Abstract
In this paper, an atomic force microscope (AFM) with an assembled cantilever probe (ACP) capable of measurement at sidewalls and edges is modeled and its nonlinear vibration is investigated. The ACP comprises a horizontal microcantilever, a vertical assembled extension located at the free end of the microcantilever and a tip located at the free end of the extension. Utilizing Hamilton principle, the governing partial differential equation (PDE) of the ACP vibration and corresponding boundary conditions are obtained. Subsequently, the governing ordinary differential equation (ODE) is derived applying Galerkin method to the aforementioned PDE. Since the ODE is nonlinear, perturbation techniques are employed to solve it for two major functional modes of AFMs: amplitude modulation (AM) and frequency modulation (FM). Effects of different factors including geometrical parameters on the frequency responses of the system are delineated during some figures in which the jump phenomena can be observed. The results show that the system becomes more nonlinear as the length of the vertical extension increases; however, increase of the tip length has a decreasing effect on the nonlinearity of the system.
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