Dynamic analysis and experimental validation of two-dimensional interface friction with time-varying normal force under base excitation

Research on the dynamic response mechanism of two-dimensional dry friction at the interface level under complex excitation remains incomplete, and experimental validation in this area is still insufficient. This study establishes a dynamic model that incorporates both base excitation and a time-varying normal force. The harmonic balance method (HBM) is employed to solve system responses, analyzing 2D friction dynamics under coupled multi-frequency base excitation and time-varying normal forces. A 2D base-excitation friction experimental apparatus is designed and constructed, enabling flexible adaptation to different material friction pairs by adjusting counterweight mass and isolation springs. It has been shown that, different friction states correspond to distinct frequency characteristics under complex excitation conditions. Mapping relationships between friction state and spectral characteristics is obtained for multiple coupled excitations, and the spectral characteristics of the system in the slip state under dual-frequency excitation are experimentally validated. Furthermore, it is discovered that for dry friction systems under base excitation, when contact stiffness significantly exceeds the elastic support stiffness of the system, the resonance point under optimal normal force occurs at \(\sqrt 2\) $\sqrt{2}$ times the natural frequency of the frictionless system. This study not only enriches the theoretical framework of dry friction system dynamics but also provides novel insights for designing 2D friction experiments. It offers theoretical support for friction state identification and time-varying normal force control strategy design in complex systems.