MECH 4104: Vibration Analysis

Free and forced vibrations of one and two degree-of-freedom systems. Vibration measurement and isolation. Numerical methods for multi-degree-of-freedom systems. Modal analysis techniques. Dynamic vibration absorbers. Shaft whirling. Vibration of continuous systems: bars, plates, beams and shafts. Energy methods. Holzer method.

Course Outline

  1. Fundamental concepts:  Classification of vibration problems; Basic components of vibratory systems; Modelling basic components of vibratory systems; Harmonic motions.
  2. Free vibration of SDOF systems:  Undamped translational systems; Undamped torsional systems; Stability considerations; Rayleigh=s Energy Method; Viscously damped systems; Coulomb and Hysteretic damping.
  3. Harmonically excited SDOF systems:  Undamped systems; Damped systems; Harmonic motion of the base; Damped systems under rotating unbalance.
  4. SDOF systems excited by general forcing functions:  General periodic forcing function; Impulsive forcing function; General forcing function; Response Spectrum; Laplace Transformation.
  5. 2DOF systems:  Free vibration of undamped systems; Coordinate coupling and Principal coordinates; Forced vibration of damped systems; Vibration absorbers.
  6. Introduction to MDOF systems:  Undamped systems; Influence coefficients; Lagrange=s Equations; Eigenvalue problem; Expansion Theorem; Forced undamped systems; Viscously damped forced systems.
  7. Numerical Methods for Natural Frequencies and Mode Shapes:  Dunkerley=s Method; Rayleigh=s Method; Holzer=s Method; Matrix Iteration Method; Standard Eigenvalue problem.
  8. Continuous Systems: Transverse vibration of strings and cables; Longitudinal vibration of rods; Torsional vibration of rods; Lateral vibration of beams; Vibration of membranes; Rayleigh and Rayleigh-Ritz Methods.

Text Book: Mechanical Vibrations by Singiresu S. Rao; 5th Edition; Pearson/Prentice Hall 2011

Suggested Supplemental References

  1. Elements of Vibration Analysis; by Leonard Meirovitch; McGrawHill 1986
  2. Theory of Vibration with Applications; by: W.T. Thomson & M.D. Dahleh, 5th Edition, Prentice Hall, 1998