Study of the sensitivity and resonant frequency of the flexural modes of an atomic force microscopy microcantilever modeled by strain gradient elasticity theory

Abstract

In this study, the resonant frequency and sensitivity of an atomic force microscopy microcantilever are analyzed utilizing the strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of the modified strain gradient theory and the Hamilton principle. Afterward, the resonant frequency and sensitivity of the proposed atomic force microscopy microcantilever are obtained numerically. The results of the current model are compared to those evaluated by both modified couple stress and classic beam theories. Results show that utilizing the strain gradient theory in the analysis of atomic force microscopy microcantilever dynamic behavior is necessary especially when the contact stiffness is high and the thickness of the microcantilever approaches the internal material length scale parameter.