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Course11210330046 lectures

Nonlinear Vibration

Prof. S. K. Dwivedy · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Week 1 : Introduction to Nonlinear Mechanical Systems

  1. What is MATLAB? Video
  2. What is Simulink? Video
  3. Getting Started with MATLAB Video
  4. Introduction to Plotting Video
  5. Calculations with Matrices Video
  6. Calculating Eigenvalues and Eigenvectors Video
  7. MATLAB Variables Video
  8. MATLAB Functions Video
  9. Logical Variables Video
  10. If-Else Statements Video
  11. Writing a FOR Loop Video
  12. Numerically Solving Systems of First Order ODEs Video
  13. Solving Systems of Linear Equations Video

Week 2 : Development of Nonlinear Equation of Motion using Symbolic Software:

  1. Lec 1 : Introduction to mechanical systems Video
  2. Lec 2 : Superposition rule, Commonly used nonlinear equations Video
  3. Lec 3 : Equilibrium points: potential function Video

Week 3: Solution of Nonlinear Equation of Motion

  1. Lec 4 : Force and moment based Approach, Lagrange Principle Video
  2. Lec 5 : ExtendedHamilton’s principle Video
  3. Lec 6 : Use of scaling and book-keeping parameter for ordering Video

Week 4: Solution of Nonlinear Equation of Motion

  1. Lec 13 : Free vibration of undamped and damped SDOF systems with quadratic and cubic nonlinearity Video
  2. Lec 14: Super and sub harmonic resonance conditions Video
  3. Lec 15 : Bifurcation analysis of fixed-point response Video

Week 5: Analysis of Nonlinear SDOF system with weak excitation

  1. Lec 16 : Nonlinear system with hard excitations Video
  2. Lec 17 : Super and sub harmonic resonance conditions Video
  3. Lec 18 : Bifurcation analysis of fixed-point response Video

Week 6: Analysis of Nonlinear SDOF system with hard excitation

  1. Lec 19: Floquet theory, Hill's infinite determinant, Resonance in parametrically excited systems Video
  2. Lect 20: Parametrically excited pneumatic artificial muscle Video
  3. Lect 21: Parametric instability of sandwich plate Video

Week 7: Vibration Analysis of Parametrically Excited system

  1. Lec 22 : Analysis of periodic, quasi-periodic and chaotic systems Video
  2. Lec 23 : Stability and bifurcation analysis of periodic and quasi-periodic response Video
  3. Lec 24 : Analysis of chaotic system Video

Week 8 : Analysis of Periodic, quasiperiodic and Chaotic System

  1. Lec 25 : Numerical methods for finding roots and solutions of ODE Video
  2. Lec 26 : Time response, phase portraits, frequency response Video
  3. Lec 27 : Poincare section, FFT, Lyapunov exponent Video

Week 9 : Numerical Methods for Nonlinear system Analysis

  1. Lec 28 : Passive and active vibration absorber with displacement and acceleration feedback Video
  2. Lec 29 : Active vibration absorber with time delay acceleration feedback by HBM Video
  3. Lec 30 : Application of Active vibration absorber with time delay combination feedbacks Video

Week 10 : Practical Application 1: Nonlinear Vibration Absorber

  1. Lec 31 : Cantilever beam with tip mass for principal parametric resonance Video
  2. Lec 32 : Cantilever beam with tip mass for combination resonance Video
  3. Lec 33 :Cantilever beam based piezoelectric based energy harvestor Video

Week 11 : Practical Application 2: Flexible system

  1. Lec 34 : Nonlinear dynamics of turning operation with delay and internal resonance Video
  2. Lec 35 : Chatter in rolling mills and dynamic analysis of artificial pneumatic muscle Video
  3. Lec 36 : Chaotic systems and control of chaos Video

Live Session

  1. Live Session 24-03-2021 Video
  2. Live Session 31-03-2021 Video
  3. Live Session 05-04-2021 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mechanical Engineering
Teacher
Prof. S. K. Dwivedy
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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