Non-Smooth Dynamics of Tapping Mode Atomic Force Microscopy

Abstract

This study examines the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include van der Waals and Derjaguin-Müller-Toporov contact forces. We investigate the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. Through the use of bifurcation locus maps in the set of parameters of the discontinuous model, the overall dynamical response scenario is assessed. We demonstrate the influence of various dissipation mechanisms that are related with the AFM touching or lacking contact with the sample. Local and global analyses are used to investigate the stability of the stable solution in the repulsive regime. The impacting nonsmooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion.