58 J. H. Porter et al. 150 160 170 180 10-7 10-6 10-5 10-4 10-3 10-2 150 160 170 180 10-7 10-6 10-5 10-4 10-3 10-2 (a) (b) Fig. 3 Modal backbones for (a) different asperity representations for μ = 0.05 and (b) different values of the friction coefficient μ with the ellipsoid Iwan asperity model 0.05 bound the experimental damping factor for most amplitude levels. In addition, the frequency drops by 21.7 and 7.82 Hz over the amplitude range for the cases of μ = 0.01 and 0.05, respectively. Thus, these two cases bound the experimental frequency drop of 16.4 Hz. Further development of the contact model is required to address the error in low amplitude natural frequency and dissipation. However, the presented results illustrate the importance of considering the eccentricity of contact asperities and provide promising behavior by bounding the frequency shift and the damping factor with friction coefficients of μ =0.01 and 0.05. Since the time of publication, an error was discovered with the calculation of the elliptical contact parameters, so the effect of using ellipsoids on the frequency is likely less than shown here but in the same direction. Acknowledgments This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship under Award Number(s) DE-SC0021110. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. References 1. Yang, B.D., Menq, C.H.: Modeling of friction contact and its application to the design of shroud contact. J. Eng. Gas Turbines Power 119(4), 958–963 (1997). https://doi.org/10.1115/1.2817082 2. Schwingshackl, C.W., Petrov, E.P., Ewins, D.J.: Measured and estimated friction interface parameters in a nonlinear dynamic analysis. Mech. Syst. Signal Process. 28, 574–584 (2012) 3. Balaji, N.N., Chen, W., Brake, M.R.W.: Traction-based multi-scale nonlinear dynamic modeling of bolted joints: formulation, application, and trends in micro-scale interface evolution. Mech. Syst. Signal Process. 139, 106615 (2020). https://doi.org/10.1016/j.ymssp.2020.106615 4. Porter, J.H., Balaji, N.N., Brake, M.R.W.: A quantitative assessment of the model form error of friction models across different interface representations for jointed structures. Mech. Syst. Signal Process. Under review 5. Eriten, M., Polycarpou, A.A., Bergman, L.A.: Physics-based modeling for fretting behavior of nominally flat rough surfaces. Int. J. Solids Struct. 48(10), 1436–1450 (2011). ISSN 0020-7683. https://doi.org/10.1016/j.ijsolstr.2011.01.028 6. Li, W., Zhan, W., Huang, P.: A physics-based model of a dynamic tangential contact system of lap joints with non-Gaussian rough surfaces based on a new solution. AIP Adv. 10(3), 035207 (2020). ISSN 2158-3226. https://doi.org/10.1063/1.5143927 7. Zhan, W., Huang, P.: Physics-based modeling for lap-type joints based on the Iwan model. J. Tribol. 140(5) (2018). ISSN 0742-4787. https:// doi.org/10.1115/1.4039530. Publisher: American Society of Mechanical Engineers Digital Collection 8. Zhan,W., Huang, P.: Modeling tangential contact based on non-Gaussian rough surfaces. In: Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology (2018). https://doi.org/10.1177/1350650118758742. SAGE Publications, London, England
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