Sharif Digital Repository

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  

In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity  

The three-dimensional split-field finite-difference time-domain (SF-FDTD) method is combined with the totalfield- scattered-field method for injecting a plane wave. A formulation is derived for calculating the incidence transformed fields of SF-FDTD on a one-dimensional auxiliary grid. The resulting fields obtained in the scattered zone are used to calculate the far fields, based on a proposed fully time-domain near-to-far-field transformation. The far-field information is used to calculate the extinction cross section of the periodic structure under oblique incidence. To analyze metallic periodic structures, a formulation with a reduced number of variables is proposed based on the auxiliary... 

Time delay in the evaluation of the attitude of a rigid body can significantly hinder the performance of the attitude control system. In this brief, we propose a dynamically smooth control law that guarantees asymptotic convergence of the rigid body attitude and angular velocity to their desired values in the presence of delayed attitude measurement. We assume that the moment-of-inertia matrix of the body is unknown. The control law includes a matrix gain that is computed by solving a delay-dependent and time-varying matrix differential equation. It is shown that the solvability of the matrix differential equation depends on a uniform controllability condition, which can be verified a priori... 

Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different... 

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... 

The coupled three-dimensional flexural vibrations of a micro-rotating shaft–disk system, as a basic model for micro-engines, are investigated in this paper by considering small-scale effects utilizing the modified couple stress theory. Governing equations of motion are derived by the use of Hamilton’s principle. Then, implementing the Galerkin approach, an infinite set of ordinary differential equations is obtained for the system. With truncated two-term equations, expressions for the first two natural frequencies are written, and for the two corresponding modes, the maximum rotational speed up to which the system will be stable is analytically determined. Parametric studies on the results... 

Micro actuators are an irreplaceable part of motion control in miniaturized systems and are intended to have a high range of deformation, high accuracy, large force, and quick response. In this article, an analytical model for a hybrid thermopiezoelectric micro actuator is developed in which a double lead-zirconnate-titanate piezoceramic (PZT) beam structure consisting of two arms with different lengths are used. Governing differential equation of motion and electrical field are derived and solved. Out of parametric studies it was observed that, under application of temperature and voltage gradients, the deflection of the actuator shows different trends depending on the geometry of the micro... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions... 

Particle dispersion in the vortex flow has been one of the most interesting subjects in recent years. Bidirectional vortex flow field is an industrial sample of the rotating flow which is used to obtain advantages of better mixing and combustion. In this work penetration and dispersion quality of the particles which are entering from various positions on the vortex engine walls have been numerically predicted. Head side, end side, and sidewall are considered as the entering positions. The particle has been assumed to be a rigid sphere. Initial velocity, diameter, and density of entering the particles are assumed to be known. If the particle length scale is considered not to be comparable... 

In this note, we show that under certain assumptions the scalar Riccati differential equation x′=a(t)x+b(t)x 2+c(t) with periodic coefficients admits at least one periodic solution. Also, we give two illustrative examples in order to indicate the validity of the assumptions  

In this work, we implement a relatively new analytical technique, the exp-function method, for solving nonlinear special form of generalized nonlinear (2 + 1) dimensional Broer-Kaup-Kupershmidt equation, which may contain high nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of exp method. It is predicted that exp-function method can be found widely applicable in engineering  

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... 

This paper proposes a globally and exponentially convergent predictive observer for attitude and position estimation based on landmark measurements and velocity (angular and linear) readings. It is assumed that landmark measurements are available with time-delay. The maximum value of the sensor delay under which the estimation error converges to zero is calculated. Synthesis of the observer is based on a representation of rigid-body kinematics and sensor delay, formulated via ordinary and partial differential equations (ODE-PDE). Observability condition specifies necessary and sufficient landmark configuration for convergence of attitude and position estimation error to zero. Finally, for... 

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  

This paper deals with the coupling flexural-torsional vibration analysis of a grid formed by two members. A mass-spring system is attached to the grid at the intersecting joint. The members of the grid are assumed to resist torsion as well as bending and shear. Moreover, the mechanical and geometrical properties of each member are different. In order to analyze the problem, a closed-form solution is obtained. In doing so, the governing differential equations of the system along with the pertinent boundary and compatibility conditions of the system are introduced. Then, the frequency parameters of the mechanical system under study are derived and given for the first five modes of vibration.... 

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... 

As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and... 

This paper proposes a globally and exponentially convergent predictive observer for attitude and position estimation based on landmark measurements and velocity (angular and linear) readings. It is assumed that landmark measurements are available with time-delay. The maximum value of the sensor delay under which the estimation error converges to zero is calculated. Synthesis of the observer is based on a representation of rigid-body kinematics and sensor delay, formulated via ordinary and partial differential equations (ODE-PDE). Observability condition specifies necessary and sufficient landmark configuration for convergence of attitude and position estimation error to zero. Finally, for... 

In this paper, the optimal performance of a planar humanlike musculoskeletal arm is investigated during reaching movements employing an optimal control policy. The initial and final states (position and velocity) are the only known data of the response trajectory. Two biomechanical objective functions are taken into account to be minimized as the central nervous system (CNS) strategy: (1) a quadratic function of muscle stresses (or forces), (2) total time of movement plus a quadratic function of muscle stresses. A two-degress of freedom (DOF) nonlinear musculoskeletal arm model (for planar movements) with six muscle actuators and four state variables is used in order to evaluate the proposed...