Experimental and analytical investigations of vibrational behavior of U-shaped atomic force microscope probe considering thermal loading and the modified couple stress theory

Abstract

In this study, experimental and analytical models of a U-shaped atomic force microscopic (AFM) probe are studied based on the modified couple stress theory (MCST). The experimental setup is a commercially fabricated U-shaped probe AN2-300 mounted in the atomic force microscope afm+ system. In the analytical model, the U-shaped probe of the AFM is simulated as a three-beam model (TBM). The governing equations of motion and boundary conditions are obtained by combination of basic equations of the modified couple stress theory and Hamilton’s principle. It is found that the natural frequencies of the AFM predicted by the MCST are size-dependent. The difference between the natural frequencies predicted by the MCST and the classical beam model is very significant when the ratio of characteristic size to internal material length scale parameter is approximately equal to one, but it is diminishing with increase in the ratio. In order to validate the results, the mathematical and experimental models have been compared with each other. It is seen that the analytical model based on MCST has excellent agreement with experimental results. Also, the natural frequencies of the probe have been obtained for different temperature values, aspect ratios, and small scale factor amounts. The results show, natural frequency decrease with increase in temperature value.