Static Vibro-Impact Oscillation of a Multiple AFM Cantilever under Tapping Mode by Using Wave Algorithm

Abstract

In this study we design a multiple cantilever for an atomic force microscope (AFM) under tapping mode as three-body vibro-impacts oscillators based on Grover wave algorithm. Static vibro-impact oscillations are derived by modifying Grover algorithm with damping and an exciting operators to express piecewise linear vibrations. We obtain the condition of steady state under tapping mode in AFM cantilever from the algorithm. Instabilities of the static oscillation caused by sudden change of the impact position is analyzed by numerical calculations. Within a small deviation, the system will converge with the steady states. The system shows better robustness from disturbance with a smaller reflection coefficient and larger collision speed. Also it is shown that the impact velocity of cantilever can be controlled by changing the amount of excitation. Moreover, since the amplitude of non-impact oscillator can be larger than that of impact one in case of small mass ratio. γ<1, vertical resolution of AFM can be improved by using the cantilever.