Analysis of the Dynamic Stiffness, Hysteresis Resonances and Complex Responses for Nonlinear Spring Systems in Power-Form Order

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro (e.g., rolling bearings considering Hertzian restoring between elements and bearing raceways) or micro the cantilever probe system atomic microscopy) scale mechanical systems, resonance could cause serious problems wear, fatigue, vibration, noise, which has attracted widespread attention. In present paper, softening/hardening stiffness characteristics continuous one-sided power-form spring addressed, respectively, by analysis monotone features resonant frequency-response skeleton lines. Herein, period-n solution branch its stability obtained harmonic balance alternating frequency/time domain (HB–AFT) method Floquet theory. Compared with previous studies, this paper will furtherly clarify influences externally normal load, power form exponent term, excitation amplitude on general systems. addition, for a contact, phenomena primary super/sub-harmonic hysteretic resonances inducing period-doubling, folding bifurcation, coexistence multiple solutions demonstrated. Besides, it gives evolution mechanism two types intermittency chaos system. The overall results may have certain basic theoretical significance engineering values control vibration noise