Journal of Theoretical
and Applied Mechanics

51, 4, pp. 799-812, Warsaw 2013

An analysis of the primary and superharmonic contact resonances – Part 3

Robert Kostek
This paper presents a study of non-linear normal contact vibrations excited by an external harmonic force in a system containing two bodies being in planar contact. The system models, for instance, the slide unit of machine tools or positioning systems. The presented results, which are obtained both with numerical and perturbation methods, show clearly the evolution of resonance phenomena under various excitation amplitudes. Apart from the primary resonance, a number of super-harmonic resonances has been excited in the non-linear single-degree-of-freedom system. Hence, a resonance graph contains a number of peaks being below the natural frequency. The contact vibrations are associated with strongly non-linear phenomena like: asymmetry of vibrations, loss of contact, bending resonance peak, multi-stability, period-doubling bifurcations, chaotic vibrations, which are far from linear dynamics. These phenomena are presented and described in this article.
Keywords: non-linear contact; vibrations; superharmonic resonance; multi-stability; bifurcation