Figure 4. Physical Representation of System AB-TT. Table 4. Modal Properties of System AB-TT. Table 5 lists the comparisons of the two FEM system models, AB-TR and AB-TT. Minimal differences exist in the natural frequencies, confirming the accuracy of the rotational stiffness approximation in model AB-TT. Table 6 lists the natural frequencies and damping of both FBS system models obtained using modal parameter estimation. A similar degree of difference exists in natural frequencies of the FBS models as the FEM models, further validating the rotational stiffness approximation. Minimal differences also exist in the percent critical damping between the two FBS models. Table 5. FEM System Model Comparison. Table 6. FBS System Model Comparison. Perturbation of Frequency Response Functions Perturbation of FRF was performed in FEMtools [20] by applying a one percent random noise to the FRF. FEMtools applies this percentage of noise by first performing an inverse Fourier transform on all FRFs and finding the maximum value within all the time histories produced. The software then produces uniform random time histories for each function using the specified percentage of this maximum value. A uniform random time history is added to each function and a Fourier transform is then performed to put all functions back in the frequency domain. Note that this technique does produce a significantly higher level of noise at less active DOF, which in test one would typically use more sensitive accelerometers or reduce the acquisition range to minimize noise at these locations. However, modal parameter estimation was performed to remove the noise prior to performing decoupling. Decoupling of System – Analytical Models The first case considers system AB-TR in which there is translational and rotational springs connecting the two beams at two locations, as previously shown in Figure 3. Using system FRF from the FBS models and FRF of beam A, the drive point connection FRF of beam B were computed. Using true FRF without noise or truncation, all techniques produce accurate results. While four DOF were coupled in the system model (two translational and two rotational), decoupling produced accurate results without the use of rotational FRF in the computation due to the low coupling stiffness relative to the transverse coupling stiffness. However, excluding rotational DOF in decoupling a system with significant rotational coupling stiffness can produce error. To determine each technique’s sensitivity to noise, a one percent uniform random noise was applied to the FRF as previously mentioned. Performing the decoupling directly with the noisy FRFs produced resulting FRFs with a significant level of 177
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