Analytical solution of flexural vibration responses on nanoscale processing using atomic force microscopy

An analytical solution is developed to deal with the flexural vibration problem during a nanomachining process which involves an atomic force microscope (AFM) cantilever. The modal superposition method is employed to analyze the response of an AFM subjected to a cutting force with an excitation force of an arbitrarily chosen frequency. The cutting forces were transformed into distributed transversal and bending loading, and were applied to the end region of the AFM by means of the tip holder. The effects of transverse stress and bending stress were adopted to solve the dynamic model. Based on the result, applying a cutting force with an excitation force near the high-order modal frequencies and using a wide tip holder are recommended when nanoscale processing using AFM is performed.