The inherently incomplete FEM and its effects on model updating techniques

Abstract

Introduction This paper addresses some of the questions regarding the improvement an analytical model of a structure using measured data in order to make it better able to predict the dynamic behavior of the structure. The issues discussed include: all models are truly reduced models; the reduced model of a linear structure is not linear; a linear model of a linear structure has a limited frequency range of applicability; there are an infinite number of reasonable models which can match measured data. These and other related concepts are discussed and demonstrakd. of course, if there is no unique solution, the question arises as to how to select the correct one and are there different correct models for different applications. It is concluded that new paths of research in this important field are necessary. Finite element modeling is of great importance in many branches of engineering. This highly developed technology has allowed the detailed analysis of complex structures and has resulted in significant advances in the ability to design systems for a large variety of purposes. However, a finite element model @EM) is an approximate discrete analytical model of a continuous structure. The use of FEMs is so commonplace that some users of this technology treat it as if there is no significant difference between the FEM and the actual structure. If one wished to develop a dynamic FEM model of a continuous structure, one approach would be to select the degrees of freedom (DOFs) so as to represent the structural characteristics in sticient detail to satisfy the purpose of the analysis. The simplest form of the resulting model may consist of a lumped mass at each DOF with linear springs connecting the adjacent masses. This would result in a banded stiffness matrix representing the load paths connecting the lumped masses and a diagonal mass matrix. Nomenclature DOF = Degree of freedom FEM = Finite element model mi = Generalized mass of mode i 0 = Frequency radkec @i = Natural frequency of mode i w = Vector of applied forces ;;I, = Vector of displacements = Stiffness matrix