Passive subharmonic elimination

Abstract

This paper investigates an approach to passively eliminate subharmonic responses in nonlinear oscillators forced at resonance. A general framework is developed for identifying asymptotic levels where parameter values can be passively tuned to achieve dynamic cancellation of subharmonics. The results apply to oscillators with an arbitrary nonlinear structure. Due to its breadth of application from atomic force microscopy to aeromechanics, the methodology is demonstrated using a reduced-order model for an inextensible cantilevered beam carrying a concentrated mass. The concentrated mass provides a simple opportunity to vary parameters to achieve subharmonic elimination characteristics. Nonlinear simulation results indicate that parameter choices derived from the perturbation scheme are robust for a significant range of forcing amplitudes. Limits of the harmonic elimination and the sensitivity of the result to control parameters are discussed as well.