Static and Dynamic Analysis of Deformable Fractal Surface in Contact With Rigid Flat

Abstract

The chapter consists of static and dynamic analyses of a fractal rough surface in contact with a rigid flat. The fractal surface is constructed using modified Weierstrass-Mandelbrot function. A rigid flat surface touches the topmost point of the rough surface, which moves towards the rough surface and deforms it. Different contact parameters (e.g., contact force, contact area, contact stress, etc. for varying fractal and material properties are obtained through finite element based static analysis. A parameter denoting the degree of nonlinearity of the contact system is extracted from the force-displacement plot of the surface. This parameter is utilized to explain the dynamic behaviour of the fractal surface which vibrates under the influence of the externally excited rigid flat surface. The dynamic analysis of the contact system is carried out by modelling the contact interface as a single degree of freedom (SDOF) spring-mass-damper system. The dynamic behavior of the system is investigated in terms of frequency response curves, time-displacement plots, and phase plots.