On the Nonlinear Energy Interactions in Harmonically Excited Post-Buckled Flexible Inverted Pendulum in the Presence of Friction

Abstract

Nonlinear energy interaction is a fascinating feature of nonlinear oscillators and has been drawing the attention of researchers since the last few decades. Omnipresent friction in mechanical systems can play a crucial role in modifying these interactions. Using post-buckled flexible inverted pendulum as a candidate system we characterize here, theoretically and experimentally, significant changes in the nonlinear energy transfer in the presence of friction at the input side. Particularly, even with relatively low friction, the energy gets transferred in the higher harmonics of excitation close to a resonant mode as against the transfer to higher modes reported previously. We term this new phenomenon as “excitation harmonic resonance locking.” Theoretical modeling and simulations, considering large deformations, based on assumed modes method, and using a simple friction model reasonably capture the experimental observation. In summary, the paper explicates the role of friction in shifting energy transfer frequencies and can be useful in understanding and designing of oscillators and nonlinear vibrating systems.