Bifurcation Analysis of Stick-Slip Motion of the Vibration-Driven System with Dry Friction

Abstract

This paper is concerned with the vibration-driven system which can move due to the periodic motion of the internal mass and the dry friction; the system can be modeled as Filippov system and has the property of stick-slip motion. Different periodic solutions of stick-slip motion can be analyzed through sliding bifurcation, two-parameter numerical continuation for sliding bifurcation is carried out to get the different bifurcation curves, and the bifurcation curves divide the parameters plane into different regions which stand for different stick-slip motion of the periodic solution. Furthermore, continuations with additional condition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math> are carried out for the directional control of the vibration-driven system in one period; the curves divide the parameter plane into different progressions.