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.
• 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.
• 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.