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Hysteresis models are strongly nonlinear, with slope discontinuities at every load reversal. Stability analysis of hysteretically damped systems is therefore challenging. Recently, a scalable hysteresis model has been reported, motivated by materials with distributed microscopic frictional cracks. In a scalable system, if x(t) is a solution, then so is $$\alpha x(t)$$ αx(t) for any $$\alpha >...
We study a well-known regenerative machine tool vibration model (a delay differential equation) near a codimension 2 Hopf bifurcation point. The method of multiple scales is used directly, bypassing a center manifold reduction. We use a nonstandard choice of expansion parameter that helps understand practically relevant aspects of the dynamics for not-too-small amplitudes. Analytical expressions are...
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