Figure 2. Physical Representation of Beams. Table 2. Modal Properties of Beams. System Description – AB-TR Two systems were considered for the analytical studies. The first system, AB-TR, contains two sets of Translational and Rotational stiffness connections. To correlate with the experimental structure, a translational stiffness of 8E7 N/m and a rotational stiffness of 6E2 rad/Nm were used at nodes 6 and 26. Figure 3 displays a physical representation of the two beam system, AB-TR. Both a physical FEM system model, as well as an FBS system model was created. The FBS system model will be used for all of the cases studied, in order to avoid error associated with lack of damping in the physical system model. Table 3 lists the natural frequencies of both sets of system models. A maximum frequency difference of 0.59% exists in the first flexible mode. The natural frequencies of the FBS models were determined using modal parameter estimation in LMS Test.Lab [19]. Note that the two rigid body modes were not extracted due to low frequency limitations of the modal parameter estimation software. Figure 3. Physical Representation of System AB-TR. Table 3. Modal Properties of System AB-TR. System Description – AB-TT The second system, AB-TT, contains Two closely-spaced Translational springs at each connection location. An appropriate distance was determined to have the equivalent translational and rotational connection stiffness as system AB-TR, a similar approach as the Equivalent Multiple Point Constraint technique. The EMPC method has been previously used to address rotational DOF for FBS modeling [5], in which multiple translational DOF are used to approximate rotational DOF. A physical FEM system model as well as an FBS system model was again created. A physical representation of system AB-TT is shown in Figure 4. Table 4 lists the natural frequencies and percent differences of the two models. Both system models of AB-TT produce nearly identical results. 176
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