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galerkin-methods
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Implicit Scheme for Stochastic Partial Differential Equations Driven by Space-Time White Noise
, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor)
Abstract
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
Free Vibration Analysis of Thin Truncated Cylindrical Shells using Galerkin Approach
, M.Sc. Thesis Sharif University of Technology ; Dehghani Firouzabadi, Rohollah (Supervisor)
Abstract
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...
Obtaining a Semi-analytical Solution for Contaminant Transport in Coastal Aquifers: Fourier-galerkin Method
, M.Sc. Thesis Sharif University of Technology ; Ataie-Ashtiani, Behzad (Supervisor) ; Jamali, Mirmosaddegh (Co-Advisor)
Abstract
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...
Design and Fabrication of a 16-Way Ultra-Wideband Spatial Power Divider/Combiner
, M.Sc. Thesis Sharif University of Technology ; Banai, Ali (Supervisor)
Abstract
High power, broadband amplifiers at microwave and millimeter wave frequencies are needed for military and civilian applications. High power, broadband, high linearity, low noise, high efficiency and graceful degradation on failure are among the most important features in amplifier design. Solid state and vacuum tube devices have many disadvantages. A promising solution has been spatial power combining technique. Spatial power combining is a method of coherently combining the power of many amplifying devices using free space as the power dividing/combining medium within a guided wave structure in contrast to traditional circuit based amplifiers. This thesis presents the design and fabrication...
Interaction of Large-scale Oceanic Currents and the Earth’s Wobble
, Ph.D. Dissertation Sharif University of Technology ; Jalali, Abbas (Supervisor) ; Behzad, Mehdi (Co-Advisor)
Abstract
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....
Analysis of Sandwich Beam Vibration Due to Moving Mass
, M.Sc. Thesis Sharif University of Technology ; Haddadpour, Hassan (Supervisor) ; Asgari, Mojtaba (Co-Supervisor)
Abstract
In this research, mathematical modeling, deriving equations of motion, solving equations and analyzing the response of motion vibrations of a moving mass with constant speed on a sandwich beam have been discussed. The sandwich beam consists of three layers, the middle layer of which is made of viscoelastic material, and the upper and lower layers are the Euler-Bernoulli beam model.At first, this sandwich beam is mathematically modeled, This mathematical modeling includes all the specifications of the system to obtain the equations that govern the behavior of the system. Then, the displacement field of the system has been extracted and the equations of motion of the system have been obtained...
Dynamic Behavior and Stability Analysis of Rotor-Seal System
, M.Sc. Thesis Sharif University of Technology ; Mohammmad Navazi, Hossein (Supervisor)
Abstract
The present research aims to achieve two main objectives in the Rotordynamic. The first one is, study and calculate the linear dynamic coefficients of a tapered gas seal, and the second one is, analysis the dynamic behavior and stability of the Timoshenko rotor supported with tapered gas seal. Classical Reynolds equation is used to calculate the dynamic coefficients of tapered gas seal. At first, using the perturbation method, the perturbed equations for gas film thickness and pressure are obtained. The finite difference method (FDM) is utilized to transfer the obtained PDEs to the algebraic system of equations. The algebraic system of equations then solved, and the zeroth and first-order...
Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces
, Article Journal of Sound and Vibration ; Vol. 333, Issue. 3 , 3 February , 2014 , pp. 801-817 ; ISSN: 0022460X ; Kazemi, M. T ; Reddy, J. N ; Haddadpoud, H ; Mahmoudkhani, S ; Sharif University of Technology
Abstract
In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the...
Hot extrusion process modeling using a coupled upper bound-finite element method
, Article Journal of Manufacturing Processes ; Vol. 16, issue. 2 , 2014 , pp. 233-240 ; ISSN: 15266125 ; Serajzadeh, S ; Sharif University of Technology
Abstract
A thermo-mechanical model has been developed for modeling of hot extrusion processes. Accordingly, an admissible velocity field was first proposed by means of stream function method and then, extrusion pressure as well as temperature variations within the metal and the die were predicted employing a combined upper bound and Petrov-Galerkin finite element analysis. In order to evaluate the model predictions, hot extrusion of AA6061-10%SiCp was considered under both isothermal and non-isothermal conditions and the predicted force-displacement diagrams under various extrusion conditions were compared with the experimental ones and reasonable consistency was found between the two sets of results...
Chatter instability analysis of spinning micro-end mill with process damping effect via semi-discretization approach
, Article Acta Mechanica ; Vol. 225, issue. 3 , 2014 , pp. 715-734 ; ISSN: 00015970 ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
Abstract
In this paper, the stability of delay differential equations (DDEs), describing self-excited vibrations in a micro-milling process, is investigated based on semi-discretization (SD) method. Due to the stubby geometry of micro-tools, the shear deformation and rotary inertia effects are considered for modeling the structure. The extended Hamilton's principle is used to derive a detailed dynamical model of the spinning micro-tool with the support of misalignment in which the gyroscopic effects cause coupling of equations. Considering the actual geometry of the micro-end mill, exact dynamic stiffness (DS) formulations are developed to investigate the tool's free vibration characteristics. The...
