National University of Sciences and Technology
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ME-812 Nonlinear Dynamics
Campus College of E&ME
Programs PG
Session Spring Semester 2017
Course Title Nonlinear Dynamics
Course Code ME-812
Credit Hours 3-0
Pre-Requisutes Linear Systems, Differential Equations, Exposure to MATLAB strongly recommended.
Course Objectives Graduate level course in nonlinear systems. It starts from the introduction to nonlinear dynamics, multiple solutions, stability analysis, bifurcation, and various techniques to analyze motions. Each topic will include examples of physical systems undergoing these phenomena. Perturbation techniques will be covered in detail to find solutions to nonlinear systems. The course will briefly describe control of bifurcations.
Detail Content
  • Introduction to nonlinear phenomenon: Equilibrium solutions, Periodic Solutions, Quasi-periodic solutions, Chaos.
  • Perturbation theory: Straight forward expansion, Linstedt-Poincare Method, Method of Renormalization, Method of Multiple Scales, Method of Averaging.
  • Analysis of nonlinear systems: Bifurcation, Phase-plane techniques, Poincare maps, Numerical Methods, Tools to analyze motions, Lyapunov stability theory, control of bifurcation.
  • The course will have a project related to Nonlinear Systems and application of knowledge acquired in the course.
Text/Ref Books
  • Nayfeh, A. H. and Balachandran, B., Applied Nonlinear Dynamics, Wiley-Interscience, New York, 1995.
  • Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.
Time Schedule Spring, 2017
Faculty/Resource Person Imran Akhtar, PhD
PhD (Virginia Tech, USA)
Discipline: Mechanical Engineering
Specialization: Computational Fluid Dynamics, Nonlinear Dynamics & Control