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Meccanica

Erschienen in:

18.03.2016

Analytical study of the frequency shifts of micro and nano clamped–clamped beam resonators due to an added mass

verfasst von: Adam Bouchaala, Ali H. Nayfeh, Mohammad I. Younis

Erschienen in: Meccanica | Ausgabe 1-2/2017

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Abstract

We present analytical formulations to calculate the induced resonance frequency shifts of electrically actuated clamped–clamped micro and nano (Carbon nanotube) beams due to an added mass. Based on the Euler–Bernoulli beam theory, we investigate the linear dynamic responses of the beams added masses, which are modeled as discrete point masses. Analytical expressions based on perturbation techniques and a one-mode Galerkin approximation are developed to calculate accurately the frequency shifts under a DC voltage as a function of the added mass and position. The analytical results are compared to numerical solution of the eigenvalue problem. Results are shown for the fundamental as well as the higher-order modes of the beams. The results indicate a significant increase in the frequency shift, and hence the sensitivity of detection, when scaling down to nano scale and using higher-order modes.

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Titel: Analytical study of the frequency shifts of micro and nano clamped–clamped beam resonators due to an added mass
verfasst von: Adam Bouchaala
Ali H. Nayfeh
Mohammad I. Younis
Publikationsdatum: 18.03.2016
Verlag: Springer Netherlands
Erschienen in: Meccanica / Ausgabe 1-2/2017
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-016-0412-4

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