Non-Linear Vibration Basics — Lesson 3

This lesson covers the fundamentals of non-linear vibration, marking the third class in the introductory module. The lesson revisits the concepts of ordering techniques and linear systems, which were discussed in the previous class. For instance, if we consider a pendulum, its motion can be described as a linear system when the displacement is small. However, when the displacement becomes large, the system becomes non-linear, and understanding these non-linear vibrations is crucial in many engineering applications.

Video Highlights

00:50 - Ordering techniques
05:55 - Scaling factor
09:23 - Bookkeeping parameter
20:00 - Commonly used nonlinear equations of motion
50:30 - Quantitative analysis of nonlinear systems 

Key Takeaways

- Scaling parameters and bookkeeping parameters are useful in ordering techniques for studying non-linear systems.
- Linear and non-linear equations can be distinguished by applying the Superposition rule.
- If the coefficient of the response in a system's equation of motion is time-varying, the system is known as parametrically excited.
- A system's response can be understood by using a scaling parameter to order the equation of motion.