonance. To obtain internal resonance phenomena, we tailored the system parameters so that the first torsion and second bending modes’ frequency ratio became commensurable (i.e., the selected frequencies ratio is 1:2). Double-jumping was observed for both the modes and broaden the bandwidth. Considering the natural frequencies in frequency-response plots, the middle resonance position bent to two opposite directions that formed two peaks. Different from the conventional internal resonance cases, the coupled two modes display both in-plane and out-of-plane motions, which displayed rich nonlinear dynamics in the behaviour of the system. The system showed a strong internal energy transfer between the bending and torsion modes.