Generalized Harmonic Balance Method — Lesson 3

This lesson covers the concept of non-linear vibration and the method of averaging. It begins with a recap of the application of the method of multiple scales to non-linear systems, particularly forced vibration. The lesson then delves into the weak form of forcing and damping, and the use of the term epsilon to represent this. The lesson further explains the procedure of the method of multiple scales, the separation of different orders of epsilon, and the solution of the equation. The lesson concludes with the concept of reduced equations, autonomous systems, and steady state.

Video Highlights

01:41 - Method of multiple scales and its application
08:31 - Method of averaging and its techniques
12:17 - Duffing oscillator and the Krylov Bogoliubov technique
40:44 - Krylov Bogoliubov Metropolis (KBM) method and its application

Key Takeaways

- The method of multiple scales is applied to non-linear systems, particularly forced vibration.
- The weak form of forcing and damping is represented by the term epsilon.
- The method of multiple scales involves separating different orders of epsilon and solving the equation.
- Reduced equations, which are known as autonomous systems, do not have a time term explicitly appearing on the right-hand side.
- In a steady state, the variables A and gamma are no longer functions of time.