Forced vibration of rectangular plates — Lesson 3

This lesson covers the vibration analysis of rectangular plates, particularly focusing on plates that are simply supported along all edges. The lesson discusses the free vibration characteristics of plates with different boundary conditions, the dynamic response of plates subjected to harmonic excitation, and the response of plates subjected to moving loads. The lesson also explains the concept of eigen frequency and eigen functions, and how they are used in vibration analysis. For instance, a rectangular plate subjected to a harmonic force at a certain point can be analyzed using these concepts. The lesson also provides a numerical example to illustrate the effect of a moving load on the dynamics of a plate.

Video Highlights

01:26 - Explanation of the solution for eigen frequency and eigen functions.
02:55 - Explanation of the problem of a simply supported plate subjected to a moving load.
33:10 - Effect of a harmonic force on the vibration of a rectangular plate.
67:29 - Explanation of the effect of a moving load on the dynamics of a plate.

Key Takeaways

- The vibration analysis of rectangular plates involves understanding the free vibration characteristics of plates with different boundary conditions.
- Eigen frequency and eigen functions play a crucial role in vibration analysis.
- The dynamic response of a plate subjected to harmonic excitation can be analyzed using these concepts.
- The response of a plate subjected to a moving load can also be analyzed, providing insights into the effect of the moving load on the dynamics of the plate.
- Displacement and bending moment of a plate can be calculated using these concepts.