چكيده به لاتين
Atomic force microscope (AFM) is one of the best known devices capable of depicting locally separated from conductive and non-conductive surfaces in atomic measure. This thesis is studying on modeling and simulating the vibrative movement of piezoelectric micro-cantilever based on Timoshenko’s beam theory in air and liquid environment. Thus at the first stage, the vibrative movement of piezoelectric micro-cantilever has been modeled in domain mode considering geometrical discontinuities. In order to solve the equation of motion, the variables isolated and multiple time scale method has been used. Analysis of the vibrative action of piezoelectric micro-cantilever has been done in dynamic mode -including non-contact mode and tapping mode. Dynamic of this system under the influence of interferential forces between tip of the probe and sample surface is including Van der Waals , Capillarity and contact forces. In liquid environment, modeling has been done according to variations caused by liquid existence around the Micro-cantilever. According to the gained results in different environments, forces onto probe cause reduction in domain and resonant frequency. According to the conclusions in result of simulation, delay in tapping mode is less than noncontact mode and sample surface’s Topography in higher oscillating mode shows a better view of inequalities and the depth of inequalities decreases in higher modes. The results of Topography simulation in liquid environment in domain mode show reduction in time delay rather than air environment. The Van der Waals gravity increases in noncontact mode at modest intervals of tip of micro-cantilever up to surface of sample. The micro-cantilever time response graph becomes asymmetric to balance position.
The length and width of piezoelectric layer effect on γ_f is a gauge of the effect of nonlinear on the system γ_f is under the survey. the simulation results suggest that the γ_f measure increases by change in the layer length in short length and after reaching to maximum, declines by increasing the layer length and the thickness effect on nonlinear modulus varies in different length of layer and this modulus declines by increasing the layer width in variant thickness. vibrative analysis of piezoelectric micro-cantilever is surveyed using String of Spheres method, Hosaka and Rankl model and the sensitivity of this method to fluid compressibility force is less then non uniform beam. According to the results of simulation, the solution based on String of Spheres theory has got less accuracy than the one based on multiple time scale. Rankl and String of Spheres model for Multiple time scale solution have got more accuracy than the same models for limited element solution and the accuracy of Hosaka model for Multiple time scale is less than Rankl model: therefore, Rankl model for Multiple time scale in Timoshenko theory has got the least fault.
Keywords: Atomic Force Microscopy, Timoshenko, Multiple Time Scale, Topography, String of Spheres, Hosaka, Rankl
