We present analytical formulations to calculate the induced resonance frequency shifts of electrically actuated clamped-clamped microbeams 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.
|Original language||English (US)|
|Title of host publication||Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control|
|State||Published - Dec 5 2016|