The Craig–Mayes Reduction: A Craig–Bampton Experimental Dynamic Substructure Using the Transmission Simulator Method

Abstract

Experimental dynamic substructures in both modal and frequency response domains using the transmission simulator method have been developed for several systems since 2007. The standard methodology couples the stiffness, mass, and damping matrices of the experimental substructure to a finite element model of the remainder of the system through multi-point constraints. This can be somewhat awkward in the finite element code. It is desirable to have an experimental substructure in the Craig–Bampton form (referred to as the Craig–Mayes form) to ease the implementation process, since many codes such as Nastran, ABAQUS, ANSYS, and Sierra Structural Dynamics have Craig–Bampton as a substructure option. A square transformation matrix is derived that produces a modified Craig–Bampton form that still requires multi-point constraints to couple to the rest of the finite element model. Finally the multi-point constraints are imported to the modified Craig–Bampton matrices to produce substructure matrices that fit in the standard Craig–Bampton form. The physical boundary degrees of freedom of the experimental substructure matrices can be directly attached to physical degrees of freedom in the remainder of the finite element model. This chapter derives the Craig–Mayes experimental substructure that fits in the Craig–Bampton form, and presents results from an analytical and an industrial example utilizing the new form. In general, this is a powerful method to represent a real system accurately: models developed using the Craig–Mayes method have been observed to have maximum frequency error less than 2% and maximum damping error on the order of 25%.