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摘要
The aim of the present study is to assess the force vibrational performance of tapering shaped cantilevers, using Euler-Bernoulli theory. Tapering-shaped cantilevers have plan view geometry consisting of a rectangular section at the clamped end and a triangular section at the tip. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. In this model, a micro cantilever, which is covered by two piezoelectric layers at the top and the bottom, is modeled at angle a. Both of these layers are subjected to similar AC and DC voltages. This paper attempts to determine the effect of the capillary force exerted on the cantilever probe tip of an atomic force microscope. The capillary force emerges due to the contact between thin water films with a thickness of h(c) which have accumulated on the sample and the probe. In addition, an attempt is made to develop the capillary force between the tip and the sample surface with respect to the geometry obtained. The smoothness or the roughness of the surfaces as well as the geometry of the cantilever tip have significant effects on the modeling of forces applied to the probe tip. In this article, the Van der Waals and the repulsive forces are considered to be the same in all of the simulations, and only is the capillary force altered in order to evaluate the role of this force in the atomic force microscope based modeling. We also indicate that the tip shape and the radial distance of the meniscus greatly influence the capillary force. The other objective of our study is to draw a comparison between tapering-and rectangular-shaped cantilevers. Furthermore, the equation for converting the tip of a tapering-shaped cantilever into a rectangular cantilever is provided. Moreover, the modal analysis method is employed to solve the motion equation. The mode shape function for the two tapering-shaped sections of the first and the second kind of Bessel functions is utilized. The nonlinear governing equation is solved by employing the Forward Time Simulation (FST). As the Atomic Force Microscopy cantilever switches from the attractive mode to the contact repulsive mode upon proximity to the surface and the reverse occurs during the departure from the sample surface, a hybrid mode is developed which is illustrated in the graphs.
- 出版日期2017-1-6
