Self-excited Vibrations and Stability of Nonlinear Systems

For certain parameters of a mechatronic system, a stable equilibrium or reference state may turn unstable. Oscillations with increasing amplitudes may result, until a stable limit cycle is reached or instead, the structure may fail in the worst case. We observe self-exited vibrations of a nonlinear system after loss of stability (Hopf bifurcation).

From a technical point of view, this kind of vibrations may have severe implications on system design or show detrimental consequences if no mitigation is available. From a theoretical point of view, methods and mathematical tools, which may be applied to systems with a small degree of freedom, are available, but may not sufficiently represent the real, more detailed system behaviour.

Further, understanding of the mechanism behind the observed phenomenon seems to be inevitable to be able to suggest passive or active mitigation strategies. It may include a change of the passive system design, include tuned mass dampers, active system devices, or other remedies.

While simulation is helpful to obtain a better insight into the dynamic behaviour of typically interacting subsystems, experiments are most essential to evaluate findings from theoretical analysis.

The Topics in Detail

  • Unstable modes (weave and wobble) of two- or three-wheeled inclined vehicles with and without human rider
  • Effects from friction induced vibrations and possible electromagnetic interactions at magnetic-track brakes
  • Self-excitation of a tram bogie in sharp curves due to a negative gradient lateral in the creep force-creepage characteristics
  • Unstable motion of the (robot or human) driver-vehicle combination
right a circle left three clouds in a graph

Figure: Periodic solutions after loss of stability at steady-state powerslide