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.