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**Search for:**partial-differential-equations

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Total 152 records

#### Far-field dynamic behavior of a half-space under an inertial strip foundation subjected to a time-harmonic force

, Article Latin American Journal of Solids and Structures ; Volume 10, Issue 3 , 2013 , Pages 453-471 ; 16797817 (ISSN) ; Malidarreh, N. R ; Choobbasti, A. J ; Vafai, A ; Sharif University of Technology
2013

Abstract

Recent research works demonstrated that the interaction between the loads and the carrying structure's boundary which is related to the inertia of the load is an influential factor on the dynamic response of the structure. Although effects of the inertia in moving loads were considered in many works, very few papers can be found on the inertial effects of the stationary loads on structures. In this paper, an elastodynamic formulation was employed to investigate the dynamic response of a homogeneous isotropic elastic half-space under an inertial strip foundation subjected to a time-harmonic force. Fourier integral transformation was used to solve the system of Poisson-type partial...

#### Non-convex self-dual Lagrangians: New variational principles of symmetric boundary value problems

, Article Journal of Functional Analysis ; Volume 260, Issue 9 , 2011 , Pages 2674-2715 ; 00221236 (ISSN) ; Sharif University of Technology
Abstract

We study the concept and the calculus of Non-convex self-dual (Nc-SD) Lagrangians and their derived vector fields which are associated to many partial differential equations and evolution systems. They indeed provide new representations and formulations for the superposition of convex functions and symmetric operators. They yield new variational resolutions for large class of Hamiltonian partial differential equations with variety of linear and nonlinear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to...

#### Improvement of dynamic response prediction of helicopters

, Article Aircraft Engineering and Aerospace Technology ; Volume 79, Issue 6 , 2007 , Pages 579-592 ; 00022667 (ISSN) ; Saghafi, F ; Sharif University of Technology
2007

Abstract

Purpose – This paper aims to focus on mathematical model development issues, necessary for a better prediction of dynamic responses of articulated rotor helicopters. Design/methodology/approach – The methodology is laid out based on model development for an articulated main rotor, using the theories of aeroelastisity, finite element and state-space represented indicial-based unsteady aerodynamics. The model is represented by a set of nonlinear partial differential equations for the main rotor within a state-space representation for all other parts of helicopter dynamics. The coupled rotor and fuselage formulation enforces the use of numerical solution techniques for trim and linearization...

#### Parallel computation of a mixed convection problem using fully-coupled and segregated algorithms

, Article 2004 ASME International Mechanical Engineering Congress and Exposition, IMECE, Anaheim, CA, 13 November 2004 through 19 November 2004 ; Volume 375, Issue 1 , 2004 , Pages 313-322 ; 02725673 (ISSN) ; Banaeizadeh, A ; Schneider, G. E ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2004

Abstract

In this work, parallel solution of the Navier-Stokes equations for a mixed convection heat problem is achieved using a finite-element-based finite-volume method in fully coupled and semi coupled algorithms. A major drawback with the implicit methods is the need for solving the huge set of linear algebraic equations in large scale problems. The current parallel computation is developed on distributed memory machines. The matrix decomposition and solution are carried out using PETSc library. In the fully coupled algorithm, there is a 36-diagonal global matrix for the two-dimensional governing equations. In order to reduce the computational time, the matrix is suitably broken in several...

#### Polynomial expansion for extraction of electromagnetic eigenmodes in layered structures

, Article Journal of the Optical Society of America B: Optical Physics ; Volume 20, Issue 12 , 2003 , Pages 2434-2441 ; 07403224 (ISSN) ; Rashidian, B ; Sharif University of Technology
Optical Society of America (OSA)
2003

Abstract

A polynomial expansion approach to the extraction of guided and leaky modes in layered structures including dielectric waveguides and periodic stratified media is proposed. To verify the method we compared the results of analysis of a typical test case with those reported in the literature and found good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than to a transcendental dispersion equation; therefore, it will be easier to use than other methods such as the argument principle method, the reflection pole method, and...

#### Attitude and Vibration Control of Flexible Satellites with Multi-Section Solar Panels Using Boundary Controller and Observer

, Ph.D. Dissertation Sharif University of Technology ; Salarieh, Hassan (Supervisor) ; Nejat Pishkenari, Hossein (Supervisor)
Abstract

Precise adjustment of orientation is vital in many important applications of satellites. Besides, in order to have sustainable power source and to reduce heavy costs of launching deployable solar arrays with large area to mass ratio are utilized. The vibrations in these flexible parts and attitude dynamics of the main hub influence eachother mutually. Thus, simultaneous attitude and vibrations control is of noticeable significance. In this thesis considering new details such as multi-section solar panels, the governing dynamic partial differential equations (PDE) are derived via Hamilton principle. In order that errors arised from discretized models be eliminated and just using regular...

