Qualification vibration tests are routinely performed on prototype hardware. Model validation cannot generally be done from the qualification vibration test because of multiple uncertainties, particularly the uncertainty of the boundary condition. These uncertainties can have a dramatic effect on the modal parameters extracted from the data. It would be valuable if one could extract a modal model of the test article with a known boundary condition from the qualification vibration test. This work addresses an attempt to extract fixed base modes on a 1.2 meter tall test article in a random vibration test on a 1.07 meter long slip table. The slip table was supported by an oil film on a granite block and driven by a 111,000 Newton shaker, hereinafter denoted as the big shaker. This approach requires obtaining dominant characteristic shapes of the bare table. A vibration test on the full system is performed. The characteristic table generalized coordinates are constrained to zero to obtain fixed base results. Results determined the first three fixed base bending mode frequencies excited by the shaker within four percent. A stick-slip nonlinearity in the shaker system had a negative effect on the final damping ratios producing large errors. An alternative approach to extracting the modal parameters directly from transmissibilities proved to be more accurate. Even after accounting for distortion due to the Harm window, it appears that dissipation physics in the bare shaker table provide additional damping beyond the true fixed base damping.
Recently, a new substructure coupling/uncoupling approach has been introduced, called Modal Constraints for Fixture and Subsystem (MCFS) [Allen, Mayes, & Bergman, Journal of Sound and Vibration, vol. 329, 2010]. This method reduces ill-conditioning by imposing constraints on substructure modal coordinates instead of the physical interface coordinates. The experimental substructure is tested in a free-free configuration, and the interface is exercised by attaching a flexible fixture. An analytical representation of the fixture is then used to subtract its effects in order to create an experimental model for the subcomponent of interest. However, it has been observed that indefinite mass and stiffness matrices can be obtained for the experimental substructure in some situations. This paper presents two simple metrics that can be used by the analyst to determine the cause of indefinite mass or stiffness matrices after substructure uncoupling. The metrics rank the experimental and fixture modes based upon their contribution to offending negative eigenvalues. Once the troublesome modes have been identified, they can be inspected and often reveal why the mass has become negative. Two examples are presented to demonstrate the metrics and to illustrate the physical phenomena that they reveal.