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.

我们研究了受粘弹性项影响的原子力显微镜模型 (AFM) 的非线性动力学模型。该数学模型基于非共振和几乎线性的响应，连同微悬臂梁的偏转，还考虑了分析尖端的原子与样品表面之间的相互作用力。我们的结果表明，考虑到粘弹性项，对该模型的非线性动力学的影响。我们还分析了分数阶微积分的广义模型，其中 Riemann-Liouville 算子导数应用于粘弹性项，从而具有 AFM 系统的分数非线性动力学。对于系统的分析，我们使用了非线性动力学的经典工具（分叉图、0-1 检验和庞加莱映射以及最大李雅普诺夫指数），