Dynamics analysis of width-varying microcantilevers: Interplay between eigenfrequencies, contact stiffness and interaction forces

In this study, the resonance-frequency dependence and modal sensitivity of the flexural vibration modes of overhang/T-shaped microcantilevers to the interaction force and surface stiffness variations were analysed, and a closed-form expression was derived. The Euler–Bernoulli beam theory was used to develop the overhang/T-shaped models, and a characteristic formula representing the dependence of cantilever frequencies on the overhang dimensions was obtained. The results of the derived expression were analysed using numerical simulations to investigate and compare the effects of the overhang width, length, repulsive and attractive forces, and surface contact stiffness on the flexural mode of overhang/T-shaped cantilevers. Furthermore, a closed-form expression for the modal sensitivities of the width-varying cantilever was derived, and the modal sensitivities were compared using numerical simulations. Finally, the effects of the interaction forces and contact stiffness on the frequency response and sensitivities of different cantilevers based on their stiffness and geometrical parameters were verified experimentally. This study can open new paths for designing, fabricating, and using width-varying cantilevers in sensing and imaging applications, particularly for cantilever array systems.