Figure 4: Experimental substructure C consisting of cylinder (B) and transmission simulator (A). Substructure uncoupling will be used to remove the gold colored transmission simulator A from the assembly. 3.2.1. Ranking modes of C The first application studied is the case where the first 18 modes will be retained for the transmission simulator with frequencies up to 1853.8 Hz and all 100 modes will be included for the composite substructure C. When this is done, the mass matrix obtained is not positive definite. The lowest six eigenvalues of the mass matrix are: -0.197, -0.0764, -0.134, -0.118, 0.398 and 0.679. Four of the eigenvalues are below zero, caused by four corresponding eigenvalues of QCM that are greater than 1.0. The metrics proposed in this paper will be used to rank the C modes to determine how they contribute to the mass approximation for substructure B. Equation (40) was again used to compute the contributions of the experimental C modes to each of the eigenvalues of QCM . Figure 5 illustrates the cumulative sum over the rows of eCM for the first six columns corresponding to the six largest eigenvalues of QCM . The four largest eigenvalues slowly increase in value until the 19th-22nd modes are added, at which point they jump above 1.0 and settle at values between 1.5 and 2.2. In contrast, the fifth and sixth eigenvalues increase slowly over all of the modes always remaining below 0.5. 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 Mode Number Cumulative Eigenvalues Eigenvalue 1 Eigenvalue 2 Eigenvalue 3 Eigenvalue 4 Eigenvalue 5 Eigenvalue 6 127
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