Exploring and exploiting complex nonlinear dynamical states in friction-excited mechanical systems

• Applicant: Professor Dr. Norbert Hoffmann, since 6/2021
• Subject Area: Mechanics ; Engineering Design, Machine Elements, Product Development
• Term: from 2018 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 406233458

• Final Report Year: 2023

Final Report Abstract

Friction plays a central role in diverse technical applications. For example, dry friction is widely adopted to increase fatigue life of mechanical components by means of reducing vibration amplitudes. One of the main problems that largely affects friction-excited engineering structures is the development of Friction-Induced Vibrations (FIV), via self-excitation mechanisms. FIV are commonly encountered in joints/bearings/wheel-rail contact, automotive and aircraft brake systems, in bioengineering, as in hip joint endoprosthesis and in everyday life, as the squeak of door hinges or of a chalk on a blackboard. FIV can generate sound, as exploited when playing violin, or as evidenced in insects which stridulate or use FIV and structure-borne vibrations to communicate. FIV are known to be affected by apparent randomness and low repeatability. Multistability among transitory nonlinear dynamical states could explain those experimental observations. We therefore studied localized and propagating nonlinear dynamical states to gain a deeper understanding of how friction excited dynamical systems evolve through multiple transitory states. The understanding helps at selecting and exploiting the system dynamics to obtain the desired frictional and dissipative behaviour. In a first work package, we studied the possibility for a frictional system to experience spatially localized FIV. e set up a discrete lumped model consisting of several coupled oscillators placed on a frictional moving belt that provided a self-excitation mechanism. The aim of the model was twofold: on one hand to be as simple as possible, while incorporating friction and stiffness nonlinearities, on the other, to introduce the typical discreteness that characterizes the contact of rough surfaces. The lumped model permitted to introduce two major self-excitation mechanisms in FIV: the first due to the decaying characteristic of the friction law with respect to the sliding velocity, the second due to the classical mode-coupling instability. The aim of a second work package was to study in detail the different propagating nonlinear phenomena that characterize frictional systems, in particular fronts and pulses. We started from a linearized version of the equilibrium equations governing the dynamics of the mechanical model, to analyse linear or quasi linear wave propagation. The detailed study of localized and propagating solutions which affects friction-excited dynamical systems was exploited in a third work package. Being aware of the dynamical behaviour of the system, we developed a strategy to select the desired dynamical state. We considered the possibility to properly vary the normal load and the belt velocity to obtain the desired dynamical state: e.g. a front, a pulse, a localized vibration.

Publications

• Multiple spatially localized dynamical states in friction-excited oscillator chains. Journal of Sound and Vibration, 417, 56-64.
  Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M. & Ciavarella, M.
  
• Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators. Journal of Sound and Vibration, 440, 202-211.
  Papangelo, A.; Fontanela, F.; Grolet, A.; Ciavarella, M. & Hoffmann, N.
  
• Nucleation and propagation of excitation fronts in self-excited systems. Physica D: Nonlinear Phenomena, 401, 132176.
  Shiroky, I.B.; Papangelo, A.; Hoffmann, N. & Gendelman, O.V.
  
• Numerical and experimental analysis of the bi-stable state for frictional continuous system. Nonlinear Dynamics, 102(3), 1361-1374.
  Tonazzi, D.; Passafiume, M.; Papangelo, A.; Hoffmann, N. & Massi, F.
  
• The Basin Stability of Bi-Stable Friction-Excited Oscillators. Lubricants, 8(12), 105.
  Stender, Merten; Hoffmann, Norbert & Papangelo, Antonio
  
• Experimental observations of nonlinear vibration localization in a cyclic chain of weakly coupled nonlinear oscillators. Journal of Sound and Vibration, 497, 115952.
  Niedergesäß, B.; Papangelo, A.; Grolet, A.; Vizzaccaro, A.; Fontanela, F.; Salles, L.; Sievers, A.J. & Hoffmann, N.
  
• Nonlinear vibration localisation in cyclic engineering structures. PhD Thesis, Hamburg University of Technology
  Niedergesäß, B.