Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam

Abstract

Abstract. We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM) microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.

Micromechanical vibro-impact systems: a review

“…The FETD method is popular in the MEMS field using commercial software, such as RF switches using ANSYS [39,40,193] and COMSOL Multiphysics [164]. The FDTD method has also been used in studying the time-dependent behavior of switches [37,155,[159][160][161][162] and tapping-mode AFM [148,149]. However, both methods require extensive time integration of second-order ODEs, making themselves computationally expensive and nearly impossible for systematic investigation and device optimization.…”

“…Distributed-parameter approach is commonly used to analyze MEMS vibro-impact systems that maintains the continuous nature of the structure and represents the response in terms of continuous variables. Based on this approach, MEMS vibro-impact systems are usually modeled as a timevarying, spatially distributed partial differential equation (PDE) coupled with the nonlinear terms and most of them are based on the Euler-Bernoulli theory [18,37,115,117,141,148,149,160,163]. A widely used method to treat these PDEs is to reduce them to tractable ordinary differential equations (ODEs) through modal analysis [18,115,117,141,163], resulting in a lumped reduced-order model.…”

“…For the past decade or so, the one-mode approximation approach has attracted much attention [21,116,140,147,148,150,168]. While serving well in most air or vacuum environments, the one-mode approximation becomes insufficient in liquid.…”

Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion

“…In the present paper, the frequency of the base displacement is taken very small with respect to the natural frequency of the system i.e., ϵ = Ω/ω << 1. The case of resonant excitations was investigated in many papers, see for instance [7]. Equation (6) can be written as a fast-slow system since it is ruled by two dynamics: the first on the time scale of order 1 (the natural frequency) and the second one on the time scale of order ϵ (the base displacement).…”