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Course11210302340 lectures

Nonlinear Vibration

Prof. S.K. Dwivedy · IIT Guwahati

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Lectures

Introduction

  1. Introduction of Nonlinear systems Video
  2. Review of Linear vibrating systems Video
  3. Phenomena associated with Nonlinear systems Video
  4. Commonly observed Phenomena in Nonlinear systems Video

Derivation of nonlinear equation of motion

  1. Force and Moment based Approach Video
  2. Energy based approach Extended Hamilton’s principle and Lagrange Priciple Video
  3. Derivation of Equation of motion of nonlinear discrete system (More examples) Video
  4. Derivation of Equation of motion of nonlinear continuous system 1 Video
  5. Derivation of Equation of motion of nonlinear continuous system 2 Video
  6. Ordering of nonlinear Equation of motion Video

Solution of Nonlinear Equations of motions

  1. Qualitative Analysis Straight forward expansion Video
  2. Numerical method Straight forward expansion Video
  3. Lindstedt Poincare’ technique Video
  4. Method of multiple scales Video
  5. Method of Harmonic balance Video
  6. Method of averaging Video
  7. Generalized Method of averaging Video
  8. Krylov-Bogoliubov-Mitropolski technique Video
  9. Incremental harmonic balance method and Intrinsic multiple scale harmonic balance method Video
  10. Modified Lindstedt Poincare’ technique Video

Stability and Bifurcation Analysis of Nonlinear Systems

  1. Stability and Bifurcation of Fixed-point response 1 Video
  2. Stability and Bifurcation of Fixed-point response 2 Video
  3. Stability and Bifurcation of Fixed-point response 3 Video
  4. Stability and Bifurcation of Fixed-point response 4 Video
  5. Stability Analysis of Periodic response Video
  6. Bifurcation of Periodic response And Introduction to quasi-periodic and Chaotic response Video
  7. Quasi-Periodic and Chaotic response Video

Numerical methods

  1. Numerical methods to obtain roots of characteristic equation and time response Video
  2. Numerical methods to obtain time response Video
  3. Numerical methods to obtain frequency response Video

Applications

  1. Free Vibration of Single degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities Video
  2. Free Vibration of Single degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities: effect of damping Video
  3. Free Vibration of multi- degree of freedom Nonlinear systems with Cubic and quadratic nonlinearities Video
  4. Forced nonlinear Vibration Single degree of freedom Nonlinear systems with Cubic nonlinearities: Video
  5. Forced nonlinear Vibration Single and multi- degree of freedom Nonlinear systems Video
  6. Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System Video
  7. Analysis of Multi- degree of freedom system Video
  8. Nonlinear Vibration of Parametrically excited system: Axially loaded sandwich beam Video
  9. Nonlinear Vibration of Parametrically excited system: Elastic and Magneto-elastic beam Video
  10. Nonlinear Vibration of Parametrically excited system with internal resonance 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
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