#### Ultrasound medical image speckle reduction using fourth-order partial differential equation

, Article 2011 7th Iranian Conference on Machine Vision and Image Processing, MVIP 2011 - Proceedings, 16 November 2011 through 17 November 2011 ; November , 2011 , Page(s): 1 - 5 ; 9781457715358 (ISBN) ; Hashemi Berenjabad, S. H ; Sharif University of Technology
Abstract

One of the drawbacks to post-process and to interpret ultrasound medical images is speckle noise. In this paper we used fourth-order partial differential equation method proposed by Lysaker et al. for speckle reduction of ultrasound images. We used two groups of images first was the synthesized noisy image and second is real ultrasonic images. A comparison between our results and to other methods showed that PDE has better SNR and PSNR in most levels of speckle

#### Size-dependent bistability of an electrostatically actuated arch NEMS based on strain gradient theory?

, Article Journal of Physics D: Applied Physics ; Volume 48, Issue 24 , May , 2015 ; 00223727 (ISSN) ; Pishkenari, H. N ; Yazdi, M. R. H ; Miandoab, E. M ; Sharif University of Technology
Institute of Physics Publishing
2015

Abstract

This paper deals with the investigation of the size-dependent nature of nonlinear dynamics, in a doubly clamped shallow nano-arch actuated by spatially distributed electrostatic force. We employ strain gradient theory together with the Euler-Bernoulli and shallow arch assumptions in order to derive the nonlinear partial differential equation governing the transverse motion of the arch with mid-plane stretching effects. Using the Galerkin projection method, we derive the lumped single degree of freedom model which is then used for the study of the size effects on the nonlinear snap-through and pull-in instabilities of the arch nano-electro-mechanicalsystem (NEMS). Moreover, using strain...

#### Vibration suppression of a strain gradient microscale beam via an adaptive lyapunov control strategy

, Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 138, Issue 3 , 2016 ; 00220434 (ISSN) ; Vatankhah, R ; Salarieh, H ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2016

Abstract

Vibration suppression of a strain gradient Euler-Bernoulli beam in presence of disturbance and uncertainties is considered in this investigation. Vibration of the system is suppressed by an adaptive boundary controller which has robustness to the environmental and control effort disturbances. The direct Lyapunov stability theorem is used to design the controller and adaptation law. The numerical results are presented to demonstrate the effectiveness of the proposed controller. Copyright © 2016 by ASME

#### Backstepping boundary control for unstable second-order hyperbolic PDEs and trajectory tracking

, Article Proceedings of the ASME Design Engineering Technical Conference, 30 August 2009 through 2 September 2009 ; Volume 4, Issue PARTS A, B AND C , 2009 , Pages 1787-1792 ; 9780791849019 (ISBN) ; Abediny, M ; Sadeghian, H ; Alasty, A ; Design Engineering Division and Computers in Engineering Division ; Sharif University of Technology
Abstract

In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated...

#### The Stability of Stochastic Partial Differential Equations in Hilbert Spaces

, M.Sc. Thesis Sharif University of Technology ; Zohori Zangeneh, Bijan (Supervisor) ; Jahanipur, Rouhollah (Supervisor)
Abstract

Stochastic Partial Differential Equations have many applications in other area of science. In this thesis we investigate two pproaches in SPDE.The first approach is semigroup and the second is variational method.Our main purpose is stability of these equations

#### Solutions for the Double Sine-Gordon equation by Exp-function, Tanh, and extended Tanh methods

, Article Numerical Methods for Partial Differential Equations ; Volume 26, Issue 2 , 2010 , Pages 384-398 ; 0749159X (ISSN) ; Davodi, A. G ; Davodi, A. G ; Sharif University of Technology
2010

Abstract

In this work, we implement some analytical techniques such as the Exp-function, Tanh, and extended Tanh methods for solving nonlinear partial differential equation, which contains sine terms, its name Double Sine-Gordon equation. These methods obtain exact solutions of different types of differential equations in engineering mathematics

#### Investigation of transient response of erbium-doped fiber lasers by semi-classical theory

, Article Journal of Optical Communications ; Volume 28, Issue 4 , 2007 , Pages 248-251 ; 01734911 (ISSN) ; Mahjoei, M ; Jamali, P ; Sharif University of Technology
Fachverlag Schiele und Sohn GmbH
2007

Abstract

The transient response of all optical gain clamped multi channel erbium doped fiber amplifiers (EDFA's) and optical fiber inverter is studied by a semi-classical model. Using the semi-classical theory, the electric field interacting with mater is considered classical and the medium is quantized according to the equations of motion for density matrix. The rate equations and "self consistency" equations, which yield amplitude and phase of the electric fields of oscillator and amplifying channels are derived by considering Maxwell's equations and equation of motion of density matrix. The governing equations form a system of coupled partial differential equations. The relaxation oscillation...

