Parametric correction of self-adjoint finite element models in the presence of multiple eigenvalues

Publisher Website
Google Scholar
Abstract
The subject of this article concerns the calculation of the direct and inverse sensitivities of linear elastodynamic systems. This study is limited to the case of conservative mechanical structures which can be represented by discrete models having symmetric positive definite matrices. The first part reviews the equations for the first derivatives of the eigensolutions with respect to the design variables in the presence of multiple eigenvalues (direct sensitivity). These expressions are derived using the modal method. The second part concerns the parametric correction of a model from the observed data. The correction method envisaged is based on the minimization of a residual which is a function of the distance between the eigensolutions of the model and the system (inverse sensitivity). The fundamental difficulties in the evaluation of the first derivatives of the eigensolutions, when the model possesses multiple eigenvalues, are avoided by the introduction of a generalized parametrization constructed on the basis of an a priori parametrization of the correction matrices.

This publication has 6 references indexed in Scilit: