Multiple spatially localized dynamical states in friction-excited oscillator chains

• Journal of Sound and Vibration

A. Papangelo (a,*), N. Hoffmann (a,b), A. Grolet (c), M. Stender (a), M. Ciavarella (d)

a) Hamburg University of Technology, Department of Mechanical Engineering, Am Schwarzenberg-Campus 1, 21073, Hamburg, Germany

b) Imperial College London, Exhibition Road, London, SW7 2AZ, UK

c) Arts et Métiers ParisTech, Department of Mechanical Engineering, 8 Boulevard Louis XIV, 59000 Lille, France

d) Politecnico di BARI, DMMM Dept., V Gentile 182, 70126, Bari, Italy

URL: https://authors.elsevier.com/a/1WBWO,Whn45Te

https://www.researchgate.net/publication/321698816_Multiple_spatially_lo...

Abstract

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a “snaking-like” bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.