Nonlinear Vibrations

Nonlinear Vibrations

  • Course code

    ME 613

  • L-T-P-C


  • Syllabus


  • Eligible Programmes


  • Nonlinear Vibrations

    Mechanical Vibrations Dynamics of conservative and non-conservative systems; Phase planes, fixed points; Local and global stability, Lyapunov theory; Analytical solution methods: Harmonic balance, equivalent linearization, perturbation techniques (Linstedt- Poincare, Multiple Scales, Averaging – Krylov-Bogoliubov-Mitropolsky); Damping mechanisms; self-excited systems, Van der Pol’s oscillator. Forced oscillations of SDOF systems, Duffing’s oscillator; primary-, secondary-, and multiple- resonances; period- multiplying bifurcations; Poincare’ maps, point attractors, limit cycles and their numerical computation, strange attractors and chaos; Types of bifurcations, Lyapunov exponents and their determination, fractal dimension. Parametric excitations, Floquet theory, Mathieu’s and Hill’s equations; effects of damping and nonlinearity; MDOF systems, solvability conditions, internal (autoparametric) resonances; Hopf bifurcation and panel flutter example. Application to continuous systems.


    [1] Nayfeh, A. H., and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, 1979..

    [2] Hayashi, C. Nonlinear Oscillations in Physical Systems, McGraw-Hill, 1964.

    [3] Evan-Ivanowski, R. M., Resonance Oscillations in Mechanical Systems, Elsevier, 1976.

    [4] Nayfeh, A. H., and Balachandran, B., Applied Nonlinear Dynamics, Wiley, 1995.

    [5] Seydel, R., From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier, 1988.

    [6] Moon, F. C., Chaotic & Fractal Dynamics: An Introduction for Applied Scientists and Engineers, Wiley, 1992.

    [7] Srinivasan, P. Nonlinear Mechanical Vibrations, New Age International, 1995.

    [8] Rao, J. S., Advanced Theory of Vibration: Nonlinear Vibration and One-dimensional Structures, New Age International, 1992.