The concept of analytical testing can be generalized to enable the systematic synthesis of several substructures into a single composite structure. The paramount assumption made is that the responses, as described using mobilities, are taken at a discrete frequency. The methodology enables the direct utilization of shake-test-derived mobilities along with analytical finite element modeling (FEM) results. Furthermore, the methodology enables a reduction of model size to include only those degrees of freedom of interest. Additionally, the methodology enables the use of general complex-valued responses for each substructure, thereby providing a rigorous method for synthesizing substructures with diverse forms and values of damping.

Partitioning of Mobility Matrices

Later developments require a generalization of the subsystem mobility matrix partitioning, and an explanation of the notation used for this purpose is first presented. The system mobility matrix can generally be partitioned according to sets of either internal or interface degrees of freedoms in the following form:

(C.1)

where the following sets are defined:

A	? set of retained internal degrees of freedom in structure A (number of degrees of freedom in set A = n A)
I	? first set of interface degrees of freedom (number of degrees of freedom in set I = n I)
M	? mth set of interface degrees of freedom (number of degrees of freedom in set M = n M)

The indices in Eq. (C.1) have three functions: They identify the...