Equilibrium and bifurcation of varying cross-section microcantilevers subject to the atomic force

This paper treats a microcantilever with varying cross-section subject to interatomic force derived from the Lennard-Jones potential. Such a microcantilever may be used in the atomic force microscope. The equilibrium configurations are calculated via the Bernoulli–Euler beam theory. The effect of the microcantilever length and its working distance from the sample on the number and the stability of the equilibrium configurations are analyzed via the Lagrange–Dirichlet theorem.