Parametrically Excited Pneumatic Artificial Muscle — Lesson 2

This lesson covers the fundamental concepts of non-linear vibration. It provides an in-depth understanding of the subject, explaining the differences between linear and non-linear vibrations. For instance, the lesson might discuss how non-linear vibrations can occur in systems where the forces acting on them are not proportional to the displacement, unlike in linear vibrations. This lesson is ideal for students and professionals who want to gain a comprehensive understanding of non-linear vibrations.

Video Highlights

01:20 - Example of a parametrically excited system
04:10 - Resonance conditions in parametrically excited systems
07:52 - Floquet theory and its application
12:28 - Monodromy matrix and stability of systems
24:44 - Instability region in the Matthew equation using Hill's Infinity determinant method

Key Takeaways

- The Hills equation and Mathieu equation are used to model parametrically excited systems.
- Parametrically excited systems can exhibit different types of resonance conditions such as principle parametric resonance and combination parametric resonance.
- The stability of a parametrically excited system can be determined by finding the eigenvalues of the monodromy matrix.