Numerical analysis of fractional dynamical behavior of Atomic Force Microscopy

Abstract

We investigate the nonlinear dynamic model of the Atomic Force Microscopy model (AFM) with the influence of a viscoelastic term. The mathematical model is based on non-resonant and almost linear responses, together with the deflection of the microcantilever, and also considers the interaction forces between the atoms of the analysis tip and the sample surface. Our results show the influence on the nonlinear dynamics of this model considering the term viscoelastic. We also analyzed the generalized model with the fractional calculus with the Riemann–Liouville operator derivative applied to the viscoelastic term and thus having the fractional nonlinear dynamics of the AFM system. For the analysis of the system, we used the classic tooling of nonlinear dynamics (Bifurcation diagram, 0–1 Test, and Poincaré maps, and the Maximum Lyapunov Exponent), however, the results showed the chaotic and periodic regions of the fractional system.