Transverse free vibration of resonant nanoplate mass sensors: Identification of an attached point mass

In this paper we analyse for the first time the bending vibration of a nanoplate with an attached mass using the strain gradient elasticity theory for homogeneous Lamé material, under Kirchhoff-Love’s kinematical assumptions. The exact eigenvalues of the nanoplate vibrating with an attached mass are obtained for a general case, and an approximate closed form expression is provided if the intensity of the mass is small with respect to the total...