## 1 Introduction
In the actual structure, due to the influence of structural stiffness, contact surface coordination, and other factors, the contact surface is usually nonuniform contact and may appear in various contact states. Thus, the macroscopic slip model can only accurately represent the situation in which all nodes of the contact surface slip or stick simultaneously, which results in a large error compared to the actual situation. In 1967, [PERSON] [12] first constructed a micro-slip model to represent the contact state of the interface by parallel and series connections of multiple single-point Coulomb friction models. The micro-slip model is suitable for structures with large contact areas and complex contact states and can consider the complex contact state of different contact nodes. The existing dry friction structures that consider the micro-slip effect tend to be described by the micro-slip model. Given that the energy dissipation of the contact nonlinear structure is obtained by the relative motion between the vibrating bodies, the dynamic characteristics of the structure are closely related to the mutual motion form of the contact interface. Aiming at the nonlinear phenomenon caused by the friction behavior of the contact interface, a suitable contact kinematics model was established. The contact kinematics models are mainly divided into four types: the 2D constant pressure dry friction model, the 2D constant allowable variable pressure dry friction model, the 3D constant pressure dry friction model, and the 3D constant allowable variable pressure dry friction model. As confirmed by scholars in this field, the contact problem of rough surfaces will greatly affect the static and dynamic performance of mechanical structures, and the joint surface generated by the contact between two surfaces will make the performance of the whole mechanical equipment nonlinear, which leads to complicated problems. It is of great significance to apply scientific and effective research methods to the contact problem of surfaces. With the development of theory and practice, the contact theory of rough surfaces has been constantly improved. The German physicist [PERSON] first investigated the contact problem. In 1882, he published an article titled On the Contact of Elastic Solids, laying a foundation for the development of contact mechanics. [PERSON] mainly studied the normal displacement caused by the contact between two spheres and the problem of determining the contact area. Based on the following assumptions, a contact model of the elastic deformation of a sphere was established: (1) surfaces are continuous and nonconforming; (2) strains are small and within the elastic limit; (3) each solid can be considered as an elastic half-space; (4) surfaces are frictionless. Since then, lots of scientists have tried to use [PERSON]'s theory to study the contact mechanics of rough interfaces. Specifically, statistical modeling and analysis, research based on fractal geometry theory, finite element numerical solution, and experimental analysis have mainly been adopted. In a search of the literature, it was found that there has been a lack of research on the influence of roughness on UPDs under different excitation methods. Therefore, the following work was carried out in this paper. Based on the friction characterization method of the complex dry friction contact surfaces, the influence of contact surface roughness on UPD vibration reduction under different excitation modes was studied. First, a finite element model with a UPD was established, and dynamic modeling of the under-platform damper was carried out in combination with the 3D dry friction model. Second, based on FGT, a characterization method of complex contact force considering the contact surface roughness was proposed for the contact surface between the UPD and the blade.