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

• Autorzy: Julio R. Claeyssen , Teresa Tsukazan , Leticia Tonetto , Daniela Tolfo
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Atomic force microscopy; nanoscale materials and structures; chemical/biological sensors; nanomachining; microscaled Timoshenko beams

Kategorie tematyczne

• 81.07.-b: Nanoscale materials and structures: fabrication and characterization(for structure of nanoscale materials, see 61.46.-w; for nanostructured materials in electrochemistry, see 82.45.Yz; see also 62.23.-c Structural classes of nanoscale systems in mechanical properties of condensed matter)
• 62.25.-g: Mechanical properties of nanoscale systems(for structure of nanoscale systems, see 61.46.-w; for structural transitions in nanoscale materials, see 64.70.Nd; for electronic transport in nanoscale systems, see 73.63.-b)
• 07.79.Lh: Atomic force microscopes
• 87.85.fk: Biosensors

• 35E05: Fundamental solutions
• 35L30: Initial value problems for higher-order hyperbolic equations
• 74H55: Stability
• 74H10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
• 35L35: Initial-boundary value problems for higher-order hyperbolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2013
• Tom: 2
• Strony: 124-144

Daty

otrzymano

2013-01-24

poprawiono

2013-04-25

zaakceptowano

2013-04-25

online

2013-06-03

Twórcy

autor

Julio R. Claeyssen

• Institute of Mathematics, Universidade Federal do Rio Grande
  do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS,
  Brazil
• Mechanical Engineering Graduate Program, Universidade Federal
  do Rio Grande do Sul, Rua Sarmento Leite, 425, 90050-170,
  Porto Alegre, RS, Brazil

autor

Teresa Tsukazan

• Institute of Mathematics, Universidade Federal do Rio Grande
  do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS,
  Brazil

autor

Leticia Tonetto

• Institute of Mathematics, Universidade Federal do Rio Grande
  do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS,
  Brazil

autor

Daniela Tolfo

• Institute of Mathematics, Universidade Federal do Rio Grande
  do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS,
  Brazil

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Identyfikatory

DOI

10.2478/nsmmt-2013-0008