Understanding Finite Cylindrical Shell Vibrations — Lesson 2

This lesson covers the concept of free vibration solutions for all-around simply supported finite cylindrical shells and the development of levy type boundary conditions for a finite shell. It delves into the geometry of a finite shell panel, the governing equations, and the boundary conditions. The lesson also explains the shell constitutive relations, the inertia matrix, and the dynamic matrix. It further discusses the free vibration of a finite circular cylindrical shell subjected to all-round simply supported boundary conditions. The lesson concludes with the explanation of the Levy solution for a circular cylindrical shell for static bending and free vibration cases.

Video Highlights

04:10 - Inertia matrix and its implications
13:09 - Eigenvalue problem for the case of free vibration
15:35 - Levy type boundary condition
33:30- Solution for the case of levy, when it is having a transverse load
38:46 - Use of a mixed formulation for the case of a levy solution

Key Takeaways

- The Levy type boundary conditions are very important in the development of a finite shell, as it helps in the understanding of vibration solutions for all-around simply supported finite cylindrical shells.
- The shell constitutive relations and the inertia matrix play a crucial role in the concept of free vibration of a finite circular cylindrical shell subjected to all-round simply supported boundary conditions.
- The Levy solution also finds potential usage in circular cylindrical shell for static bending and free vibration cases.
- The mixed formulations play a crucial role in accurately predicting the behavior of the shell.