Fundamental frequencies of a nano beam used for atomic force microscopy (AFM) in tapping mode

ABSTRACTIn this study we investigate the motion of a torsionally restrained beam used in tapping mode atomic force microscopy (TM-AFM), with the aim of manufacturing at nano-scale. TM-AFM oscillates at high frequency in order to remove material or shape nano structures. Euler-Bernoulli theory and Eringen’s theory of non-local continuum are used to model the nano machining structure composed of two single degree of freedom systems. Eringen’s theory is effective at nano-scale and takes into account small-scale effects. This theory has been shown to yield reliable results when compared to modelling using molecular dynamics.The system is modelled as a beam with a torsional boundary condition at one end; and at the free end is a transverse linear spring attached to the tip. The other end of the spring is attached to a mass, resulting in a single degree of freedom spring-mass system. The motion of the tip of the beam and tip mass can be investigated to observe the tip frequency response, displacement and contact force. The beam and spring–mass frequencies contain information about the maximum displacement amplitude and therefore the sample penetration depth and this allows