Vibration in Continuous Systems

This course covers the comprehensive understanding of vibration in continuous systems. It starts with the exploration of the impact of concentrated masses on the natural frequency of a beam. The course then delves into the analytical solution of a continuous system, the mode supervision technique, and the effect of concentrated masses on the beam's vibration characteristics. For instance, it discusses the vibration characteristics of an aircraft wing and the impact of fuel content in the tank. The course also emphasizes the importance of avoiding dynamic failures such as resonance. It further explores the vibration characteristics of a beam carrying multiple concentrated masses at arbitrary locations. The course concludes with a practical example of a beam carrying any number of concentrated masses at any arbitrary locations. Additionally, the course covers the state-based method used in solving vibration problems, including the technique of solving a vibration problem where continuous and lump parameter systems are involved. It also provides examples of single degree freedom and multi-degree freedom systems.