Forced vibration of shape memory alloy spring oscillator and the mechanism of sliding bifurcation with dry friction

Abstract

The main purpose of this article is to investigate the qualitative effects of different factors on the response of forced vibration of shape memory alloy spring oscillator. Specially, the introduction of dry friction factor causes the governing equations to change from a smooth system to a (Filippov-type) non-smooth system in which the sliding phenomenon was observed. The mechanism, geometric structure, and analytic conditions of sliding bifurcations in a general n-dimensional piecewise smooth system were discussed in detail. The theoretical results obtained are verified by numerical analysis, and the feasibility of involved theories is estimated by calculation of sliding time.