Non-Linear Vibration Responses

This course covers the comprehensive understanding of non-linear vibration, with a special focus on parametrically excited systems. It starts with the basic understanding of what a parametrically excited system is, using real-life examples such as a cantilever beam subjected to an excitation force or a spring mass damper system. The course further explains the concept of Euler buckling load and how a beam or column starts to buckle when a constant force exceeds this load. It also delves into the concept of parametrically excited systems, where a force is applied in one direction and displacement occurs in a perpendicular direction. The course 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.