Introduction to nonlinear vibrations

Lecturer(s): Joël PERRET LIAUDET, Fabrice THOUVEREZ
Course ⋅ 16 hPW ⋅ 8 hStudy ⋅ 4 h


This course is an introduction to the main phenomena related to the problems of nonlinear vibrations. The minimum knowledge and rules useful to the engineer will be introduced to diagnose and treat these problems. Many examples from engineering problems will illustrate the course. We can mention the dynamics of frictional contacts (squeal noise), clearance systems (rattling), rotors dynamics and gear transmissions, bridges subjected to wind .


nonlinear vibrations, dynamics of systems, stability, bifurcations, nonlinear modes, principal resonances, super-harmonics, sub-harmonics, self-sustained vibrations, galloping, flutter phenome


  • Generalities on nonlinear vibratory problems in engineering, classification of sources
  • Description and Analysis Tools, Nonlinear Modal Analysis
  • Loss of equilibrium stability and self-sustained vibrations (galloping phenomena, squealing)
  • Phenomena of nonlinear resonances (principal and harmonics)
  • Concept of strange responses (chaos)
  • Introduction to methods specific to the treatment of nonlinear phenomen

Learning Outcomes

  • detect and / or diagnose nonlinear vibration phenomena
  • characterize the main kinds of vibration responses
  • identify the main phenomena that lead to these dynamic responses
  • model some nonlinear problems and use specific methods


final = 50% knowledge + 50% know how knowledge = 100% final exam know how = 100% continuous monitoring