This lesson covers the concept of non-linear vibration and its applications. It delves into the study of different systems, such as the cantilever beam, magneto elastic beam, and viscoelastic beam, and their base excitation. The lesson further explores the non-linear dynamics of these systems, including the application of axial load leading to parametrically excited systems. The process of deriving the spacio-temporal equation and converting it into its temporal form using the Galerkin method is also discussed. The lesson concludes with an examination of different resonance conditions, system stability, bifurcation points, and the characterization of fixed point periodic, quasi-periodic, and chaotic responses.
06:58 - PEH introduction
08:00 - Applications
20:08 - Mathematical Modeling
33:23 - Stability analysis
34:30 - Results and discussion
- Non-linear vibration has diverse applications in different systems.
- The Galerkin method is used to convert the spacio-temporal equation into its temporal form.
- Different resonance conditions can affect the stability of the system.
- Bifurcation points, including pitchfork, saddle node, and hop bifurcation points, play a crucial role in system dynamics.
- Fixed point periodic, quasi-periodic, and chaotic responses can be characterized using the Poincare section.