Non-Linear Vibration Analysis and Applications

This course covers the comprehensive understanding of non-linear vibration analysis and its applications. It starts with the exploration of non-linear differential equations, focusing on the Runge Kutta method for solving these equations. The course also introduces the use of MATLAB for equation solving and response plotting. It further delves into the concept of state space, phase portraits, and the Lindstedt Poincare method. The course also provides a detailed understanding of the method of multiple scales and the method of averaging for solving non-linear equations of motion. The course concludes with the application of these methods to real-world examples, such as a spring mass damper system subjected to quadratic and cubic non-linearity.