Solving Vibration Problems: Exact Solutions — Lesson 2

This lesson covers the solution for vibration problems, specifically focusing on the exact solutions of a simplified problem. The lesson starts with the explanation of the equation of motion and the application of the separation of variable. It then moves on to discuss the differential Eigen value problem and the boundary conditions. The lesson further explains the approximation of the uniform beam and how to get the exact solution. The lesson also covers the concept of Eigen vectors and how to find them. It then discusses the concept of rigid body motion and flexible modes. The lesson concludes with the explanation of how to solve the response problem and the importance of boundary conditions in solving these problems.

Video Highlights

05:28 - Discussion on the solution for the equation and the concept of Eigen vector.
12:49 - Discussion on the concept of Eigen value and Eigen function.
39:12 - Explanation of the concept of torsional vibration and the boundary conditions.
67:13 - Discussion on the concept of mode shape and the solution for the torsion problem.

Key Takeaways

- The equation of motion and the application of the separation of variable are crucial in solving vibration problems.
- The differential Eigen value problem and the boundary conditions play a significant role in finding the solution.
- The approximation of the uniform beam can help in getting the exact solution.
- Understanding the concept of Eigen vectors is essential in solving these problems.
- The concept of rigid body motion and flexible modes are important in understanding the vibration of the system.
- Solving the response problem requires a good understanding of boundary conditions.