Dynamical behavior of a nonlinear single-degree-of-freedom system with negative viscous and positive frictional damping. (English) Zbl 1238.70017

Jakšić, Nikola

Meccanica 43, No. 3, 365-367 (2008).

From the text (conclusion): This short note presents the dynamical behavior of an autonomous nonlinear s.d.o.f. system. A negative viscous damping model and the Coulomb dry friction model are added to the undamped linear system. Where \(-1 < \delta <0\) an unstable limit cycle appears, dividing the phase-plane into the region of stable motion (inside the limit cycle) and unstable motion (outside the limit cycle). In the case of \(\delta \leq -1\) heteroclinic orbits divide the phase-plane into regions of stable and unstable motion. Criteria are established to find out the stability of the the given initial condition.

MSC:

70K40	Forced motions for nonlinear problems in mechanics
70F40	Problems involving a system of particles with friction

Keywords:

nonlinear system; Coulomb friction; negative viscous damping; stability of motion; mechanics of solids and structures

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