This paper presents a theoretical model of corrugated foil strip (bump foil) deformation in compliant foil bearings and dampers. The friction forces between bump foils and the housing or the top foil, local interaction forces, variable load distributions, and bump geometries are taken into consideration. Following the trend of earlier published experimental data, the bumps near the fixed end have a much higher predicted stiffness (lower deflection) than those near the free end. Higher friction coefficients tend to increase stiffness and may pin down bumps near the fixed end. An increase in the friction coefficient between the top foil and the bump is a more effective method of achieving both Coulomb damping and higher stiffness. In addition to bump geometry, the load distribution profile greatly influences bump stiffness. A follow-up paper will present the experimental verification and discuss the comparison between theoretical and experimental results.

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