Existence and stability of limit cycles in a delayed dry-friction oscillator |
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| Authors: | Julián M Londoño Giorgio Serino Mario di Bernardo |
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| Institution: | 1.Dep. of Structural Engineering,University of Naples “Federico II”,Naples,Italy;2.Dep. of Systems and Computer Engineering,University of Naples “Federico II”,Naples,Italy;3.Department of Engineering Mathematics,University of Bristol,Bristol,UK |
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| Abstract: | Periodic, chaotic, chattering, and bifurcation behavior are fundamental consequences of the nonsmooth nature of systems with
dry friction. This work is concerned with the analysis of a single degree of freedom system which is additionally damped by
a delayed dry friction device. We get a complete set of closed-form expressions to describe the dynamics of the delay-induced
phenomena exhibited by the system. The conditions to determine the existence and stability of limit cycles are clearly defined.
This analysis is addressed in the context of both classic stability theory for nonlinear systems and the qualitative theory
of Piecewise Smooth Dynamical Systems. Through exhaustive numerical simulations the effectiveness of the set of closed-form
expressions is confirmed. Excellent agreement was found between the numerical and analytical results. |
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