Harmonic Balance method — Lesson 1

This lesson covers the introduction to the third module of non-linear vibration. It provides a comprehensive understanding of the subject, starting with the first lecture. The lesson is designed to help learners grasp the fundamental concepts of non-linear vibration, which is a crucial aspect of mechanical engineering. For instance, understanding non-linear vibration can help in designing structures that can withstand different types of forces and vibrations.

Video Highlights

02:35 - Concept of state vectors and the motion of a system
09:26 - Quasi-periodic response
25:35 - Potential well concept for conservative SDOF system
38:40 - Straight forward expansion method for solving non-linear equations

Key Takeaways

- Non-linear vibrations can be studied using numerical solution methods, such as the harmonic balance method and the Lindstedt Poincare method.
- The state vectors of a system can represent the motion of the system.
- The solution of a non-linear differential equation can yield different types of responses depending on the system and the equation used.
- In non-linear equations, the complementary function and the particular integral are two parts of the total solution.