State-Based Method in Vibration Problems — Lesson 2

This lesson covers the concept of the state-based method used in solving vibration problems. It delves into the technique of solving a vibration problem where continuous and lump parameter systems are involved. The lesson further explains the formulation known as the state-based solution method, which can be used for general types of damping. It also discusses the development of state-based equations, eigenvalues, and eigenvectors of the system. The lesson provides examples of single degree freedom and multi-degree freedom systems. It also proves whether the authority conditions of the eigenvectors in the state-based method exist or not.

Video Highlights

03:16 - Discussion on the method of dynamic analysis, useful for forming solving the first order OD.
09:00 - Explanation of the concept of proportional damping and non-proportional damping.
22:06 - Demonstration of how to construct the damping Matrix using the Matlab procedure.
40:14 - Introduction to the state base equation for MDF system with General case of damping.
55:01 - Explanation of the Authority condition of the complex eigenvectors.

Key Takeaways

- The state-based method is a technique used in solving vibration problems involving continuous and lump parameter systems.
- This method transforms the second-order system of dynamic equations into a first-order system, making the integration process simpler.
- The state-based method is particularly useful in problems where the control of vibration is required, such as in active control of vibration.
- The method can handle general types of damping, including non-proportional damping.
- The method has the existence of authority conditions of the eigenvectors.