Contents:
Introduction – Mechanical vibration: Linear nonlinear systems, types of forces and responses – Conservative and non conservative systems, equilibrium points, qualitative analysis, potential well, centre, focus, saddle-point, cusp point – Commonly observed nonlinear phenomena: multiple response, bifurcations, and jump phenomena.
Derivation of nonlinear equation of motion : Force and moment based approach – Lagrange Principle – Extended Hamilton’s principle – Multi body approach – Linearization techniques – Development of temporal equation using Galerkin’s method for continuous system – Ordering techniques, scaling parameters, book-keeping parameter. Commonly used nonlinear equations: Duffing equation, Van der Pol’s oscillator, Mathieu’s and Hill’s equations.

Approximate solution method : Straight forward expansions and sources of nonuniformity – Harmonic Balancing method – Linstedt-Poincare’ method – Method of Averaging
Perturbation analysis method : Method of Averaging – Method of multiple scales – Method of multiple scales – Method of normal form – Incremental Harmonic Balance method – Modified Lindstedt-Poincare’ method
Stability and Bifurcation Analysis : Lyapunov stability criteria – Stability analysis from perturbed equation – Stability analysis from reduced equations obtained from perturbation analysis – Bifurcation of fixed point response, static bifurcation: pitch fork, saddle-node and trans-critical bifurcation – Bifurcation of fixed point response, dynamic bifurcation: Hopf bifurcation – Stability and Bifurcation of periodic response, monodromy matrix, poincare’ section

Numerical techniques : Time response, Runga-Kutta method, Wilson- Beta method – Frequency response curves: solution of polynomial equations, solution of set of algebraic equations – Basin of attraction: point to point mapping and cell-to-cell mapping – Poincare’ section of fixed-point, periodic, quasi-periodic and chaotic responses – Lyapunov exponents – FFT analysis, Fractal Dimensions
Applications : SDOF Free-Vibration: Duffing Equation – SDOF Free-Vibration: Duffing Equation – SDOF Forced-Vibration: Van der pol’s Equation – SDOF Forced-Vibration: Van der pol’s Equation – Parametrically excited system- Mathieu-Hill’s equation, Floquet Theory – Parametrically excited system- Instability regions – Multi-DOF nonlinear systems – Continuous system: Micro-cantilever beam analysis

Other Resources

Course Curriculum

Mod-01 Lec-01 Introduction of Nonlinear systems Details 56:24
Mod-01 Lec-02 Review of Linear vibrating systems Details 57:11
Mod-01 Lec-03 Phenomena associated with Nonlinear systems Details 58:50
Mod-01 Lec-04 Commonly observed Phenomena in Nonlinear systems Details 58:7
Mod-02 Lec-01 Force and Moment based Approach Details 1:1:57
Mod-02 Lec-02 Energy based approach Extended Hamilton’s principle and Lagrange Priciple Details 56:55
Mod-02 Lec-03 Derivation of Equation of motion of nonlinear discrete system (More examples) Details 53:55
Mod-02 Lec-04 Derivation of Equation of motion of nonlinear continuous system 1 Details 52:43
Mod-02 Lec-05 Derivation of Equation of motion of nonlinear continuous system 2 Details 54:1
Mod-02 Lec-06 Ordering of nonlinear Equation of motion Details 54:57
Mod-03 Lec-01 Qualitative Analysis Straight forward expansion Details 52:31
Mod-03 Lec-02 Numerical method Straight forward expansion Details 54:13
Mod-03 Lec-03 Lindstedt Poincare’ technique Details 52:49
Mod-03 Lec-04 Method of multiple scales Details 51:9
Mod-03 Lec-05 Method of Harmonic balance Details 0:53
Mod-03 Lec-06 Method of averaging Details 53:6
Mod-03 Lec-07 Generalized Method of averaging Details 52:47
Mod-03 Lec-08 Krylov-Bogoliubov-Mitropolski technique Details 49:45
Mod-03 Lec-09 Incremental harmonic balance method and Intrinsic multiple Details 47:42
Mod-03 Lec-10 Modified Lindstedt Poincare’ technique Details 51:17
Mod-04 Lec-01 Stability and Bifurcation of Fixed-point response 1 Details 53:26
Mod-04 Lec-02 Stability and Bifurcation of Fixed-point response 2 Details 54:32
Mod-04 Lec-03 Stability and Bifurcation of Fixed-point response 3 Details 53:57
Mod-04 Lec-04 Stability and Bifurcation of Fixed-point response 4 Details 53:22
Mod-04 Lec-05 Stability Analysis of Periodic response Details 54:1
Mod-04 Lec-06 Bifurcation of Periodic response And Introduction to quasi-periodic Details 53:31
Mod-04 Lec-07 Quasi-Periodic and Chaotic response Details 59:53
Mod-05 Lec-01 Numerical methods to obtain roots of characteristic equation and time response Details 55:2
Mod-05 Lec-02 Numerical methods to obtain time response Details 56:8
Mod-05 Lec-03 Numerical methods to obtain frequency response Details 56:27
Mod-06 Lec-01 Free Vibration of Single degree of freedom Nonlinear systems Details 52:2
Mod-06 Lec-02 Free Vibration of Single degree of freedom Nonlinear systems: effect of damping Details 56:16
Mod-06 Lec-03 Free Vibration of multi- degree of freedom Nonlinear systems with Cubic Details 55:34
Mod-06 Lec-04 Forced nonlinear Vibration Single degree of freedom Nonlinear systems Details 1:6:10
Mod-06 Lec-05 Forced nonlinear Vibration Single and multi- degree of freedom Details 52:3
Mod-06 Lec-06 Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System Details 57:28
Mod-06 Lec-07 Analysis of Multi- degree of freedom system Details 51:23
Mod-06 Lec-08 Nonlinear Vibration of Parametrically excited system: Axially loaded sandwich beam Details 54:33
Mod-06 Lec-09 Nonlinear Vibration of Parametrically excited system: Elastic and Magneto-elastic beam Details 52:53
Mod-06 Lec-10 Nonlinear Vibration of Parametrically excited system with internal resonance Details 1:1:29

This Course and video tutorials are delivered by IIT Guwahati, as of NPTEL video courses & elearning program of Govt of India.

Course Reviews

N.A

ratings
  • 5 stars0
  • 4 stars0
  • 3 stars0
  • 2 stars0
  • 1 stars0

No Reviews found for this course.

About

FreeVideoLectures Provides you complete information about best courses online, Video tutorials, helps you in building a career !!

help@freevideolectures.com

Learn More About us

About Us
Privacy Policy
FAQ

FREEVIDEOLECTURES.COM ALL RIGHTS RESERVED.
top
FreeVideoLectures.com All rights reserved.

Setup Menus in Admin Panel