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Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy. (English) Zbl 1178.74122
Summary: The nonlinear equations of motion for the scan process in noncontacting atomic force microscopy are consistently derived using the extended Hamilton’s principle. A modal dynamical system obtained from the continuum model reveals that scan control appears in the form of parametric excitation. The system is analyzed asymptotically and numerically to yield escape bounds limiting the noncontacting mode of operation. Approximate stability bounds are deduced from both a global Melnikov integral and a local Moon-Chirikov overlap criterion. The Melnikov-Holmes stability curve and the overlap criterion are found to be similar for small damping. However, for very small damping, typical of ultra-high vacuum conditions, where the Melnikov bound becomes trivial, the Moon-Chirikov criterion yields an improved stability threshold.

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
74M25 Micromechanics of solids
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