Sobol method application in dimensional sensitivity analyses of different AFM cantilevers for biological particles

Abstract

Due to the more delicate nature of biological micro/nanoparticles, it is necessary to compute the critical force of manipulation. The modeling and simulation of reactions and nanomanipulator dynamics in a precise manipulation process require an exact modeling of cantilevers stiffness, especially the stiffness of dagger cantilevers because the previous model is not useful for this investigation. The stiffness values for V-shaped cantilevers can be obtained through several methods. One of them is the PBA method. In another approach, the cantilever is divided into two sections: a triangular head section and two slanted rectangular beams. Then, deformations along different directions are computed and used to obtain the stiffness values in different directions. The stiffness formulations of dagger cantilever are needed for this sensitivity analyses so the formulations have been driven first and then sensitivity analyses has been started. In examining the stiffness of the dagger-shaped cantilever, the micro-beam has been divided into two triangular and rectangular sections and by computing the displacements along different directions and using the existing relations, the stiffness values for dagger cantilever have been obtained. In this paper, after investigating the stiffness of common types of cantilevers, Sobol sensitivity analyses of the effects of various geometric parameters on the stiffness of these types of cantilevers have been carried out. Also, the effects of different cantilevers on the dynamic behavior of nanoparticles have been studied and the dagger-shaped cantilever has been deemed more suitable for the manipulation of biological particles.