Nonlinear dynamic analysis of a timoshenko beam resting on a viscoelastic foundation and traveled by a moving mass
, Article Shock and Vibration ; Vol. 2014 , 2014 ; ISSN: 10709622 ; Kargarnovin, M. H ; Sharif University of Technology
Abstract
The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam's nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam's cross-sectional rotation are derived using Hamilton's principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam's neutral axis due to the beam's fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear...
Dynamic stability of cantilevered functionally graded cylindrical shells under axial follower forces
, Article Thin-Walled Structures ; Vol. 79, issue , June , 2014 , p. 138-146 ; Kazemi, M. T ; Haddadpour, H ; Mahmoudkhani, S ; Sharif University of Technology
Abstract
Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer...
Nonlinear dynamic analysis of an axially loaded rotating Timoshenko beam with extensional condition included subjected to general type of force moving along the beam length
, Article JVC/Journal of Vibration and Control ; Volume 19, Issue 16 , 2013 , Pages 2448-2458 ; 10775463 (ISSN) ; Kargarnovin, M. H ; Sharif University of Technology
2013
Abstract
In this paper the non-planar nonlinear dynamic responses of an axially loaded rotating Timoshenko beam subjected to a three-directional force traveling with a constant velocity is studied. On deriving the nonlinear coupled partial differential equations (PDEs) of motion the stretching effect of the beam's neutral axis due to the pinned-pinned ends' condition in conjunction with the von Karman strain-displacement relation are considered. The beam's nonlinear governing coupled PDEs of motion for the bending rotations of warped cross-section, longitudinal and lateral displacements are derived using Hamilton's principle. To obtain the dynamic responses of the beam, derived PDEs of motion are...
Bending-torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle
, Article Journal of Sound and Vibration ; Volume 332, Issue 12 , 2013 , Pages 3002-3014 ; 0022460X (ISSN) ; Askarian, A. R ; Kheiri, M ; Sharif University of Technology
2013
Abstract
Stability analysis of a horizontal cantilevered pipe conveying fluid with an inclined terminal nozzle is considered in this paper. The pipe is modelled as a cantilevered Euler-Bernoulli beam, and the flow-induced inertia, Coriolis and centrifugal forces along the pipe as well as the follower force induced by the jet-flow are taken into account. The governing equations of the coupled bending-torsional vibrations of the pipe are obtained using extended Hamilton's principle and are then discretized via the Galerkin method. The resulting eigenvalue problem is then solved, and several cases are examined to determine the effect of nozzle inclination angle, nozzle aspect ratio, mass ratio and...
Timoshenko versus Euler-Bernoulli beam theories for high speed two-link manipulator
, Article Scientia Iranica ; Volume 20, Issue 1 , 2013 , Pages 172-178 ; 10263098 (ISSN) ; Kakavand, F ; Sharif University of Technology
2013
Abstract
In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler-Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a...
Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model
, Article International Journal of Engineering Science ; Volume 64 , 2013 , Pages 14-22 ; 00207225 (ISSN) ; Firouz Abadi, R. D ; Haddadpour, H ; Sharif University of Technology
2013
Abstract
The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied...
Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow
, Article Journal of Fluids and Structures ; Volume 36 , 2013 , Pages 18-31 ; 08899746 (ISSN) ; Askarian, A. R ; Zarifian, P ; Sharif University of Technology
2013
Abstract
This paper aims to investigate aeroelastic stability boundary of subsonic wings under the effect of thrust of two engines. The wing structure is modeled as a tapered composite box-beam. Moreover, an indicial function based model is used to calculate the unsteady lift and moment distribution along the wing span in subsonic compressible flow. The two jet engines mounted on the wing are modeled as concentrated masses and the effect of thrust of each engine is applied as a follower force. Using Hamilton's principle along with Galerkin's method, the governing equations of motion are derived, then the obtained equations are solved in frequency domain using the K-method and the aeroelastic...
Resonance frequencies and stability of two flexible permanent magnetic beams facing each other
, Article Journal of Sound and Vibration ; Volume 331, Issue 26 , 2012 , Pages 5745-5754 ; 0022460X (ISSN) ; Mohammadkhani, H ; Sharif University of Technology
2012
Abstract
This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler-Bernoulli beam model along with Hamiltons principle. Assuming that the beams tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies....
Three-dimensional simulation of fully coupled hydro-mechanical behavior of saturated porous media using Element Free Galerkin (EFG) method
, Article Computers and Geotechnics ; Volume 46 , 2012 , Pages 75-83 ; 0266352X (ISSN) ; Pak, A ; Sharif University of Technology
2012
Abstract
Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method...
Natural frequency improvement of a suspended FGM bridge
, Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011, 11 November 2011 through 17 November 2011 ; Volume 8 , November , 2011 , Pages 699-704 ; 9780791854945 (ISBN) ; Ahmadian, M. T ; Lashkari, S. G ; Barari, A ; Sharif University of Technology
Abstract
In this paper application of Functionally Graded Materials (FGMs) in suspension bridge structures for the purpose of vertical vibration improvement is investigated. Functionally graded materials are inhomogeneous composites, which are usually made from a mixture of metal and ceramic. Initially the classical equation of motion is modified based on the FGM model and natural frequencies of structure are extracted by Galerkin method. The material properties of structure vary continuously in the longitude direction according to power law form. In this regard, combination of materials is structured in such a way that the desired frequencies of the bridge are achieved by designing the proper power...