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ME-817 Advanced Theory of Vibrations
Campus College of E&ME
Programs PG
Session Spring Semester 2017
Course Title Advanced Theory of Vibrations
Course Code ME-817
Credit Hours 3-0
Pre-Requisutes Dynamics, vibrations
Course Objectives
  • To provide an introduction to modal analysis techniques for analysing multiple degree-of-freedom (MDOF) discrete system.
  • To introduce exact methods for analysing MDOF continuous systems using wave theory.
  • To introduce approximate methods for analysing MDOF continuous systems using assumed mode, flexibility matrix and finite element method.
  • To provide an introduction to vibration and shock control using viscoelastic and smart materials.
Detail Content Discrete systems: Equation of motion: Newton’s law, Lagrange’s equation; Eigenvalue problem: natural frequencies and mode shapes; orthogonality of modes; proportional and non-proportional damping, static and dynamic coupling; modal analysis;

Continuous systems: Wave theory: derivation and solution of wave equations for longitudinal, flexural, torsional, and transverse vibrations of rods, beams, plates and shells. Exact frequency equation: free and forced vibration using closed form solutions. Rayleigh-Ritz approach: free forced via assumed modes. Flexibility matrix approach; finite element method.

Control: Viscoelasticity: complex modulus of viscoelastic materials, anti-vibration mount. Smart material: piezoelectric, shape memory alloys. Smart structures: collocated sensors and actuators, PZT shunts, active vibration control, semi active vibration dampers.
Text/Ref Books
  • Mechanical Vibrations, S. S. Rao, Prentice Hall, 4th edition.
  • Theory of Vibration with Applications, W. T. Thomson, Prentice Hall, 4th edition.
  • Fundamentals of Mechanical Vibrations, S. G. Kelly, McGraw-Hill, 2nd edition.
  • Modal Testing, Theory and Practice By D. J. Ewins, Wiley.
Time Schedule Spring, 2017
Faculty/Resource Person Naveed Akmal Din, PhD
PhD (University of Manchester) UK
Discipline: Mechanical Engineering
Specialisation: Vibrations, Modal Analysis, Smart structures