Energy dissipation in mechanical joints occurs as a result of micro-slip motion between contacting rough surfaces. An account of this phenomenon is especially challenging due to the vast differences in the length and time scale differences between the macro-mechanical structure and the micron-scale events at the joint interface. This paper considers the contact between two nominally flat surfaces containing micron-scale roughness. The rough surface interaction is viewed as a multi-sphere elastic interaction subject to a periodic tangential force. It combines the Mindlin’s formulation [1, 2] for the elastic interaction of two spheres with the Greenwood and Williamson’s  statistical approach for the contact of two nominally flat rough surfaces so as to develop a model for multi-sphere problem in which sphere radii, contact load and the number of spheres in contact can only be known in a statistical sense and not deterministically.
Damping in Lap Joints Due to Partial and Full Micro-Slip Using a Three Dimensional Elastic Contact of Rough Surfaces
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Farhang, K, Sepehri, A, Segalman, D, & Starr, M. "Damping in Lap Joints Due to Partial and Full Micro-Slip Using a Three Dimensional Elastic Contact of Rough Surfaces." Proceedings of the ASME 2008 International Mechanical Engineering Congress and Exposition. Volume 11: Mechanical Systems and Control. Boston, Massachusetts, USA. October 31–November 6, 2008. pp. 499-509. ASME. https://doi.org/10.1115/IMECE2008-69077
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