Nonlinear Vibration (English)

   Monday, April 01, 2024   

Starting a new Lecture Notes Series on Nonlinear Vibration

Youtube Lecture Playlist Credits 

Channel Name: NPTEL IIT Guwahati

So Let Us Start to This Journey of Learning 

Nonlinear Vibration By Lecture Notes together!

Lecture 1: Nonlinear Vibration

Lecture 2: Lec 1 : Introduction to mechanical systems

Lecture 3: Lec 2 : Superposition rule, Commonly used nonlinear equations

Lecture 4: Lec 3 : Equilibrium points: potential function

Lecture 5: Lec 4 : Force and moment based Approach, Lagrange Principle

Lecture 6: Lec 5 : ExtendedHamilton’s principle

Lecture 7: Lec 6 : Use of scaling and book-keeping parameter for ordering

Lecture 8: Lec 7 : Numerical solution, Analytical solutions: Harmonic Balance method

Lecture 9: Lec 8 : Straight forward expansion

Lecture 10: Lec 9 : Lindstd-Poincare’ method

Lecture 11: Lec 10 : Method of Averaging

Lecture 12: Lec 11 : Method of multiple scales

Lecture 13: Lec 12: Method of generalized Harmonic Balance method

Lecture 14: Lec 13 : Free vibration of undamped and damped SDOF systems with quadratic and cubic nonlinearity

Lecture 15: Lec 14: Super and sub harmonic resonance conditions

Lecture 16: Lec 15 : Bifurcation analysis of fixed-point response

Lecture 17: Lec 16 : Nonlinear system with hard excitations

Lecture 18: Lec 17 : Super and sub harmonic resonance conditions

Lecture 19: Lec 18 : Bifurcation analysis of fixed-point response

Lecture 20: Lect 19: Floquet theory, Hill's infinite determinant, Resonance in parametrically excited systems

Lecture 21: Lect 20: Parametrically excited pneumatic artificial muscle

Lecture 22: Lect 21: Parametric instability of sandwich plate

Lecture 23: Lec 22 : Analysis of periodic, quasi-periodic and chaotic systems

Lecture 24: Lec 23 : Stability and bifurcation analysis of periodic and quasi-periodic response

Lecture 25: Lec 24 : Analysis of chaotic system

Lecture 26: Lec 25 : Numerical methods for finding roots and solutions of ODE

Lecture 27: Lec 26 : Time response, phase portraits, frequency response

Lecture 28: Lec 27 : Poincare section, FFT, Lyapunov exponent

Lecture 29: Lec 28 : Pasive and Active vibration absorber with displacement and acceleration feedback

Lecture 30: Lec 29 : Active vibration absorber with time delay acceleration feedback by HBM

Lecture 31: Lec 30 : Application of Active vibration absorber with combination feedback

Lecture 32: Lec 31 : Cantilever beam with tip mass for principal parametric resonance

Lecture 33: Lec 32 : Cantilever beam with tip mass for combination resonance

Lecture 34: Lec 33 :Cantilever beam based piezoelectric based energy harvestor

Lecture 35: Lec 34 : Nonlinear synamics of turning operation with delay and internal resonance

Lecture 36: Lec 35 : Chatter in rolling mills and dynamic analysis of artificial pneumatic muscle

Lecture 37: Lec 36 : Chaotic systems and control of chaos