This study proposes a mathematical model to investigate the nonlinear contact behavior of bolted joint interfaces under the combined effects of surface roughness and normal preload. Based on the asperity contact mechanics, the explicit analytical expressions for the restoring force and the natural frequency as functions of deflection have been derived. The vibration differential equation for the bolted joint interface is formulated by integrating the surface topography, material properties, and preload-induced displacement effects. The natural frequency variation with initial displacement and the effect of rough topography on the restoring force and natural frequency are analyzed using multi-scale and Taylor series methods. The amplitude–frequency response of the contact vibration under harmonic excitation is successfully obtained. The power-law relationship between the contact force and contact deformation is experimentally verified. The deviation between experimental results and the theoretical model is caused by the difficulty in directly measuring contact deformation and partial offset at the interface. The results show that the rough bolted joint interface has nonlinear static and dynamic contact behavior. The amplitude jump phenomenon occurs, and the main resonance region expands with increasing surface roughness. In contrast, an ideal smooth bolted joint interface exhibits linear contact vibration characteristics. This study provides a theoretical foundation for correlating the surface topography with vibration response.
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