NPTEL : NOC:Nonlinear Vibration (Mechanical Engineering)

Co-ordinators : Prof. S. K. Dwivedy


Lecture 1 - Introduction to mechanical systems

Lecture 2 - Superposition rule, Commonly used nonlinear equations

Lecture 3 - Equilibrium points: potential function

Lecture 4 - Force and moment based Approach, Lagrange Principle

Lecture 5 - Extended Hamilton’s principle

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

Lecture 7 - Numerical solution, Analytical solutions: Harmonic Balance method

Lecture 8 - Straight forward expansion

Lecture 9 - Lindstd-Poincare’ method

Lecture 10 - Method of Averaging

Lecture 11 - Method of multiple scales

Lecture 12 - Method of generalized Harmonic Balance method

Lecture 13 - Free vibration of undamped and damped SDOF systems with quadratic and cubic nonlinearity

Lecture 14 - Super and sub harmonic resonance conditions

Lecture 15 - Bifurcation analysis of fixed-point response

Lecture 16 - Nonlinear system with hard excitations

Lecture 17 - Super and sub harmonic resonance conditions

Lecture 18 - Bifurcation analysis of fixed-point response

Lecture 19 - Floquet theory, Hill's infinite determinant, Resonance in parametrically excited systems

Lecture 20 - Parametrically excited pneumatic artificial muscle

Lecture 21 - Parametric instability of sandwich plate

Lecture 22 - Analysis of periodic, quasi-periodic and chaotic systems

Lecture 23 - Stability and bifurcation analysis of periodic and quasi-periodic response

Lecture 24 - Analysis of chaotic system

Lecture 25 - Numerical methods for finding roots and solutions of ODE

Lecture 26 - Time response, phase portraits, frequency response

Lecture 27 - Poincare section, FFT, Lyapunov exponent

Lecture 28 - Pasive and active vibration absorber with displacement and acceleration feedback

Lecture 29 - Active vibration absorber with time delay acceleration feedback by HBM

Lecture 30 - Application of Active vibration absorber with combination feedback

Lecture 31 - Cantilever beam with tip mass for principal parametric resonance

Lecture 32 - Cantilever beam with tip mass for combination resonance

Lecture 33 - Cantilever beam based piezoelectric based energy harvestor

Lecture 34 - Nonlinear dynamics of turning operation with delay and internal resonance

Lecture 35 - Chatter in rolling mills and dynamic analysis of artificial pneumatic muscle

Lecture 36 - Chaotic systems and control of chaos