An Euler-Bernoulli second-strain gradient beam theory for cantilever sensors

Because of their high surface over volume ratio, the mechanical behavior of micrometer sized structures differs from that of usual macroscopic objects. Their surface plays a key role, and this property has been proposed to devise micromechanical sensors of environmental changes [1]. In particular, a significant effort has been put on the development of biological sensors [2], thus highlighting the need for a more basic understanding of coupled surface phenomena [3]. These micromechanical sensors are usually operated in either static or dynamic mode. The latter allows one to detect the change in mass experienced by a micromechanical resonator. One