# InfoCoBuild

## Nonlinear Vibration

Nonlinear Vibration. Instructor: Prof. S. K. Dwivedy, Department of Mechanical Engineering, IIT Guwahati. This course is meant for the senior undergraduate and postgraduate students of Mechanical Engineering, Civil Engineering and Aerospace Engineering. The course provides a brief introduction to linear and nonlinear vibration, and then it discusses the development of nonlinear governing equation of motion, analytical solution methods, stability and bifurcation analysis, numerical techniques, and applications of nonlinear vibrations. (from nptel.ac.in)

 Introduction to Nonlinear Systems

 Introduction Lecture 01 - Introduction to Nonlinear Systems Lecture 02 - Review of Linear Vibrating Systems Lecture 03 - Phenomena associated with Nonlinear Systems Lecture 04 - Commonly Observed Phenomena in Nonlinear Systems Derivation of Nonlinear Equation of Motion Lecture 05 - Force and Moment based Approach Lecture 06 - Hamilton's Principle and Lagrange Principle Lecture 07 - Derivation of Equation of Motion of Nonlinear Discrete System Lecture 08 - Derivation of Equation of Motion of Nonlinear Continuous System Lecture 09 - Derivation of Equation of Motion of Nonlinear Continuous System (cont.) Lecture 10 - Ordering Techniques in the Nonlinear Equations Solution of Nonlinear Equations of Motions Lecture 11 - Qualitative Analysis - Straight Forward Expansions Lecture 12 - Numerical Method - Straight Forward Expansions Lecture 13 - Lindstedt-Poincare Method Lecture 14 - Method of Multiple Scales Lecture 15 - Method of Harmonic Balance Lecture 16 - Method of Averaging Lecture 17 - Generalized Method of Averaging Lecture 18 - Krylov-Bogoliubov-Mitropolsky Method of Averaging Lecture 19 - Incremental Harmonic Balance Method, Intrinsic Multiple Harmonic Balance Method Lecture 20 - Modified Lindstedt Poincare Method Stability and Bifurcation Analysis of Nonlinear Responses Lecture 21 - Stability and Bifurcation of Fixed Point Response 1 Lecture 22 - Stability and Bifurcation of Fixed Point Response 2 Lecture 23 - Stability and Bifurcation of Fixed Point Response 3 Lecture 24 - Stability and Bifurcation of Fixed Point Response 4 Lecture 25 - Stability and Bifurcation Analysis of Periodic Responses Lecture 26 - Bifurcation of Periodic Responses, Introduction to Quasi-Periodic and Chaotic Responses Lecture 27 - Quasi-Periodic and Chaotic Responses Numerical Methods Lecture 28 - Numerical Methods to Obtain Roots of Characteristic Equation and Time Response Lecture 29 - Numerical Methods to Obtain Time Response Lecture 30 - Numerical Methods to Obtain Frequency Response Applications Lecture 31 - Free Vibration of Single Degree of Freedom Nonlinear Systems With Cubic and Quadratic Nonlinearities Lecture 32 - Free Vibration of Single Degree of Freedom Nonlinear Systems With Cubic and Quadratic Nonlinearities: Effect of Damping Lecture 33 - Free Vibration of Multi-Degree of Freedom Nonlinear Systems With Cubic and Quadratic Nonlinearities Lecture 34 - Forced Vibration of Single Degree of Freedom Nonlinear Systems With Cubic Nonlinearities Lecture 35 - Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System Lecture 36 - Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System (cont.) Lecture 37 - Nonlinear Forced-Vibration of Multi-Degree-of-Freedom System Lecture 38 - Nonlinear Vibration of Parametrically Excited System: Axially Loaded Sandwich Beam Lecture 39 - Nonlinear Vibration of Parametrically Excited System: Elastic and Magneto-Elastic Beam Lecture 40 - Nonlinear Vibration of Parametrically Excited System with Internal Resonances

 References Nonlinear Vibration Instructor: Prof. S. K. Dwivedy, Department of Mechanical Engineering, IIT Guwahati. This course is meant for the senior undergraduate and postgraduate students of Mechanical Engineering, Civil Engineering and Aerospace Engineering.