Correcting indefinite mass matrices due to substructure uncoupling

The transmission simulator method of experimental dynamic substructuring captures the interface forces and motions through a fixture called a transmission simulator. The transmission simulator method avoids the need to measure connection point rotations, facilitates substructuring for systems with continuous connections and enriches the modal basis of the substructure model. To use this approach, one first attaches the transmission simulator to the experimental substructure and then measures the free modes of the assembly. A finite element model of the transmission simulator is then used to subtract the transmission simulator and to couple the experimental substructure to the assembly of interest. Unfortunately, in several cases the process of subtracting the transmission simulator has caused the mass matrix for the experimental substructure to become indefinite, making the substructure model difficult or impossible to use and potentially leading to erroneous results. The authors previously developed metrics that could be used to identify which modes of the experimental model led to the indefinite mass matrix. This work presents a method that utilizes those metrics with a sensitivity analysis to adjust the transmission simulator mass matrix so that the subtraction does not produce an indefinite mass matrix. A second method is presented in which the mass matrix is made positive definite by coupling additional mass to the substructure. The methods are evaluated using both numerical and experimental test cases, showing promising results.