This lesson covers the study of numerical methods for non-linear system analysis, particularly in the context of vibration. It delves into the process of solving a set of non-linear equations, including single equations and characteristic equations. The lesson also explores the application of these methods in determining the frequency function and response of a system. It further discusses the characterization of different types of responses such as fixed point, periodic, quasi-periodic, and chaotic responses. The lesson concludes with an introduction to plotting the time response phase portrait, Poincare section, FFT, and Lyapunov exponents.

- The study of non-linear vibrations in a flexible beam involves understanding different types of beams like elastic, viscoelastic, and magneto-elastic beams.
- The response of a system to vibration can be periodic, quasi-periodic, or chaotic, particularly in the case of combination parametric resonance conditions.
- Bifurcation points in the system, such as saddle node and Hopf bifurcation points, can significantly impact the system's stability and response to resonance.

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