Sharif Digital Repository

We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed, grows with increasing second-order coupling  

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  

A nonlinear inverse finite element method is developed for estimation of initial blank shape and strain distribution in final shape. This method often based on implicit static algorithms, causes sometimes convergence problems because of strong nonlinearities. In order to avoid the converging problems, especially in the quasi vertical walls, an appropriate initial guess is introduced. By using this initial guess, the number of iterations in the nonlinear numerical solution is decreased, solution speed is significantly increased and complicated geometries can be analyzed by this method with good accuracy. Application to a Srail part shows good agreement between commercially available finite... 

Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the... 

Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the... 

To deal with strong nonlinearity in nonlinear systems, a new method called cascade multiple-model predictive controller based on gap metric and stability margin, is proposed. The gap metric is utilized to describe the nonlinear system by a linear model bank. It is possible to select nominal local models from the linear model bank by an algorithm based on the gap metric and stability margin to avoid the redundancy of the local controllers. By scheduling proportional controller for each nominal local model, the robust stability is guaranteed whereas there will be no guarantee for the desired performance. Then, by designing a model predictive controller in the cascade structure, the closed loop... 

A simplified efficient finite element method called the inverse approach (IA) has been developed to estimate initial blank and strain distribution in sheet metal forming. This algorithm is an inverse method since the position of points in final shape is known and their corresponding position in the initial blank should be determined. This approach deals with the geometric compatibility of finite elements, plastic deformation theory, and virtual work principle. This method often based on implicit static algorithms, sometimes causes convergence problems because of strong nonlinearities. This paper introduces an initial guess to speed up the convergence of Newton- Raphson solution. The... 

Dual axis micromirrors are actuated using strongly nonlinear electrostatic actuation and their operating range suffers from the pull-in problem. So investigation of their dynamics and control issues has become a challenge for the researchers. The current paper makes use of fuzzy controllers for the purpose of stabilizing the dual axis micromirror at the desired tilt angles beyond pull-in. At first the dynamic model of the micromirror is presented. Then for the purpose of finding the linguistic laws governing the system behavior, several step voltages are introduced to the system. The proposed fuzzy controller consists of singleton fuzzifier, product inference engine and center average... 

In this study, the homotopy analysis method (HAM) is used to study dynamic pull-in instability in microbeams considering different sources of nonlinearity. Electrostatic actuation, fringing field effect and midplane stretching causes strong nonlinearity in microbeams. In order to investigate dynamic pull-in behavior, using Galerkin's decomposition method, the nonlinear partial differential equation of motion is reduced to a single nonlinear ordinary differential equation. The obtained equation is solved analytically in time domain using HAM. The problem is studied by two separate manners: direct use of HAM and indirect use of HAM in conjunction with He's Modified Lindstedt- Poincaré Method.... 

Despite their simple structure and design, microcantilevers are receiving increased attention due to their unique sensing and actuation features in many MEMS and NEMS. Along this line, a non-linear distributed-parameters modeling of a microcantilever beam under the influence of a nanoparticle sample is studied in this paper. A long-range Van der Waals force model is utilized to describe the microcantilever-particle interaction along with an inextensibility condition for the microcantilever in order to derive the equations of motion in terms of only one generalized coordinate. Both of these considerations impose strong nonlinearities on the resultant integro-partial equations of motion. In... 

In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations...