چكيده به لاتين
The nanomanipulation process is carried out in an environment with micro/nano size, so that micro/nano particles are manipulated using a probe with micro size. Experimental studies show that the size effect plays an important role in micro and nano structures. Classical continuum mechanics cannot accurately predict the behavior of these structures. There are various models that can be used to investigate the dynamic behavior of nanoparticles during nanomanipulation. In this thesis, a non-classical Mindlin plate model incorporating voltage effects has been proposed by focusing on the modified couple stress theory. By applying Hamilton's principle, the governing equations of the Mindelin multilayer plate have been derived. These equations take into account the influence of size and voltage, allowing for the analysis of the microplate's free vibrations and static bending. In order to solve the governing equations, the finite element approach and the Galerkin method have been employed. The bending and stretching deformations have been modeled using a 20-degree-of-freedom quadrilateral element, and the validation of results was examined using existing studies data. The results show that increasing the length scale parameter (decreasing the ratio of thickness to the length scale parameter) increases the stiffness of the plate and the frequency of the system. Examining the effects of voltage reveals that the stiffness of the system depends not only on the magnitude of the voltage but also on its sign. Examining the presented model with the experimental results related to the AFM cantilever reveals an error of 0.02% compared to the experimental data, demonstrating the accuracy of the proposed model. Next, the non-linear effects of piezoelectric materials that lead to phenomena such as hysteresis, creep, and thermal drift in the atomic force microscope were investigated in this study and should be considered in modeling. A modified Prandtl-Ishlinskii model was used to simulate hysteresis. The effects of logarithmic creep in structural equations were investigated. The effects of thermal drift were modeled using a static model. At the end of this section, the simulation results were validated against experimental data. For particles whose geometry can be estimated as a micro or nanobeam, the Euler-Bernoulli and Timoshenko beam nonlinear models with modified coupling stress theory have been used. First, the behavior of a nanoparticle during the manipulation has been modeled using non-classical Euler-Bernoulli and Timoshenko theories with small and large deformations. Then, the finite element approach has been used to solve the governing equations of motion. Stiffness and mass matrices, and external force vector have been extracted and shape functions have been obtained for different conditions. A mesh independence study has been conducted to validate the solution method. At the end, simulations of gold particle and bacteria manipulation have been performed using various models. The effects of the length scale parameter and aspect ratio have been investigated, and the dynamic behavior of the particle during the manipulation process has been demonstrated using various models. The results show that incorporating the length scale parameter into the classical equations leads to a decrease in the deformations calculated in the non-classical models. Likewise, nonlinear effects result in the computation of higher order strain terms in the stiffness matrix, thereby reducing the maximum deformation of the particle. For a 200 nm path, the difference between the non-classical nonlinear and classical nonlinear Timoshenko models, compared to the linear classical Timoshenko model, is 69.59 nm and 2.97 nm, respectively. Next, the modeling of 3D manipulation of nanoparticles by applying atomic friction models in the working conditions was presented. In order to accurately model the 3D manipulation process, atomic friction models such as Prandtl–Tomlinson and contact mechanics were adopted based on the geometry of the particle and the manipulation conditions. The forces acting on the nanoparticle were then extracted. The dynamic behavior of the cylindrical nanoparticle was modeled using the non-classical non-linear Timoshenko beam model and Mindlin plate theory was used to model the cantilever. Critical force and time values for manipulation were extracted and compared with existing experimental results. The results showed a strong correlation between the simulation results of MWCNTs with a length of 4.2 μm and a diameter of 100 nm, and the experimental results. In addition to the critical force and time, the results related to particle bending were presented using classical, non-classical, linear, and non-linear Timoshenko theories.
