An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator

Marcel Guardia, SJ Hogan, Tere Martinez-Seara

Research output: Contribution to journalArticle (Academic Journal)peer-review

47 Citations (Scopus)

Abstract

In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: $F$, which corresponds to the intensity of the friction, and $\omega$, the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and focus our attention on two of them: $A_1:=(\omega\ii, F)=(2, 1/3)$ and $B_1:=(\omega\ii, F)=(3,0)$. We derive analytic expressions in ($\omega\ii$, $F$) parameter space for the codimension-1 bifurcation curves that emanate from $A_1$ and $B_1$. Our results show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen.
Translated title of the contribution An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator English 769 - 798 29 SIAM Journal on Applied Dynamical Systems 9 3 https://doi.org/10.1137/090766826 Published - 2010

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