Comparison of FRF and Modal Methods for Combining Experimental and Analytical Substructures

This paper investigates methods for coupling analytical dynamic models of subcomponents with experimentally derived models in order to predict the response of the combined system, focusing on modal substructuring or Component Mode Synthesis (CMS), the experimental analog to the ubiquitous Craig-Bampton method. While the basic methods for combining experimental and analytical models have been around for many years, it appears that these are not often applied successfully. The CMS theory is presented along with a new strategy, dubbed the Maximum Rank Coordinate Choice (MRCC), that ensures that the constrained degrees of freedom can be found from the unconstrained without encountering numerical ill conditioning. The experimental modal substructuring approach is also compared with frequency response function coupling, sometimes called admittance or impedance coupling. These methods are used both to analytically remove models of a test fixture (required to include rotational degrees of freedom) and to predict the response of the coupled beams. Both rigid and elastic models for the fixture are considered. Similar results are obtained using either method although the modal substructuring method yields a more compact database and allows one to more easily interrogate the resulting system model to assure that physically meaningful results have been obtained. A method for coupling the fixture model to experimental measurements, dubbed the Modal Constraint for Fixture and Subsystem (MCFS) is presented that greatly improves the result and robustness when an elastic fixture model is used.