Non-Linear Vibration Models — Lesson 1

This lesson covers the derivation of non-linear vibration equations. It begins with an introduction to the second module, which focuses on deriving the equation of motion. The lesson then delves into the differences between linear and non-linear equations of motion, explaining that the latter is an extension of the former. The lesson also discusses two types of models: discrete or lumped parameter models and distributed or continuous models. It provides examples of discrete models, such as a single spring mass damper system, which is a single degree of freedom (SDOF) system.

Video Highlights

00:40 - Nonlinear equation of motion
04:29 - Equation of motion using force or movement
13:44 - Newton's second law and D'Alembert's principle
29:49 - Equation of motion using moment method
33:45 - Equation of motion for two degrees of freedom systems

Key Takeaways

- Physical systems can be modeled using discrete or lumped parameter models, or distributed or continuous models.
- Depending on the application, a distributed mass system can be reduced to a lumped parameter system by truncating the number of degrees of freedom.
- D'alembert principle is useful in reducing a dynamic system to an equivalent static system where the virtual work principle can be applied.
- Newton's second law can be difficult to apply in systems with multiple degrees of freedom due to the complexity of finding the constraint forces.