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

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. © 2016 Springer Science+Business Media Dordrecht