11 Improved Expansion Results Using Regularized Solutions 111 11.3.2 Complicated Model: Coupled Components The coupled components model is schematically depicted in Fig. 11.2 and all the associated properties are listed in Table 11.2. The model is comprised of three beams intricately coupled together to serve as a practical example of a system-subsystemcomponent assembly. The system beam, beam A, is 140 inches long and connected to ground by soft springs at each end. The subsystem, beam B, is 50 inches long and coupled at both ends to the system beam A 45 inches from either end. The component, beam C, is 10 inches long and coupled at one end to the subsystem beam B 90 inches from the origin, or 45 inches down the length of beam B. The coupled components model resembles a structure commonly encountered in environments engineering analysis, in which several subsystems and components are coupled to, or within, a larger system. Obtaining the response of the subsystems and components is a challenge because of limited number of acquisition channels, inability to instrument deeply embedded subsystems and small components, and noise contamination. Expansion is a viable approach to appropriately characterize the response of non-instrumented components but is susceptible to noise. This model serves to demonstrate how well regularization can enhance the expansion results of a representative engineering system under the limitations of practical instrumentation. Fig. 11.2 Schematic depiction of the coupled components model Table 11.2 Coupled components model properties Overall properties Parameter Value Units System Beam A Young’s Modulus 1.00E+07 psi Density 2.59E-04 slug • in−3 Width 3.00 in Height 1.50 in Wall thickness 0.188 in Coupling Springs 1.00E+06 lb • in−1 Ground Springs 1.00E+03 lb • in1 Parameter Value Units Subsystem Beam B Length 140 in Nodes 141 Parameter Value Units Component Beam C Length 50 in Nodes 51 Parameter Value Units Length 10 in Nodes 11
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