#### Effects of rotary inertia and shear deformation on nonlinear vibration of micro/nano-beam resonators

, Article 2005 ASME International Mecahnical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, 5 November 2005 through 11 November 2005 ; Volume 7 MEMS , 2005 , Pages 439-445 ; 1096665X (ISSN); 079184224X (ISBN); 9780791842249 (ISBN) ; Alasty, A ; ASME Micro Electro Mecahnical Systems Division ; Sharif University of Technology
2005

Abstract

In this paper, the large amplitude tree vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the...

#### The Variational Approach to Stochastic Partial Differential Equations

, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor)
Abstract

n this thesis we have investigated stochastic evolution equations by variational method. For these equations, explicit and implicit numerical schemes are presented. We have performed these numerical schemes for stochastic heat equation. We have investigated 2-D Navier-Stokes equation too

#### Third Order differential Equations Describing Pseudospherical Surfaces

, M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)
Abstract

Third order differential equations which describe pseudospherical surfaces are considered. The complete classification of a class of such equations is given. A linear problem with one or more parameters, also known as zero curvature representation, for which the equation is the integrability condition, is explicitly given. The classification provides five large families of differential equations. Third order nonlinear dispersive wave equations, such as the Camassa–Holm equation and Degasperis–Procesi equation are examples contained in the classification. Many other explicit examples are included

#### Analysis and Differential Equations on Fractals

, M.Sc. Thesis Sharif University of Technology ; Ranjbar Motlagh, Alireza (Supervisor)
Abstract

In this thesis we consider dynamical aspects of fractals. More precisely, answering questions like how heat diffuses on fractals and how does a material with fractal structure vibrates? To give an answer to these questions we need a PDE theory on fractals. Since fractals do not have smooth structures, defining differential operators like Laplacian is not possible from a classical viewpoint of analysis, to overcome such a difficulty we also need a theory of analysis on fractals. So as a good instance of analysis on fractals we first define Laplacian on Sierpinsky gasket and we try to extend the concept on other finitely ramified self-similar fractals. We also construct Dirichlet forms,...

#### Regularity of the Free Boundary in Semilinear Problems

, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract

There are some situations where we would like to solve a partial differential equation (PDE) in a domain whose boundary is not known a priori; such a problem is called free boundary problem and the boundary is called free boundary. For this kind of problems, aside from standard boundary conditions, an extra condition is imposed at the free boundary and the goal would be finding the free boundary in addition to finding a solution for PDE. One of the classical examples of free boundary problems is the Stefan problem (melting of ice) in which ice and water temperatures are determined from the heat equation and we would be interested in finding the boundary between ice and water. Another famous...

#### Vibration Boundary Control in Micro-beams Equipped with a Layer of Piezoelectric Actuator

, M.Sc. Thesis Sharif University of Technology ; Salarieh, Hassan (Supervisor) ; Alasti, Aria (Supervisor) ; Vatankhah, Ramin ($item.subfieldsMap.e)
Abstract

Nowadays, micro systems in many area of science and technology have special importance and status. The main function of these systems is based on the deformation of a beam at micro scale. Therefore study of behavior and control of micro-beams will have a great importance. Among micro-beams, clamped-free and clamped-clamped micro beams that actuated by piezoelectric and electrostatic actuators have wider applications. For example, clamped-free micro-beams are used in atomic force microscopy (AFM), micro switches, mass sensors and micro-accelerometers and clamped-clamped micro-beams are used in micro mirrors and Grating Light Valves (GLV). In this thesis, the studied system is clamped-free...

#### Image Processing Using Calculus of Variations and PDEs Tools

, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract

The aim of this thesis is to investigate recent methods for Image Processing(Any signal process which it’s input is an image and it’s ouput is an image or a set of Image parameters) using Calculus of variation tools. Methods which are to be investigated has been divided into two well known parts of Image Processing : Image Restoration and Image Segmentation.Image Processing Chapter includes two sections: one calculus of variations methods(energy method), other methods based on PDEs(heat equation and Malik-Perona equation). In studing each of this methods, It has been tried to include experimental results and negative and positive points of them.In Image Segmentation Chapter, first...