چكيده به لاتين
Atomic force microscopy (AFM) has been known as an innovative tool in the fields of surface topography, determination of different mechanical properties and manipulation of particles at the micro- and nanoscales. Micro-cantilever (MC) and probe are two main components of this micro-robot. The dimensions of these components in terms of micro scale and vibration amplitude have been provided in nanoscale. It is greatly important to improve the system performance in higher vibration modes by increasing the accuracy of micro and nanoscale modeling with regard to the variable cross-section along with the effect of the probe on the vibration behavior of AFM piezoelectric MC and MC modeling based on the Timoshenko beam theory using modified couple stress (MCS) method. That’s because micro- and nanoscale methods of classical continuum mechanics cannot properly predict the system behavior and need to be improved. AFM applications in different operating environments require evaluating the effect of different environments on the vibration behavior of the system. The evaluation of these environments requires examining the forces exerted on the MC by the environment and sample surface with different roughness levels. Moreover, consideration of different geometries of AFM piezoelectric MC is of utmost importance to select the most appropriate geometry for the more accurate topography of the environment. Besides, it is necessary to investigate the effect of dimensions on the sensitivity of vibration amplitude and frequency of the system using sensitivity analysis methods in order to select appropriate MC dimensions including thickness, width and length of different MC layers such as silicon, piezoelectric and electrode layers.
The present study intended to not only increase the accuracy of modeling with regard to geometric discontinuities based on Timoshenko Beam Model using MCS theory but also increase the accuracy of the prediction of system behavior by integrating the effect of hysteresis into vibration equations of the system based on Bouc-Wen Model. The vibration equations of the system based on GDQ method is faster than equations based on FEM in terms of the convergence of response i.e. the results converge with a fewer number of elements. Discrete equations have been solved using Newmark algorithm and Laplace transforms in the free and forced vibration modes of AFM piezoelectric MC. The surface roughness affects the vibration behavior of the system in an air medium. The present study has also investigated the effect of surface roughness along with probe-tip roughness on van der Waals force for different materials in the air and vacuum media. Moreover, the development of capillary force was evaluated by calculating the radius of Meniscus Bridge formed between the probe tip and sample surface based on the instantaneous variation of the probe-sample gap; accordingly, a new model was developed by establishing a connection between Meniscus Bridge formation and probe-to-sample gap. Furthermore, the probe-sample contact force was modified using contact mechanics theory. The expansion of the operating environment to liquid medium with respect to different AFM piezoelectric MC geometries including rectangular, dagger and V-shape geometries has also been sought in the present study to select the most appropriate geometry for more accurate topography in a liquid medium. In this regard, in addition to ordinary environmental forces such as compressive hydrodynamic forces and squeeze forces applied in previous studies, the fluid shear forces on MC sides were developed in the present study by solving Navier-Stokes equations and were added to the other equations.
Finally, the speed of solving the equations was increased by performing sensitivity analysis based on EFAST method. Investigating the coupling effect of geometric and force parameters on the amplitude and frequency of the system increased and eliminating low-effect parameters. Furthermore, the results of the simulation were compared with experimental results by performing experimental tests in different operating environments including air and vacuum media with different percentages of moisture content and liquid. The experimental tests performed in the free vibration mode including frequency and time response as well as the forced mode comprises sample surface topography and its effect on the vibration amplitude of AFM micro-robot. Moreover, the quality and accuracy of sample surface topography were improved by eliminating the undesirable effect of the capillary force.
