40 Nonlinear Reduced Order Modeling of a Curved Axi-Symmetric Perforated Plate: Comparison with Experiments 445 40.4 Conclusion The examination of the nonlinear normal modes (NNMs) has provided insight to the underlying modal and harmonic coupling observed in the perforated plates investigated. The nominal model, assuming a flat geometry, showed only an increase in the fundamental frequency of vibration as the response amplitude is increased. With the inclusion of the initial curvature of the perforated plates, a strong coupling is observed between mode 1 and mode 6 of the plate for the first NNM. Therefore, the inclusion of mode 1 and mode 6 into the nonlinear reduced order models is needed. As the structure is pushed at higher input forces the mode 6 deformation becomes more pronounced as shown experimentally and numerically. Although more tuning is needed to accurately account for the amount of coupling between mode 1 and mode 6. Though the models have shown the ability to describe the trend of the dynamic behavior of the perforated plates, more work is needed to fully identify the modal coupling in the experimental results. Additionally, an examination of the stress distribution of the change in deformation observed in the plates is needed for accurate prediction of the failure of these plate. References 1. Kerschen, G., et al.: Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23(1), 170–194 (2009) 2. Peeters, M., et al.: Nonlinear normal modes, Part II: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23(1), 195–216 (2009) 3. Allen, M.S., et al.: A numerical continuation method to compute nonlinear normal modes using modal reduction. In: 53rd AIAA Structures, Structural Dynamics, and Materials Conference. Honolulu, Hawaii (2012) 4. Kuether, R.J., Allen, M.S.: A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models. Mech. Syst. Signal Process. (2013) 5. Gordon, R.W., Hollkamp, J.J.: Reduced Order Models for Acoustic Response Prediction. Air Force Research Laboratory (2011) 6. Peeters, M., Kerschen, G., Golinval, J.C.: Dynamic testing of nonlinear vibrating structures using nonlinear normal modes. J. Sound Vib. 330(3), 486–509 (2011) 7. Peeters, M., Kerschen, G., Golinval, J.C.: Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech. Syst. Signal Process. 25(4), 1227–1247 (2011) 8. Ehrhardt, D.A.: A full-field experimental and numerical investigation of nonlinear normal modes in geometrically nonlinear structures. In: Engineering Mechanics. University of Wisconsin-Madison (2015) 9. Kuether, R.J., Allen, M.S.: Computing nonlinear normal modes using numerical continuation and force appropriation. In: ASME 2012 International Design Engineering Technical Conferences IDETC/CIE 2012. Chicago, IL (2012) 10. Ehrhardt, D.A., Allen, M.S., Yang, S., Beberniss, T.J.: Full-field linear and nonlinear measurements using continuous-scan laser Doppler vibrometry and high speed three-dimensional digital image correlation. Mech. Syst. Signal Process. (2015). In Review 11. Jhung, M.J., Jo, J.C.: Equivalent material properties of perforated plate with triangular or square penetration pattern for dynamic analysis. Nucl. Eng. Technol. 38(7) (2006) 12. Gordon, R.W., Hollkamp, J.J.: Reduced-order Models for Acoustic Response Prediction. Air Force Research Laboratory, Dayton, OH (2011) 13. Hollkamp, J.J., Gordon, R.W.: Reduced-order models for nonlinear response prediction: implicit condensation and expansion. J. Sound Vib. 318(4–5), 1139–1153 (2008) 14. Hollkamp, J.J., Gordon, R.W., Spottswood, S.M.: Nonlinear modal models for sonic fatigue response prediction: a comparison of methods. J. SoundVib. 284(3–5), 1145–1163 (2005)
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