24 T. Roberts and P. J. Cornwell welded structure had consistently higher natural frequencies than the other two structures. Although the welded structure was heavier than the solid structure, the stiffer material properties of the weld-filler material resulted in higher natural frequencies. The mass properties were found to be of less significance than other properties of the structures. The FE models of the solid and welded structures confirmed the results from the experimental modal tests; the natural frequencies from the FE models and the experiments compared very well. The bolted structure FE model, however, did not match the experimental results quite as well as the other two models. In order to simulate the tightness of the bolted joint, different sized contact regions were used in the FE models. In general, larger contact regions correlated to higher natural frequencies, and the larger contact regions tended to compare better to the experimental modal results. When damage was introduced into the bolted structure by removing a bolt, changes in experimental modal properties proved to be inadequate to distinguish between the undamaged and damaged structures. There was virtually no difference in the natural frequencies between the bolted structure with all four bolts (undamaged) and that with one bolt completely missing (damaged). However, natural frequency results from the FE models did show some differences between the damaged and undamaged structures. One would expect that removing a bolt and its contact region from the model would lower the natural frequencies; this expectation held true, although some of the results were still counter-intuitive. Before removing the bolt from the model, the 17-mm contact region model had higher natural frequencies than the 10-mm contact region model. When a bolt was removed from the model, however, the 10-mm contact region model had higher natural frequencies than the 17-mm contact region model. These results, though not expected, confirm that the models are very sensitive to the contact parameters used to represent the bolted joint and that other properties, such as mass and material parameters, have a smaller effect on the model. The fractional strain energy method was used to compare the different structures. In the case of the experimental results, the strain energy method was not able to detect differences between solid, welded, and bolted structures nor was it able to distinguish the undamaged from the damaged bolted structures. Comparing the FE models with the SEM was more successful. The SEM could not detect a difference between the solid and welded FE structures, but the method was able to detect a difference between solid and bolted FE structures. Lastly, the SEM was used to compare the bolted FE models with and without damage (a bolt and its contact region removed from the model). The comparison of the undamaged and damaged FE models with 17-mm contact regions correctly identified the general area of the damage, but the SEM incorrectly identified the precise location of the damage. The comparison of the undamaged and damaged FE models with 10-mm contact regions correctly identified the precise area where the damage was located. Unfortunately, even though the method was able to determine differences in the FE models, its failure in the case of the experimental data indicates serious limitations of the method. Therefore, even though the SEM may be successful when using FE results, it may not useful when using experimental data. References 1. McCarthy, M., McCarthy, C., Lawlor, V., Stanley, W.: Three-dimensional finite element analysis of single-bolt, single-lap composite bolted structures. Compos. Struct. 71(2), 140–158 (2005) 2. Sun, D., Liao, R.: Damping prediction technique of the bolted structure considering pretension force. Open Civil Eng. J. 9, 622–626 (2015) 3. Xu, W.: Effect of Bolted Joint Preload on Structural Damping. University of South Florida (2013) 4. Zaman, I., Khalid, A., Araby, S., Ghazali, M.: The effects of bolted joints on dynamic responses of structures. In: IOP Conferene Series: Materials Science and Engineering 50 (2013) 5. Kedra, R., Rucka, M.: Damage detection in a bolted lap joint using guided waves. In: International Conference on Structural Dynamics (2017) 6. Du, F., Xu, C., Ren, H., Yan, C.: Structural health monitoring of bolted joints using guided waves: a review. Struct. Health Monit.Sens. Process. 8, 163–180 (2018) 7. Kim, J., Yoon, J., Kang, B.: Finite element analysis and modeling of a structure with bolted joints. Appl. Math. Model. 31(5), 895–911 (2007) 8. Mohammed, R.: Finite Element Analysis of Fillet Welded Joint. University of Southern Queensland, Toowoomba (2015) 9. Stubbs, N., Kim, J.-T., Farrar, C.R.: Verification of a nondestructive damage localization and sensitivity estimatory algorithm. In: 13th International Modal Analysis Conference (1995) 10. Cornwell, P., Doebling, S., Farrar, C.: Application of the strain energy damage detection method to plate-like structures. J. Sound Vib. 224(2), 359–374 (1999) 11. Liao, X., Zhang, J., Xu, X.: Analytical model of bolted joint structure and its nonlinear dynamic characteristics in transient excitation. Shock Vib. 2016, 11 (2016) 12. Doebling, S.W., Cornwell, P.J., Farrar, C.R.: DIAMOND: a graphical interface toolbox for comparative modal analysis and damage identification. In: Sixth International Conference on Recent Advances in Structural Dynamics, Southampton (1997)
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