Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy

Abstract

The nonlinear dynamical behavior of a single-mode model of noncontact AFM is analyzed in terms of attractors robustness and basins integrity. The model considered for the analyses, proposed in (Hornstein and Gottlieb in Nonlinear Dyn. 54:93-122, 2008), consistently includes the nonlinear atomic interaction and is studied under scan excitation (which appears as parametric excitation) and vertical excitation (which is prevalently external). Local bifurcation analyses are carried out to identify the overall stability boundary in the excitation parameter space as the envelope of system local escapes, to be compared with the one obtained via numerical simulations. The dynamical integrity of periodic bounded solutions is studied, and basin erosion is evaluated by means of two different integrity measures. The obtained erosion profiles allow us to dwell on the possible lack of homogeneous safety of the stability boundary in terms of robustness of the attractors, and to identify practical escape thresholds ensuring an a priori design safety target

Influence of a locally-tailored external feedback control on the overall dynamics of a non-contact AFM model

“…As done for the results presented in [27] concerning the uncontrolled system, terms related to internal feedback control and the non-linear term related to α 2 are neglected, in the light of observations about the orders of magnitude of various coefficients in commercial AFMs [28], and in view of obtaining a simplified model to perform the numerical analyses.…”

“…Indeed, the basic experimental analyses preferably accomplished within the AFM community have to be fruitfully paralleled by in-depth phenomenological studies, to be conducted with the tools of non-linear dynamics, able to grasp the fundamental aspects of system response, along with their changes in terms of a variety of involved parameters. The subsequent comparison with the results of the underlying uncontrolled AFM system, already presented by the authors in [27], finally, may permit the comprehensive and critical evaluation of the effectiveness and general consequences of control actuation on the system dynamics, with a main view to the overall response scenario.…”

“…Following the same pattern as in [27], the two cases of controlled model subject to either scan parametric excitation or external vertical excitation are presented, yet with a richer and more involved analysis of the response made necessary by the presence of also the control parameters, besides the system ones, and by their combined effects on the dynamics.…”

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

“…Basin portraits have been used to study dynamical integrity in nonlinear systems ranging from the macro-scale down to the nanoscale. These systems include unsynchronized power systems, planar pendula, vibration-based energy harvesters, nonlinear mechanical oscillators, atomic force microscopes, and actuated carbon nanotubes [34,35,36,37,38,39].…”

Jump and pull-in dynamics of an electrically actuated bistable MEMS device

“…Taking them into [21,22], where all the basic aspects are illustrated and discussed, including the difference with respect to the classical stability concepts, the main current advances in analytical tools for quantifying the integrity of a system against disturbances, and the actual substantial developments in the direction of practical applications. Dynamical integrity predictions have been recently widely referred in the literature in micro and nanosystems, both for interpreting and predicting the experimental behavior [23,24], and for getting hints towards engineering design [25,26], and for controlling the global dynamics [27].…”