Free vibration of rectangular plates — Lesson 2

This lesson covers the vibration of rectangular plates, focusing on the eigen frequencies and eigen shapes of these plates. It delves into the decoupling procedure of the undamped free vibration equation using the mode superposition technique. The lesson also discusses different boundary conditions, such as when a plate is simply supported on all edges, clamped, or free. It further explains the natural frequency and mood shapes of plates with two opposite edges simply supported, known as Labis boundary conditions. The lesson concludes with the solution of an initial value problem with a numerical example.

Video Highlights

01:42 - Importance of considering different boundary conditions in vibration problems.
03:04 - Significance of nodal lines in the mode shape of a rectangular plate.
45:55 - Solving for the constants of integration using initial conditions.
57:40 - Calculating the displacement, velocity, and acceleration amplitudes of a rectangular plate.

Key Takeaways

- The vibration of rectangular plates involves eigen frequencies and eigen shapes.
- The decoupling procedure of the undamped free vibration equation can be achieved using the mode superposition technique.
- Different boundary conditions, such as simply supported, clamped, or free edges, can significantly impact the vibration of the plate.
- Labis boundary conditions refer to plates with two opposite edges simply supported.
- The natural frequency and mood shapes of plates can be determined under different boundary conditions.
- Initial value problems can be solved using numerical examples.