40 Nonlinear Reduced Order Modeling of a Curved Axi-Symmetric Perforated Plate: Comparison with Experiments 443 0.92 0.94 0.96 0.98 1 1.02 1.04 10-4 10-3 10-2 Normalized Frequency Center Deflection, m PP01 PP02 PP01 Exp. PP02 Exp. Fig. 40.7 Peak amplitude at center of plate capable of changing the nonlinearity from a softening to hardening effect. The turning point can be captured experimentally; however the failure occurs as the change in frequency begins to increase limiting the full characterization of the increase in frequency. The full field deformation at the point where the change in the fundamental frequency of vibration provides a good comparison of the dynamic response in nonlinear regimes as shown in Fig. 40.8. The colorbar accompanying each figure corresponds to the peak deformation observed in the full-field deformation. The full-field deformations observed for the modeled PP01, shown in Fig. 40.8a, b, has a peak deformation of 1.67 mm for the first harmonic and 0.29 mm for the third harmonic. The companion experimental deformations are shown in Fig. 40.8c, d, where a peak deformation of 1.94 mm is measured for the first harmonic and 0.41 mm for the third harmonic. The first harmonic for this structure is 16 % higher than predicted by the model, and the third harmonic is 40 % higher. The full-field deformations for PP02, shown in Fig. 40.8e, f, has a peak amplitude of 1.78 mm for the first harmonic and 0.27 mm for the third harmonic. The experimental deformations are shown in Fig. 40.8g, h, where a peak deformation of 2.43 mm is observed for the first harmonic and a peak deformation of 0.23 mm is observed for the third harmonic. The first harmonic for this structure is 36 % greater than that predicted by the model and the third harmonic is 17 % lower than predicted by the model. The difference between the harmonic amplitudes of the models suggest a modal coupling not accounted for in the NLROM. A further examination of the higher harmonics of the experimental setup is needed to characterize the modal coupling and will guide the next step in the creation of NLROMs. One interesting thing to note is the asymmetry in the third harmonic shown in Fig. 40.8h, which is not as pronounced in the experimental results, and could be a result of the base excitation loading which limits the ability to excite asymmetries in the structure fully.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==