Non-Linear Vibration and Oscillations

This course covers the comprehensive understanding of non-linear vibration and oscillations, focusing on single degree of freedom non-linear systems. For instance, the course uses the Duffing equation as a primary example to explore various applications and modifications. It delves into the study of free vibration force vibration, weakly non-linear systems, and the impact of strong and weak forcing. The course also discusses different types of responses such as fixed point response, periodic response, quasi-periodic response, and chaotic response. Furthermore, it explains how to characterize these responses using time response plots, phase portraits, and Poincare sections. The course also provides an understanding of the method of multiple scales and how to analyze the free vibration response of a non-linear system with quadratic and cubic non-linearity. Lastly, it covers the concept of numerical methods for non-linear system analysis, including how to solve a set of non-linear equations and numerical solutions for ODE and DD equations.