Relative sensitivity of nano-mechanical cantilevers to stiffness and mass variation

Abstract

Investigating the relative sensitivity of nano-mechanical cantilever resonators to variations in stiffness and mass caused by adsorbates is essential. The analysis helps improve accuracy and stability as well as evaluating if undesired increases in mass and stiffness can be disregarded. A new dimensionless mathematical model based on the Rayleigh–Ritz method for studying the relationship between the relative sensitivity and related coupled parameters is proposed in this study. The results reveal that the geometric parameters of the cross-section tend to enhance the added bending rigidity more than the added linear density. The added stiffness and added mass exhibit precisely counteractive influences symmetrically to the cantilever’s length axis centre. Commonly, the location of the adsorbate is more crucial than the cross-section property in determining the dominant factor between added stiffness and added mass. The model agrees well with both finite element analysis and experimental results. By identifying optimal adsorbate locations and bending modes, this model can enhance the accuracy and stability of measuring desired properties related to the Young’s modulus and density of the adsorbate.