Eigen Value Problems in Vibrations

xThis course covers the comprehensive understanding of Eigen value problems in the context of vibrations. It starts with the exploration of boundary conditions, including geometric and natural or force boundary conditions, and their implications in various problems. The course further delves into the concept of admissible functions, comparison functions, and Eigen functions. It also discusses the significance of self-adjoined systems and positive definite systems in obtaining solutions. The course then moves on to the exact solutions of vibration problems, focusing on the equation of motion, the application of the separation of variable, and the approximation of the uniform beam. It also covers the concept of Eigen vectors, rigid body motion, and flexible modes. The course concludes with the understanding of aeroelastic equations, their types, and the techniques to solve them, such as direct collocation, collocation with generalized coordinates, Galerkin's method, and Rayleigh Ritz approach. An example of a beam with a tip mass is used to illustrate these concepts.

This course has been developed by Prof. C. Venkatesan from IIT Kanpur for NPTEL. It is now accessible through Ansys Innovation Space courtesy of the partnership between Ansys and NPTEL, under the CC BY-SA license. For more details, visit https://nptel.ac.in/courses/101104005.