Principles of Non-Linear Vibration

This course covers the principles and equations of non-linear vibration. It starts with the derivation of non-linear vibration equations, highlighting the differences between linear and non-linear equations of motion. The course further explores two types of models: discrete or lumped parameter models and distributed or continuous models. For instance, a single spring mass damper system, a single degree of freedom system, is used as an example of a discrete model. The course also delves into the principles of non-linear vibration, focusing on the derivation of non-linear equations of motion using Newton's second law, D'alembert's principle, and the Lagrange principle. The application of these principles to distributed mass systems, also known as continuous systems, is discussed in detail. For example, the Lagrange principle is used to derive the equation of motion for a pendulum, a common example of a non-linear vibration system.

This course has been developed by Prof. S.K. Dwivedy from IIT Guwahati 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/112103300.