Mechanical - Nonlinear Vibration (English)

   Friday, April 18, 2025   

Starting a new Lecture Notes Series on Mechanical - Nonlinear Vibration

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Mechanical - Nonlinear Vibration By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction of Nonlinear systems

Lecture 2: Mod-01 Lec-02 Review of Linear vibrating systems

Lecture 3: Mod-01 Lec-03 Phenomena associated with Nonlinear systems

Lecture 4: Mod-01 Lec-04 Commonly observed Phenomena in Nonlinear systems

Lecture 5: Mod-02 Lec-01 Force and Moment based Approach

Lecture 6: Mod-02 Lec-02 Energy based approach Extended Hamilton's principle and Lagrange Priciple

Lecture 7: Mod-02 Lec-03 Derivation of Equation of motion of nonlinear discrete system (More examples)

Lecture 8: Mod-02 Lec-04 Derivation of Equation of motion of nonlinear continuous system 1

Lecture 9: Mod-02 Lec-05 Derivation of Equation of motion of nonlinear continuous system 2

Lecture 10: Mod-02 Lec-06 Ordering of nonlinear Equation of motion

Lecture 11: Mod-03 Lec-01 Qualitative Analysis Straight forward expansion

Lecture 12: Mod-03 Lec-02 Numerical method Straight forward expansion

Lecture 13: Mod-03 Lec-03 Lindstedt Poincare' technique

Lecture 14: Mod-03 Lec-04 Method of multiple scales

Lecture 15: Mod-03 Lec-05 Method of Harmonic balance

Lecture 16: Mod-03 Lec-06 Method of averaging

Lecture 17: Mod-03 Lec-07 Generalized Method of averaging

Lecture 18: Mod-03 Lec-08 Krylov-Bogoliubov-Mitropolski technique

Lecture 19: Mod-03 Lec-09 Incremental harmonic balance method and Intrinsic multiple

Lecture 20: Mod-03 Lec-10 Modified Lindstedt Poincare' technique

Lecture 21: Mod-04 Lec-01 Stability and Bifurcation of Fixed-point response 1

Lecture 22: Mod-04 Lec-02 Stability and Bifurcation of Fixed-point response 2

Lecture 23: Mod-04 Lec-03 Stability and Bifurcation of Fixed-point response 3

Lecture 24: Mod-04 Lec-04 Stability and Bifurcation of Fixed-point response 4

Lecture 25: Mod-04 Lec-05 Stability Analysis of Periodic response

Lecture 26: Mod-04 Lec-06 Bifurcation of Periodic response And Introduction to quasi-periodic

Lecture 27: Mod-04 Lec-07 Quasi-Periodic and Chaotic response

Lecture 28: Mod-05 Lec-01 Numerical methods to obtain roots of characteristic equation and time response

Lecture 29: Mod-05 Lec-02 Numerical methods to obtain time response

Lecture 30: Mod-05 Lec-03 Numerical methods to obtain frequency response

Lecture 31: Mod-06 Lec-01 Free Vibration of Single degree of freedom Nonlinear systems

Lecture 32: Mod-06 Lec-02 Free Vibration of Single degree of freedom Nonlinear systems: effect of damping

Lecture 33: Mod-06 Lec-03 Free Vibration of multi- degree of freedom Nonlinear systems with Cubic

Lecture 34: Mod-06 Lec-04 Forced nonlinear Vibration Single degree of freedom Nonlinear systems

Lecture 35: Mod-06 Lec-05 Forced nonlinear Vibration Single and multi- degree of freedom

Lecture 36: Mod-06 Lec-06 Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System

Lecture 37: Mod-06 Lec-07 Analysis of Multi- degree of freedom system

Lecture 38: Mod-06 Lec-08 Nonlinear Vibration of Parametrically excited system: Axially loaded sandwich beam

Lecture 39: Mod-06 Lec-09 Nonlinear Vibration of Parametrically excited system: Elastic and Magneto-elastic beam

Lecture 40: Mod-06 Lec-10 Nonlinear Vibration of Parametrically excited system with internal resonance