Sharif Digital Repository

Existing closed form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be applied for coastal aquifers where seawater intrusion induces a variable velocity field. The Fourier series method is adapted to obtain a semi-analytical solution for contaminant transport in confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. The developed method can be applied for different scenarios of contamination. Two scenarios dealing with, respectively, contaminant leakage from a source at the aquifer top surface and aquifer contamination from the landward boundary are... 

The turbulence in the atmosphere will limit the performance of astronomical telescopes on the ground thus a technique for solving this problem is needed that is Adaptive optics technique. We know Adaptive optics in its simplest definition as a process to improve the quality of image by means of deformation of the wave fronts to compensate the beam path anomalies. The main components of this system are the wave front sensor and deformable mirror. Deformable mirror is used in the system of this technique also plays an important role in the correction of anomalies of eye. Type of actuators that can be used for deformable mirror, pattern of them, and also the way of connecting the actuators to... 

In the present study, the buckling of generally laminated truncated conical shells having thickness variation expressed by a linear function, subjected to axial compression with simply or clamped supports has been considered. To begin with, the fundamental relations for a conical shell with variable thickness have been derived applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy; non-linear terms of Donnell equations by the help of adjacent-equilibrium criterion are linearized. Governing equations are solved using power series method and are applicable for all combinations of classical boundary conditions. The results are validated with Galerkin... 

Presence of fluid in closed ends beam can increase beam hardness against pressure and buckling loads. This behavior is due to incompressibility or very low compressibility of fluids. there is a lot of research in the literature focusing on fluid solid interaction in pipe flow, but there is not any reported research studying on fluid filled beam, where fluid doesn’t flow across the beam. In this research hollow beam is modeled with Euler -Bernoulli beam theorem. Potential energy and kinetic energy is derived with considering the incompressibility of fluid. Nonlinear system of equations is derived using Hamilton principle . this system is taken to time domain using Galerkin and assumed mode... 

Micro and nano electromechanical systems technology has experienced lots of progress in recent years. These systems are widely used in sensors and actuators due to their small size low weight and low energy consumption. Electrostatically actuation is one of the simplest and most prevalent methods of actuation and sensing in these systems. Electrostatically actuated micro and nanobeams are used in many devices such as micro and nano switches, resonators, signal filters, tunable capacitors, pressure and mass sensors, etc. Experimental results and measurements have shown that classical theories contain error in prediction of static and dynamic ... 

In this project, vibration and stability condition of a pipe conveying flow has been studied for use in firefighting plane. The Plane is a multi-rotor that carries the pipe to a certain height and it does the washing work there, bassed on the fluid flow from the nozzle embedded in the end of the pipe. Due to the flexibility of the pipe in this application, structure modeling is based on cable without bending stiffness. The Galerkin method is used to solve equations by considering the assumed mode shape for structure. At first, by analyzing free vibrations, different boundary conditions were considered for the pipe and the natural frequencies and natural shape modes were extracted in... 

In this thesis, we investigate interactions of a double-gyre in the North Atlantic and the earth’s Chandler wobble using a single-layer ocean model based on depth-averaged Navier-Stokes equations and multiple-scale spectral solutions to it. The overall transfers of energy and angular momentum from the double-gyre to the Chandler wobble are used to calibrate the turbulence parameters of the idealized ocean model and Smagorinsky eddy viscosity is used to estimate turbulent diffusion terms. Our model is tested against a multilayer quasi-geostrophic ocean model in turbulent regime, and base states used in parameter identification are obtained from mesoscale eddy resolving numerical simulations.... 

Due to a rapid growth in the consumption of fossil fuels, the emission of greenhouse gases has multiplied in the atmosphere in the past few decades. This issue can directly affect on the rise of global temperature. Because of the intensification of the global warming, international organizations are looking for ways to reduce the greenhouse effect. One of these methods is injecting and trapping greenhouse gases, especially carbon dioxide, resulting from the operation of power plants and other large industries and preventing it from entering the atmosphere. The injection of carbon dioxide in underground salt water reservoirs can have various effects such as mechanical, hydraulic, thermal, and... 

Because the structural stability is directly related with structural damage, it is considered one of the most important issues in the industry. One of the applied cases in the stability issue discuss about the stability of the beam under follower loads. Follower loads obtained from aerodynamic pressure, rocket’s thrust, dry friction of the rotating disk, drilling and etc. Because the follower loads are always perpendicular to the beam cross section, thus with changing the angle of their location, their directions are changed. Spatial dependence makes a non-conservative and dynamic problem. So these loads causes dynamic instability that say flutter. In this study, the stability of a... 

