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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)

Lecture 37 - Nonlinear Forced-Vibration of Multi-Degree-of-Freedom System


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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