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

doi:10.1002/jemt.24180

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 journal › Article › peer-review

5 Citations (Scopus)

109 Downloads (Pure)

Abstract

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 language	English
Pages (from-to)	3237-3244
Number of pages	8
Journal	Microscopy Research and Technique
Volume	85
Issue number	9
Early online date	16 Jun 2022
DOIs	https://doi.org/10.1002/jemt.24180
Publication status	Published (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.

Funding

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.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy
SDG 17 Partnerships for the Goals

Keywords

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

Access to Document

10.1002/jemt.24180

MRT-22-062_Proof_hiAuthor Accepted Manuscript, 864 KB

Cite this

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title = "Frequency equation and semi‐empirical mechanical coupling strength of microcantilevers in an array",

abstract = "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.",

keywords = "Medical Laboratory Technology, Instrumentation, Histology, Anatomy, microcantilever, coupling strength, AFM, frequency equation, overhang-shaped",

author = "Dat, \{Le Tri\} and Pham, \{Vinh N. T.\} and Vy, \{Nguyen Duy\} and Payam, \{Amir F.\}",

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: {\textcopyright} 2022 Wiley Periodicals LLC.",

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doi = "10.1002/jemt.24180",

language = "English",

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AU - Dat, Le Tri

AU - Pham, Vinh N. T.

AU - Vy, Nguyen Duy

AU - Payam, Amir F.

N1 - 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.

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N2 - 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.

AB - 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.

KW - Medical Laboratory Technology

KW - Instrumentation

KW - Histology

KW - Anatomy

KW - microcantilever

KW - coupling strength

KW - AFM

KW - frequency equation

KW - overhang-shaped

UR - https://www.scopus.com/pages/publications/85131930831

U2 - 10.1002/jemt.24180

DO - 10.1002/jemt.24180

M3 - Article

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SN - 1059-910X

VL - 85

SP - 3237

EP - 3244

JO - Microscopy Research and Technique

JF - Microscopy Research and Technique

IS - 9

ER -

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

Abstract

Bibliographical note

Funding

UN SDGs

Keywords

Access to Document

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