In this thesis we study sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst parameter greater than one-half. In addition, the mean-square numerical approximations of such problems are investigated, performed by the spectral Galerkin method in space and the linear implicit Euler method in time. We see that by using the obtained sharp regularity properties of the problems one can identify optimal mean-square convergence rates of the full discrete scheme. At the end, these theoretical findings are accompanied by several numerical... 

In this thesis we study Galerkin methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. The strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler–Maruyama method, are also investigated. We see that the obtained error estimates in both cases as well as the regularity results for the mild solution of the SPDE are optimal. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin. At the end, these theoretical findings are accompanied by several numerical... 

In this study, the linear dynamic response of an inclined FGM Timoshenko beam on linear viscoelastic foundation subjected to a traveling mass with constant and variable velocity is investigated. Timoshenko beam theory and von-karman strain-displacement relations are utilized to model the problem. the FGM beam is made of metal and ceramic and it is assumed that material properties of the beam vary continuously in the thickness direction according to the exponential law and the power-law form. The kelvin-voigt damping model is applied to model the internal damping of the FGM beam. The partial differential equations of motion for the bending rotation of cross-section, longitudinal and... 

In this thesis, a reduced model of a distributed one-dimensional Solid Oxide Fuel Cell (SOFC) system is presented. Consequently the reduced model is used to estimate the states of the exact model. The reduced model is derived using the exact solution of the distributed model and implementing the Karhunen-Loève-Galerkin procedure. To achieve an exact solution of the distributed model, method of lines is used. In the method of lines, accuracy of the solution depends on the number of grid points. To increase the accuracy, the number of grid points should be increased which will lead to a high order dynamic model. Such a model is not suitable for state estimation, optimization or control... 

Microelectromechanical have wide application in mechanic, aerospace, medical, transport and information technology.
Due to large scale application and production, low costs and low energy consumption, these systems have been used in wide range of fields of engineering. Electrostatically actuated microbeams are extensively used as microelectromechanical systems (MEMS) such as microswitch and microresonator. The main component of electrically driven is microbeam. Microbeam acts as top surface of a capacitor with fixed bottom. The capacitance of capacitor changes due to the deflection of the microbeam. In this study static deflection of electrostatically actuated microbeam has been... 

Recently, there has been a strong interest in the development of a new class of meshfree methods. As an alternative to the finite element method (FEM), mainly due to elimination of high cost mesh generation processes. In addition, the size effect is currently a subject of increasing interest since it is an important parameter in predicting, correctly, the mechanical behavior of materials with microstructure. It was well established that classical linear elastic continua which neglects the higher order terms is not able to describe size effects. In contrast, enhanced continuum theories such as nonlocal or gradient-dependent models do involve an internal length scale. Thorough this length... 

In this thesis, we consider an implicit approximation scheme for the stochastic heat equation with additive and multiplicative space-time white noise. we use the spectral Galerkin method in space combined with the linear implicit Euler method in time to simulate weak approximation error  

Hydraulic fracturing is a process during which a viscous fluid under relatively high pressure and flow rate is injected into a wellbore to induce and propagate a system of cracks in the ground.Hydraulic fracturing of underground formations has been widely used in different fields of
engineering, such as petroleum engineering, geotechnical engineering, environmental engineering, mining engineering,and so on.Despite the technological advances in the techniques of in-situ hydraulic fracturing, the industry lacks a realistic and reliable numerical model to design cost - effective and efficient hydraulic fracturing treatment.This is due to the complex interaction and strong coupling between... 

In the present work, the buckling behavior of a composite beam with circular, rectangular and pentagonal cross sections is investigated. The structural model is based on the first order shear deformation theory (FSDT) and incorporates other non-classical effects such as primary and secondary warpings and restrained warping. The linear buckling equations are derived from the non-linear governing equations of motion and their associated boundary conditions and solved using the Galerkin method for a composite beam with the clamped-free end condition and the special layup configuration of Circumferentially Asymmetric Stiffness (CAS) which induces elastic couplings between torsional and flexural... 

In this thesis, buckling of truncated conical shells made of composite laminates with general lamination sequence is investigated. The conical shell is considered under axial compression with simply supported or clamped boundary condition. First, Donnel type nonlinear equations and boundary conditions for doubly curved shells are obtained using Hamilton principle. Second, using adjacent equilibrium criterion, the nonlinear equations was linearized then with defining lame parameters and curvature radius, the linear equations of conical shell was extracted. The power series and Galerkin method was used to solve differential equations. The obtained results are in good agreement with available... 

The current study is dedicated to free vibration analysis of a thin cylindrical shell with an oblique end. To this end, governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The differential form of equations is obtained by applying by part integration to the integral form of equations of motion. Equations of motions have been solved by Galerkin method for two different kinds of boundary conditions. Convergence process for different kinds of conditions has been done and results compared with papers. The effect of different parameters such as, length of cylinder, oblique angle, thickness etc. on the fundamental frequencies has been...