Frequency based localization of structural discrepancies

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 modelled poorly or well. It is shown how the pattern of discrepancies in the analytical and experimental test values for 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. The success of the procedure depends on the numerical conditioning of a modal reference matrix. Strategies to insure 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 localization of a mass discrepancy in a real structure based on lab tests.