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The exhaustive list of topics in Nonlinear Vibration in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Nonlinear Vibration.
  • Mechanical vibration:
  • Linear nonlinear systems.
  • Types of forces and responses.
  • Conservative and non conservative systems.
  • Equilibrium points.
  • Qualitative analysis.
  • Potential well, centre, focus.
  • Saddle-point.
  • Cusp point.
  • Commonly observed nonlinear phenomena:
    • Multiple response.
    • Bifurcations.
    • Jump phenomena.
    • Force and moment based approach.
    • Lagrange Principle.
    • Extended Hamilton’s principle.
    • Multi body approach.
    • Linearization techniques.
    • Development of temporal equation using Galerkin’s method for continuous system.
    • Ordering techniques.
    • Scaling parameters.
    • Book-keeping parameter.
  • Commonly used nonlinear equations:
    • Duffing equation.
    • Van der Pol’s oscillator.
    • Mathieu’s and Hill’s equations.
    • Straight forward expansions.
    • Sources of nonuniformity.
    • Harmonic Balancing method.
    • Linstedt-Poincare’ method.
    • Method of Averaging.
    • Method of multiple scales.
    • Method of normal form.
    • Incremental Harmonic Balance method.
    • Lyapunov stability criteria.
    • Stability analysis from perturbed equation.
    • Stability analysis from reduced equations obtained from perturbation analysis.
    • Bifurcation of fixed point response.
  • Static bifurcation:
    • Pitch fork.
    • Saddle-node.
    • Trans-critical bifurcation.
    • Bifurcation of fixed point response.
    • Dynamic bifurcation: Hopf bifurcation.
    • Stability and Bifurcation of periodic response.
    • Monodromy matrix.
    • Poincare’ section.
    • Time response.
    • Runga-Kutta method.
    • Wilson- Beta method.
  • Frequency response curves:
    • Solution of polynomial equations.
    • Solution of set of algebraic equations.
  • Basin of attraction:
    • Point to point mapping.
    • Cell-to-cell mapping.
    • Poincare’ section of fixed-point.
    • Periodic.
    • Quasi-periodic and chaotic responses.
    • Lyapunov exponents.
    • FFT analysis.
    • Fractal Dimensions.
    • SDOF Free-Vibration: Duffing Equation.
    • SDOF Forced-Vibration: Van der pol’s Equation.
    • Parametrically excited system- Mathieu-Hill’s equation.
    • Floquet Theory.
    • Multi-DOF nonlinear systems.
    • Continuous system: Micro-cantilever beam analysis.