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**

- Free vibration of SDOF systems: Undamped translational systems; Undamped torsional systems; Stability considerations; Rayleigh=s Energy Method; Viscously damped systems; Coulomb and Hysteretic damping
*.* - Harmonically excited SDOF systems: Undamped systems; Damped systems; Harmonic motion of the base; Damped systems under rotating unbalance.
- SDOF systems excited by general forcing functions: General periodic forcing function; Impulsive forcing function; General forcing function; Response Spectrum; Laplace Transformation.
- 2DOF systems: Free vibration of undamped systems; Coordinate coupling and Principal coordinates; Forced vibration of damped systems; Vibration absorbers.
- Introduction to MDOF systems: Undamped systems; Influence coefficients; Lagrange=s Equations; Eigenvalue problem; Expansion Theorem; Forced undamped systems; Viscously damped forced systems.
- Numerical Methods for Natural Frequencies and Mode Shapes: Dunkerley=s Method; Rayleigh=s Method; Holzer=s Method; Matrix Iteration Method; Standard Eigenvalue problem.
- 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; 5^{th} Edition; Pearson/Prentice Hall 2011

**Suggested Supplemental References**

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