Vibration Analysis and Rayleigh's Method — Lesson 2

This lesson covers the concept of vibration analysis and the application of Rayleigh's method in determining natural frequencies. It delves into the principles of energy minimization and the use of assumed deflected functions to calculate potential and kinetic energy. The lesson also explains how Rayleigh's method can be extended to include more terms in the assumed deflected function, thereby increasing the accuracy of results and extracting higher frequencies. It further illustrates the application of these concepts through examples of a non-uniform beam and a cantilever beam. The lesson concludes with a discussion on the importance of selecting the right shape function to improve the accuracy of the method.

Video Highlights

01:15 - Explanation of how the release method is extended to include more terms in the assumed deflected function.
03:14 - Release method and how it has been extended to find out the eigen frequencies of a structural system.
05:48 - Choosing a displacement function that satisfies both the displacement and force boundary conditions.
21:40 - Using the release principle to extract the eigen frequencies of a system.
39:10 - Example of a cantilever beam of uniform cross-section and how to calculate its natural frequencies using the release method.

Key Takeaways

- Rayleigh's method is an approximate method for vibration analysis that uses energy principles and assumed deflected functions.
- The method can be extended to include more terms in the assumed deflected function, thereby increasing the accuracy of results and extracting higher frequencies.
- The assumed deflected function should satisfy both the displacement and force boundary conditions to ensure accurate results.
- The method can be applied to different structures, such as a non-uniform beam or a cantilever beam.
- The selection of the right shape function plays a crucial role in improving the accuracy of the method.