Sharif Digital Repository

In recent years, the world has seen a great progress in micro electro-mechanical systems (MEMS). Small size, low weight, high accuracy and low energy consumption have made these devices applicable in a variety of usages. In MEMS devices, mechanical components are used for specific purposes among which one of the most widely used are micro plates. Microplates are used in the structure of many devices such as microswitchs and atomic force microscopes. Therefore, studying of static and dynamic behavior of microplates is important. As the object gets smaller (to the scale of micro and nano meters), the classic theory of mechanics of continuous media cannot predict the behavior due to its... 

In this study dynamic response of Timoshenko beam and rectangular Kirchhoff plate under moving mass are investigated. Applying Hamilton’s principle, governing differential equations of beam and plate are derived considering the effect of moving mass. Afterward, a numerical-analytical solution based on eigen function expansion method for analyzing nonuniform beams and plates by means of beams’ and plates’ free vibration modes is presented and convergence of the solution is proved by proving that the governing differential equations of Timoshenko beam and Kirchhoff plates are self adjoint. Modal orthogonality circumstances are discussed due to their important role in eigen function expansion... 

In this research it is aimed to have an investigation on the thermo-mechanical analysis of functionally graded skew plates. In order to analyze the behavior of the skew FGM plates, a constant pressure load as a mechanical load is distributed through the plate. Also the thermo-mechanical load is a combination of this mechanical load and a temperature gradient in upper and lower surface applied as in-phase . Various boundary conditions considered in analysis are combination of simply support and clamped edges including CCCS, CCSS, CCCC. The analysis are based on CPT and the Von-Karman theory is used in the solution. The graded materials are distributed through the thickness according to P-FGM... 

In this study, free vibration analysis of moderately thick rectangular FG plates with general boundary conditions is investigated. Governing equations of motion are obtained based on the Mindlin plate theory. A semi analytical solution is presented for the governing equations using extended Kantorovich method (EKM). Results are compared and validated with available results in the literature. Effects of different parameters such as boundary conditions, material and geometrical parameters on natural frequencies of the FG plates are investigated  

The behavior of a beam under moving mass has been always interested in the dynamic of structures. In this study, the dynamic response of beam and plate with general boundary conditions under moving mass were investigated using the Dynamic Green Function. Since the majority of previous studies did not consider the Coriolis acceleration, therefore, this acceleration was used in the present study. Boundary conditions are modeled by the rotational and translational restraint. By moving close to the spring constants of the rotational and translational restraint to extreme values (zero and/or infinity), the boundary conditions can be attained for the desired combinations of end boundary conditions... 

The purpose of this research is to provide an analytical solution using first order shear deformation theory for nonlinear bending of rectangular FG plate under mechanical and thermal loads with different boundary conditions. To achieve this goal, extended Kantorovich method have been used. This method has a high convergence rate and is more accurate than other approximate methods, such as the Ritz and Galerkin methods, because the partially differential equations are converted to ordinary differential equations. In order to solving nonlinear odes the perturbation method is used. Material of the plate is a mixture of ceramic and metal and is modeled as an isotropic and non-homogeneous... 

In this study the axisymmetric and asymmetric problem of interaction between a transversely isotropic half-space and various rst order shear deformation plate theories including Mindlin, Reissner and Vasil'ev are addressed. In order to improve the accuracy of solution, the surface boundary conditions of the half-space are modied.Moreover, the results compared with the exact solution and the most appropriate result is identied. The displacement Green's functions are obtained for both cases, modied and unmodied boundary conditions which can be expressed in a closed form and a numerically evaluated part. The latter is calculated exploiting Built-in numerical interrelation function of... 

This research presents an innovative analytical solution to static, free vibration and buckling of an isotropic, homogeneous Mindlin plate with uniform thickness. This method satisfies all classical boundary conditions including free, simply supported and clamped as well as non-classical ones. Moreover, Mindlin plates on Winkler foundation of arbitrary stiffness function are investigated. In this study, the deflection and rotation of straight normal line of the plate about x and y axes are represented as the functions of sine and cosine Fourier series, accompanied by auxiliary functions. These auxiliary functions are of great importance because these functions satisfy arbitrary boundary... 

The importance of transversely isotropic and functionally graded materials and also plates in industry necessitates studies on these kinds of structures. This study works on the buckling of simply supported rectangular transversely isotropic FGM plates subjected to in-plane uniaxial or biaxial static loads. For this purpose, discretization method is applied and the aforesaid inhomogeneous plate is divided into arbitrary number of sublayers parametrically (N). With the help of displacement potential functions, coupled different equations for each sublayer are simplified to two uncoupled different equations in terms of the potential functions. These governing equations for transversely...