Frequency based localisation of structural discrepancies

Abstract

The intent of modal analysis is to develop a reliable model of a structure by working with the analytical and experimental modal properties of frequency, damping and mode shape. In addition to identifying these modal properties it would be desirable to determine spatially which parts of the structure are modeled poorly or well. This information could be used to improve the finite element model, or to point to faults in the structure and hence help to evaluate mechanical integrity. This paper shows how the pattern of discrepancies in the pole and the driving point zero frequencies of a structure can be linked to discrepancies in the mass or stiffness of the structural elements. Only nominal mode shapes, as opposed to mode shape discrepancies, are required. Because first-order errors in mode shape cause only second-order localisation errors, the nominal mode shapes need not be measured, but can be taken from a finite element model. The success of this procedure depends on the numerical conditioning of a modal reference matrix. Strategies to ensure adequate numerical conditioning require a formulation which avoids geometric and energy storage symmetries of the structure, and ignores structural elements which contribute negligibly small potential or kinetic energy to the excited modes. Physical insight into the numerical conditioning problem is provided by a numerical example and by the localisation of a mass discrepancy in a real structure based on laboratory tests.