Frequency equation and semi‐empirical mechanical coupling strength of microcantilevers in an array

Le Tri Dat, Vinh N. T. Pham, Nguyen Duy Vy, Amir F. Payam

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)


A characteristic equation for the frequencies of the T-shaped and overhang-shaped cantilevers is derived for the first time. We show that there are optimum values of the overhang lengths and widths that maximize the frequency and the number of maxima is corresponding to the mode number. The frequency of higher-order modes could be tuned by changing the overhang dimensions. Especially, a semi-empirical formula for the coupling strength (κ) between cantilevers in an array is proposed where the strength presents a cubic decrease with the overhang width (ξ) and a linear increase with the overhang length (η) , κ=η/ξ3 . There is a very good agreement between the proposed formula and the values obtained in recent experiments by other researchers.
Original languageEnglish
Pages (from-to)3237-3244
Number of pages8
JournalMicroscopy Research and Technique
Issue number9
Early online date16 Jun 2022
Publication statusPublished (in print/issue) - Sept 2022

Bibliographical note

Funding Information:
Authors are thankful to Dr. Hien Duy Tong (Nanosens Research B.V., The Netherlands) for fabrication of cantilevers. N.D. Vy is thankful to the Van Lang University. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.01‐2019.345.

Publisher Copyright:
© 2022 Wiley Periodicals LLC.


  • Medical Laboratory Technology
  • Instrumentation
  • Histology
  • Anatomy
  • microcantilever
  • coupling strength
  • AFM
  • frequency equation
  • overhang-shaped


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