behrooz farshi - Iran University of Science and Technology Tehran, Iran
amir hajizadeh - International Institute of Earthquake Engineering and Seismology Tehran, Iran

Rayleigh's quotient when minimized would yield the lowest eigen value and the corresponding eigen vector of equations expressing the indamped structural dynamic properties of a linear elastic system. Rayleigh's quotient R(x), represents the ratio of two quadratic polynomials in X, for linear systems and lends itself readily for numerical minimization by any of the available unconstrained minimization algorithms. The procedure employed here in, is the well known Conjugate Gradient Method which requires low storage capacity as well as few numerical operations.The minimization procedure would be inconstrained for fundamental mode as the procedure would always converge to the lowest R(x).