DETERMINATION OF EIGENVALUES OF MODIFIED STRUCTURES USING THE FIRST ORDER PERTURBATION METHOD AND THE RAYLEIGH'S QUOTIENT: A COMPARATIVE STUDY

摘要

The central focus of this work is an analytical comparison of the eigenvalues determination of discrete structures under small modifications on structural parameters (inertia and stiffness) by using the first order perturbation method and the Rayleigh's quotient. Also it is proposed an expression to evaluate the "quality" of the obtained results. This parameter is compared to other ones, available in the bibliography, using numerical examples. The obtained conclusions are exemplified by two problems: a clamped-free beam with variations in a concentrated mass in the free border; and a clamped-free beam with variable cross-section through its length.