Size effect of a uniformly distributed added mass on a nanoelectromechanical resonator

We develop a new analytical formulation to determine the size effect of an added mass on the natural frequencies of an electrostatically actuated resonator. A clamped–clamped nanobeam is used as a mass sensor and modeled using Euler–Bernoulli beam theory. The added mass is uniformly distributed and its size is modeled by a Unit-Step function. The mathematical problem is solved numerically using Galerkin approximation. In order to validate the analytical model, a finite element method (FEM) is used to determine the natural frequencies of the nanobeam resonator and the induced frequency shifts due to the attached particles modeled with different size ratios. The effect of the mesh size on the natural frequencies is investigated. A good agreement is demonstrated between the analytical approach and the FEM technique.