Size-dependent random vibration analysis of AFM probe with tip mass considering surface viscoelastic effect

Abstract

In the present paper, the random vibration response of an atomic force microscope (AFM) cantilever with a tip mass which is excited by a white-noise random displacement at the tip has been studied based on the nonlocal theory of Eringen for the first time. The Laplace transform method has been utilized to find the frequency response function of the beam and effect of various parameters such as tip mass, contact stiffness, contact damping and nonlocal parameter on the mean square value of vibrations has been analyzed numerically and illustrated graphically. It has been revealed through numerical examples that the amount of the tip mass has a powerful effect on the random vibration response of the beam, and the effect of the tip mass must be taken into account to perform a viable and realistic random vibration analysis in the field of Atomic Force Microscopy. Also, it has been shown that the contact damping, on the one hand, reduces the amplitude and mean value of vibrations and, on the other hand, when this coefficient increases the input force increases and the mean value of vibration increases as well.