Vol. 30 No. 3 (2020)

Exact Mode Shapes of T-shaped and Overhang-shaped Microcantilevers

Le Tri Dat
Ton Duc Thang University
Vu Lan
Quang Trung High School, Binh Phuoc
Nguyen Duy Vy
Ton Duc Thang University

Published 20-10-2020


  • microcantilever,
  • mode shape,
  • analytical method,
  • overhang-shaped,
  • T-shaped

How to Cite

Dat, L. T., Lan, V., & Vy, N. D. (2020). Exact Mode Shapes of T-shaped and Overhang-shaped Microcantilevers. Communications in Physics, 30(3), 301. https://doi.org/10.15625/0868-3166/30/3/15080


Resonance frequencies and mode shapes of microcantilevers are of important interest in micro-mechanical systems for enhancing the functionality and applicable range of the cantilevers in vibration transducing, energy harvesting, and highly sensitive measurement. In this study, using the Euler-Bernoulli theory for beam, we figured out the exact mode shapes of cantilevers of varying widths such as the overhang- or T-shaped cantilevers. The obtained mode shapes have been shown to significantly deviate from the approximate forms of a rectangular cantilever that are commonly used in mechanics and physics. They were then used to figure out the resonance frequencies of the cantilever. The analytical solutions have been confirmed by using the finite element method simulations with very low deviation. This study suggested a method for correctly obtaining the resonance frequency of microcantilevers with complicated dimensions, such as the doubly clamped cantilever with the undercut, with the overhangs at the clamped positions, or with an attached mass in the middle.


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