Journal of Theoretical
and Applied Mechanics

51, 3, pp. 687-696, Warsaw 2013

An analysis of the primary and superharmonic contact resonances – Part 2

Robert Kostek
This paper presents results of investigations of non-linear normal contact micro-vibrations excited by a harmonic force in a system of two bodies in planar contact. The system models, for instance, slide units of machine tools or their positioning systems. The main aim of the computational analysis is to present resonance graphs and time histories obtained with numerical and perturbation methods. Good agreement between the perturbation and numerical results leads to the conclusion that the perturbation solution is correct. The obtained perturbation solution describes well both the primary resonance and the superharmonic resonances. Characteristic phenomena typical for non-linear vibrations are depicted, viz. asymmetry of vibrations, multi-harmonic vibrations, non-elliptical phase portraits, loss of contacts, bending resonance peaks, bi-stabilities, and multi-stability.
Keywords: non-linear contact; vibrations; superharmonic resonance; multi-stability