Tuning inertial nonlinearity for passive nonlinear vibration control

This paper examines the viability of completely passive control approach based on multiple timescale perturbation methods to elicit desired dynamic cancellation or suppression of nonlinear vibration characteristics. Without appeal to feedback, auxiliary oscillating systems, or nonlinear energy sinks, we demonstrate how inertial nonlinearity balancing can more simply realize distortion-free vibrational responses that are robust to very strong forcing amplitudes across resonant, super-harmonic, and sub-harmonic excitation frequencies as well as opportunities to passively suppress hysteresis, cusp-fold bifurcations, and higher harmonics. Of particular merit are the variegated results concerning critical design points for passive control of sub-harmonic resonances. To most simply capture the essence and broad relevance of the approach, we focus upon a variant of the Duffing oscillator that describes moderately large amplitude vibration of a cantilever beam, various link systems, and kinematically constrained particle motion. The results herein are anticipated to be the most relevant to NEMS/MEMS- based sensing research and technology as well as vibration-based mechanical energy harvesting or mechanical filtering.