This lesson covers the concept of non-linear vibration, specifically focusing on parametrically excited systems. The lesson begins with an explanation of what a parametrically excited system is, using examples such as a cantilever beam subjected to an excitation force and a spring mass damper system. The lesson then delves into the concept of Euler buckling load, explaining how a column or beam will start to buckle when a constant force exceeds the Euler buckling load. The lesson also discusses the concept of parametrically excited systems, where a force is applied in one direction and displacement occurs in a perpendicular direction. The lesson concludes with a detailed explanation of how to use Floquet theory to determine the stability of a system, and how to find the parametric instability region.

- Understanding of non-linear vibration and its different responses: periodic, quasi-periodic, and chaotic.
- Knowledge of the stability and bifurcation of the periodic response.
- Ability to distinguish between periodic, quasi-periodic, and chaotic responses.
- Understanding of the time response phase portrait, Poincare section, and Lyapunov exponent to characterize the chaotic response.
- Familiarity with different types of systems like the Duffing oscillator and the van der Pol oscillator.

You are being redirected to our marketplace website to provide you an optimal buying experience. Please refer to our FAQ page for more details. Click the button below to proceed further.