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

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• 作者：Adam Bouchaala ; Ali H. Nayfeh ; Mohammad I. Younis
• 关键词：Micro/nano beams ; Frequency shift ; Carbon nanotubes ; Added mass ; Perturbation techniques ; Galerkin methods
• 刊名：Meccanica
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：52
• 期：1-2
• 页码：333-348
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering;
• 出版者：Springer Netherlands
• ISSN：1572-9648
• 卷排序：52

文摘

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.