Sharif Digital Repository

In the last decade, many potent analytical methods have been utilized to find the approximate solution of nonlinear differential equations. Some of these methods are energy balance method (EBM), homotopy perturbation method (HPM), variational iteration method (VIM), amplitude frequency formulation (AFF), and max-min approach (MMA). Besides the methods mentioned above, the Akbari-Ganji method (AGM) is a highly efficient analytical method to solve a wide range of nonlinear equations, including heat transfer, mass transfer, and vibration problems. In this study, it was constructed the approximate analytic solution for movement of two mechanical oscillators by employing the AGM. In the derived... 

In this paper we consider the nonlinear third-order quasi-linear differential equationx‴+k2x′=εfx,x′,x″and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problemx‴+k2x′=fx,x′,x″also is considered. © 2001 Academic Press  

In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations. The validity of this method has been successful by applying it for these nonlinear equations. The results obtained by this method have a good agreement with one obtained by other methods. This work illustrates the validity of the homotopy analysis method for the nonlinear differential equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems. © 2008 Springer Science+Business Media B.V  

Electrical impedance tomography is a simple and economic medical imaging technology which permits regional assessment of the electrical properties of organs within the body based on measurements made from electrodes on the surface of the body. Block method is a new solution for electrical impedance tomography used to enhance image resolution and to improve reconstruction algorithm. Image reconstruction by block method is an ill-posed and nonlinear problem also has memory and time consuming process which can be improved by using modified equations. Improving forward solution for block electrical impedance tomography method can make linear equations for image reconstruction algorithm  

In this paper, the existence of periodic solutions of autonomous ordinary differential equations of a 4th and 5th order is investigated. The method used is based on the Brower's degree theorem using the homotopy invariant a property of a topological degree. © Sharif University of Technology, April 2008  

The feasibility of integrating co-flow fluidic thrust-vectoring idea into the dynamics of a small flapless aerial tail-sitter is investigated in this article. The aircraft trimmability in different phases of flight and stability in take-off and level flight, are the main issues of concern for the study presented herein. In this respect, the vehicle's characteristic equations are derived by linearization of the general non-linear equations of motion. Since the vehicle was supposed to be merely controlled by fluidic thrust-vectoring, the concept was novel and some new derivatives are introduced. Margins of the required thrust-vector angle, to obtain a steady-state flight condition, are... 

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible... 

The non-linear bubble dynamics equations in a compressible liquid have been modified by considering the effects of compressibility of both the liquid and the gas at the bubble interface. A new bubble boundary equation has been derived, which includes a new term resulting from the liquid bulk viscosity effect. The influence of this term has been numerically investigated by considering the effects of water vapour and chemical reactions inside the bubble. The results clearly indicate that the new term has an important damping role at the collapse, so that its consideration dramatically decreases the amplitude of the bubble rebounds after the collapse. This damping feature is more remarkable for... 

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  

The structural instability of an array of cantilevers, each of which interacts with two neighbouring beams through electrostatic and van der Waals forces, is studied. Distributed and lumped parameter modelling of the array result in a set of coupled nonlinear boundary value problems and a set of coupled nonlinear equations, respectively. These coupled nonlinear systems are solved numerically for different numbers of beams in the array to obtain the pull-in parameters. The pull-in parameters converge to constant values with an increase in the number of beams in the array. These constants, which are important in the design of cantilever arrays, are compared for the distributed and lumped... 

In this paper, the effects of different parameters on the nonlinear aeroelastic behavior of functionally graded flat plates are investigated. Considering the through-the-thickness continuous variation of the material properties, a combination of the simple rule of mixtures and the Mori-Tanaka scheme is used for estimating the effective properties at each point. The von-Karman large strains and the piston theory are used to model the structural nonlinearity and aerodynamic loading, respectively. By Hamilton's principle the governing nonlinear partial differential equations of motion are derived and then converted to a set of nonlinear ordinary differential equations using the Galerkin method.... 

In this paper, the whale optimization algorithm is proposed for harmonics elimination in a cascaded multilevel inverter. In selective harmonic elimination pulse width modulation, the selected low-order harmonics are eliminated by solving nonlinear equations, while the fundamental of output waveform is adjusted to a desired value. In this paper, whale optimization algorithm is applied to a 7-level cascaded H-bridge inverter to solve the equations. Also, it was validated by experimental results, since this algorithm has an ability to search in entire solution space, the probability of catching a global best solution is very high. This method has higher accuracy and probability of convergence... 

In this paper, the whale optimization algorithm is proposed for harmonics elimination in a cascaded multilevel inverter. In selective harmonic elimination pulse width modulation, the selected low-order harmonics are eliminated by solving nonlinear equations, while the fundamental of output waveform is adjusted to a desired value. In this paper, whale optimization algorithm is applied to a 7-level cascaded H-bridge inverter to solve the equations. Also, it was validated by experimental results, since this algorithm has an ability to search in entire solution space, the probability of catching a global best solution is very high. This method has higher accuracy and probability of convergence... 

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior... 

In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces. Then, the stability of static equilibrium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of different design parameters on the mirror's pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the... 

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  

Growing technology, escalating capability, and increasing complexity in many real world systems demand the applications of multivariate statistical analysis approaches by simulation. In these approaches, generating multivariate random vectors is a crucial part of the system modeling and analyzing. The NORTA algorithm, in which generating the correlation matrices of normal random vectors is the most important task, is one of the most efficient methods in this area. To do this, we need to solve some complicated equations. Many researchers have tried to solve these equations by three general approaches of (1) solving nonlinear equations analytically, (2) solving equations numerically, and (3)... 

In this paper we will present some approaches on Reynolds stress production by vortex transport phenomena and nonlinear voracity generation in momentum equation. First of all we represent a history of recent works to describe how fluid particle motions can be associated with Reynolds stress through either displacement or acceleration terms. In the next section we will describe how vortex stretching causes the Reynolds stress production and what is the dominant effect near and far from the boundary where viscous effects have to be considered. On the other hand, some vortex considered methodologies such as those synthesize boundary layer, as a collection of vortical objects seem to be... 

In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipulator will be addressed. Since each leg has a spherical actuator (three inputs for each leg) and manipulator has three legs; totally, there are nine inputs. Due to the fact that the manipulator has six degree of freedom, only six independent inputs are needed. Thus actuation could be done in different ways. If the triangles representing base and platform are equilateral, there are twenty different ways of actuation that should be studied during forward kinematic analysis. Rather than adopting the standard Denavit-Hartenberg approach, a simple method for forward kinematic analysis for all these different...