Natural Frequency Errors Mode Shape Errors Figure 3: Comparison of Natural Frequency and Mode Shape Errors Associated with Reduction to 4 DOF It should be noted that the mode shape error is based on the modal coherence metric (for mode “i”), ^ ` > @^ ` > @2 ( ) 1 A i T E i i M E ) ) ) (18) The accuracies of the two reduction strategies for the 400 element stretched string model reduced to 16 analysis degrees of freedom are summarized in Figure 4. Natural Frequency Errors Mode Shape Errors Figure 4: Comparison of Natural Frequency and Mode Shape Errors Associated with Reduction to 16 DOF 4.3 BRANCHED SHELL EXAMPLE The shell structure, shown below in Figure 5, serves as the second illustrative example in this paper. It consists of five substructures, namely (1) a lower cylindrical skirt (fully fixed at its base), (2) a lower hemispherical bulkhead, (3) lower cylindrical section, (4) upper cylindrical section, and (5) upper hemispherical bulkhead. The overall dimensions of the aluminum structure are length, L=100 inches, radius, R=20 inches, and wall thickness, h=0.4 inches. 364
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