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Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory

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Claeyssen J. R., Tsukazan T., Tonetto L., Tolfo D.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2013
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tom 2
124-144
EN
A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous boundary conditions. Transients are identified from intial values of permanent responses. Eigenanalysis for determining frequencies and matrix mode shapes is done with the use of a fundamental matrix response that characterizes solutions of a damped second-order matrix differential equation. It is observed that surface effects are influential for the natural frequency at the nanoscale. Simulations are performed for a bi-segmented free-free beam and with a micro-cantilever beam actuated by a piezoelectric layer laminated in one side.
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Multidisciplinary approaches in theory, applications and modeling of nanoscale systems

54%
Melnik R. V. N.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2013
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tom 2
1-9
EN
This editorial provides an overview of both fundamental and applied research areas covered by the journal of Nanoscale Systems: Mathematical Modeling, Theory and Applications (NanoMMTA), as well as of articles published in the journal inaugural volume. The unique feature of NanoMMTA is its focus on the interface between the study, development, and application of systems at the nanoscale with theoretical methods and experimental techniques on the one hand and mathematical, statistical, and computational tools on the other. NanoMMTA is the first international, interdisciplinary, peer-reviewed journal focusing specifically on this interface. This emerging multidisciplinary field at the interface of mathematical modeling, nanoscience and nanotechnology includes applications and advancements of these tools in all of the disciplines facing the challenges associated with the nanoscale systems.
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