Parametric Instability of Sandwich Plate — Lesson 3

This lesson covers the study of non-linear vibration and its various applications, particularly focusing on parametrically excited systems. The lesson delves into the derivation of the equation of motion for a parametrically excited system, using the finite element method. It further explains how to determine the parametric instability region using the Sue method. The lesson also revisits the Proquade theory and the method of multiple scales to find the instability region. The lesson concludes with the study of a multi-degree of freedom system and a continuous system to understand the instability region and the response of the parametrically excited system.

Video Highlights

00:44 - Static and Dynamic Bifurcations
02:58 - Introduction to sandwich plate and its applications
14:00 - Finite element modeling of isotropic sandwich plate 
24:40 - Study of resonance conditions
31:00 - Study of LPRE

Key Takeaways

- The equation of motion for a parametrically excited system can be derived, and the parametric instability region can be found using the Sue method.
- Knowledge of how to derive the equation of motion for a parametrically excited system.
- The Proquet theory and the method of multiple scales can be used to find the instability region of a parametrically excited system.
- Sandwich plates, particularly those with viscoelastic cores, find applications in industries such as space, automotive, and transportation engineering.
- The response of a parametrically excited system can be influenced by factors such as the stiffness of the material and the presence of damping properties.