Sharif Digital Repository

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... 

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... 

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... 

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... 

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... 

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  

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 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  

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... 

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  

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... 

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...