Metrics for diagnosing negative mass and stiffness when uncoupling experimental and analytical substructures

When testing to identify an experimental model of a substructure, it is often beneficial to exercise the interface by attaching a fixture such as a rigid mass. An analytical representation of the fixture must then be used to subtract its effects from the assembly. However, this can cause the mass and stiffness matrices to become indefinite in some situations. This paper presents two new 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.