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Course Description

A vibration whose amplitude is large enough so that the elastic restoring force on the vibrating object is not proportional to its displacement is known as Nonlinear vibration.

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Course Syllabus
  • Mod-01 Lec-01 Introduction of Nonlinear systems
  • Mod-01 Lec-02 Review of Linear vibrating systems
  • Mod-01 Lec-03 Phenomena associated with Nonlinear systems
  • Mod-01 Lec-04 Commonly observed Phenomena in Nonlinear systems
  • Mod-02 Lec-01 Force and Moment based Approach
  • Mod-02 Lec-02 Energy based approach Extended Hamilton's principle and Lagrange Priciple
  • Mod-02 Lec-03 Derivation of Equation of motion of nonlinear discrete system (More examples)
  • Mod-02 Lec-04 Derivation of Equation of motion of nonlinear continuous system 1
  • Mod-02 Lec-05 Derivation of Equation of motion of nonlinear continuous system 2
  • Mod-02 Lec-06 Ordering of nonlinear Equation of motion
  • Mod-03 Lec-01 Qualitative Analysis Straight forward expansion
  • Mod-03 Lec-02 Numerical method Straight forward expansion
  • Mod-03 Lec-03 Lindstedt Poincare' technique
  • Mod-03 Lec-04 Method of multiple scales
  • Mod-03 Lec-05 Method of Harmonic balance
  • Mod-03 Lec-06 Method of averaging
  • Mod-03 Lec-07 Generalized Method of averaging
  • Mod-03 Lec-08 Krylov-Bogoliubov-Mitropolski technique
  • Mod-03 Lec-09 Incremental harmonic balance method and Intrinsic multiple
  • Mod-03 Lec-10 Modified Lindstedt Poincare' technique
  • Mod-04 Lec-01 Stability and Bifurcation of Fixed-point response 1
  • Mod-04 Lec-02 Stability and Bifurcation of Fixed-point response 2
  • Mod-04 Lec-03 Stability and Bifurcation of Fixed-point response 3
  • Mod-04 Lec-04 Stability and Bifurcation of Fixed-point response 4
  • Mod-04 Lec-05 Stability Analysis of Periodic response
  • Mod-04 Lec-06 Bifurcation of Periodic response And Introduction to quasi-periodic
  • Mod-04 Lec-07 Quasi-Periodic and Chaotic response
  • Mod-05 Lec-01 Numerical methods to obtain roots of characteristic equation and time response
  • Mod-05 Lec-02 Numerical methods to obtain time response
  • Mod-05 Lec-03 Numerical methods to obtain frequency response
  • Mod-06 Lec-01 Free Vibration of Single degree of freedom Nonlinear systems
  • Mod-06 Lec-02 Free Vibration of Single degree of freedom Nonlinear systems: effect of damping
  • Mod-06 Lec-03 Free Vibration of multi- degree of freedom Nonlinear systems with Cubic
  • Mod-06 Lec-04 Forced nonlinear Vibration Single degree of freedom Nonlinear systems
  • Mod-06 Lec-05 Forced nonlinear Vibration Single and multi- degree of freedom
  • Mod-06 Lec-06 Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System
  • Mod-06 Lec-07 Analysis of Multi- degree of freedom system
  • Mod-06 Lec-08 Nonlinear Vibration of Parametrically excited system: Axially loaded sandwich beam
  • Mod-06 Lec-09 Nonlinear Vibration of Parametrically excited system: Elastic and Magneto-elastic beam
  • Mod-06 Lec-10 Nonlinear Vibration of Parametrically excited system with internal resonance
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