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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
The nonlinear response of a reduced model of an orthotropic single-layered plate with thermomechanical coupling is investigated in the presence of thermal excitations, in addition to mechanical ones. Different issues are addressed via accurate and extended local and global analyses. (i) Assessing the possible occurrence, disappearance or modification of mechanical buckling as a result of thermal aspects; (ii) exploiting global dynamics to unveil the effects of coupling; (iii) highlighting the crucial role played by the slow thermal transient evolution in modifying the fast steady mechanical response; (iv) framing the influence of coupling and underlining the need to use a thermomechanical model to grasp the actual plate dynamics; and (v) getting hints of technical interest as to the outcome robustness with respect to variations in the external/internal thermal parameters.
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AbstractThe dynamical behavior of a mono-dimensional bar with distributed microcracks is addressed in terms of free and forced wave propagation. The multiscale model, derived from a generalized continuum formulation, accounts for the microstructure by means of a microdisplacement variable, added to the standard macrodisplacement, and of internal parameters representing density and length of microcracks. The influence of coupling between micro-and macrodisplacement overall response on the system is discussed, as well as the effect of the damage parameters on the propagating waves.
An external feedback control is inserted in a nonlinear continuum formulation of a noncontact AFM model. The aim of the feedback is to keep the system response to an operationally suitable one, thus allowing reliable measurement of the sample surface by avoiding possible unstable microcantilever sensor motions.\ud
The study of the weakly nonlinear system dynamics about the desired fixed point close to primary resonance is carried out via multiple-scale asymptotics, whose outcomes are validated via numerical simulations of the original system equations of motion. The latter include controllable periodic dynamics and additional\ud
periodic and distinct quasiperiodic solutions that appear beyond the asymptotic stability thresholds. The results highlight the effectiveness of the applied feedback control technique and also enable the derivation of a comprehensive system bifurcation structure highlighting the stability thresholds for robust controllable\ud
AFM dynamics
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