Non-Linear Vibration and Bifurcation

This course covers the comprehensive understanding of non-linear vibration, damping, and bifurcation. It starts with the exploration of non-linear vibration and different types of damping in non-linear systems, including the concept of a damper and its function in a linear spring mass damper system. The course then delves into the types of damping, such as viscous and Coulomb damping, and their impact on the system. It also introduces active and passive dampers and their manipulation to alter the system's damping property. The course further discusses bifurcation in non-linear vibration, including its types like saddle node, pitchfork, and trans-critical bifurcation, and how to identify them using eigenvalues and Jacobian matrices. The course concludes with the stability and bifurcation of non-linear systems, focusing on static and dynamic bifurcations, and the use of numerical methods to solve differential equations.