Sensibilidad de Segundo Orden en Problemas de Vibraciones e Inestabilidad Estructural

Abstract

This paper presents a pertubation approach for the first and second order sensitivity of eigenvalue problems, Il.S they arise in buckling and vibration of structural systems. A particular feature introduced in the formulation is the dependence of all matrices defining the problem, not
only on the design parameter, but also on the precritical state. This means that the displacement sensitivity of the fundamental path (in buckling problems) or a prestressed state (in vibration problems) are introduced in the analysis. Two techniques are considered in this work: first, the direct method; and second, the adjoint method. First and second order sensitivity equations for eigenvalues and eigenvectors are derived, and it is shown that second order sensitivity of eigenvalue does not require of a new adjoint problem to be solved.