Introduction to Nonlinear Vibrations

Content
  • dynamic systems
  • basic ideas of asymptotic methods
  • perturbation methods: Linstedt-Poincare, averaging, multiple scales
  • limit cycles
  • nonlinear resonance
  • basics of the bifurcation analysis, bifurcation diagrams
  • types of bifurcations
  • discontinuous systems
  • dynamic chaos
Language of instructionGerman
Bibliography
  • Hagedorn P. Nichtlineare Schwingungen. Akademische Verlagsgesellschaft, 1978.
  • Nayfeh A.H., Mook D.T. Nonlinear Oscillation. Wiley, 1979.
  • Thomsen J.J. Vibration and Stability, Order and Chaos. McGraw-Hill, 1997.
  • Fidlin A. Nonlinear Oscillations in Mechanical Engigeering. Springer, 2005.
  • Bogoliubov N.N., Mitropolskii Y.A. Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach, 1961.
  • Nayfeh A.H. Perturbation Methods. Wiley, 1973.
  • Sanders J.A., Verhulst F. Averaging methods in nonlinear dynamical systems. Springer-Verlag, 1985.
  • Blekhman I.I. Vibrational Mechanics. World Scientific, 2000.
  • Moon F.C. Chaotic Vibrations – an Introduction for applied Scientists and Engineers. John Wiley & Sons, 1987.