This lesson covers the study of non-linear vibration analysis, focusing on the solution of non-linear equations of motion using straightforward expansion and the Lindstedt Poincare method. It reviews the use of numerical methods and MATLAB to solve these problems. The lesson also explains the concept of energy equations, the relationship between kinetic and potential energy, and how to plot the phase portrait of a system. It further delves into the Runge Kutta 4th order method for solving differential equations and provides a practical example of solving a simple harmonic motion equation.
00:33 - Solution using straight forward expansion
11:41 - Runge Kutta 4th order method to solve differential equations
30:00 - Straight forward expansion and Lindstedt Poincare method
- The initial conditions of a system are crucial in determining the solution of differential equations.
- The Runge Kutta 4th or 5th order method is widely used for numerical solving of differential equations.
- The phase portrait of a system, which shows how the response varies, can be plotted by plotting displacement and velocity.