09-131 M. Guardia, S. J. Hogan, T. M. Seara

An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator (781K, zip) Aug 3, 09

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Abstract. In this paper, we consider analytically 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 we 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 $B_1$. We show excellent agreement with recent numerical calculations by P. Kowalczyk and P. Piiroinen.

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