Superharmonic and subharmonic resonances of atomic force microscope subjected to crack failure mode based on the modified couple stress theory

Abstract

The primary purpose of this paper is to investigate the nonlinear dynamic behavior of the atomic force microscopy (AFM) cantilever under the effect of concentrated point load at free end and the crack failure mode in the vicinity of the clamped-edge. The crack was modeled as rotational spring and the cracked AFM considered as a simply support-free micro-beam with a rotational spring in the simply support end. In the frame work of Euler–Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory the nonlinear equation of motion for the cracked AFM is derived by Hamilton’s principle and then discretized by using the Galerkin’s method. The method of multiple scale is employed to investigate, nonresonant hard excitation, superharmonic resonance and subharmonic resonance. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, tip-mass, the magnitude and the location of the external excitation force on the stability of the response amplitude, and the unstable regions were identified.