Search results for: non-linear characteristics

Authors: Haider M. Alsaeq

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The present research is an attempt to figure out the best configuration of composite cylindrical shells of the sandwich type, i.e. the lightest design of such shells required to sustain a certain load over a certain area. The optimization is based on elastic-plastic geometrically nonlinear incremental-iterative finite element analysis. The nine-node degenerated curved shell element is used in which five degrees of freedom are specified at each nodal point, with a layered model. The formulation of the geometrical nonlinearity problem is carried out using the well-known total Lagrangian principle. For the structural optimization problem, which is dealt with as a constrained nonlinear optimization, the so-called Modified Hooke and Jeeves method is employed by considering the weight of the shell as the objective function with stress and geometrical constraints. It was concluded that the optimum design of composite sandwich cylindrical shell that have a rigid polyurethane foam core and steel facing occurs when the area covered by the shell becomes almost square with a ratio of core thickness to facing thickness lies between 45 and 49, while the optimum height to length ration varies from 0.03 to 0.08 depending on the aspect ratio of the shell and its boundary conditions.

Keywords: composite structure, cylindrical shell, optimization, non-linear analysis, finite element

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: F. Sabri, J. Jamali

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In this article, the wrinkling failure of orthotropic composite membranes due to in-plane shear deformation is investigated using nonlinear finite element analyses. A nonlinear post-buckling analysis is performed to show the evolution of shear-induced wrinkles. The method of investigation is based on the post-buckling finite element analysis adopted from commercial FEM code; ANSYS. The resulting wrinkling patterns, their amplitude and their wavelengths under the prescribed loads and boundary conditions were confirmed by experimental results. Our study reveals that wrinkles develop when both the magnitudes and coverage of the minimum principal stresses in the laminated composite laminates are sufficiently large to trigger wrinkling.

Keywords: composite, FEM, membrane, wrinkling

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Andrzej Mitura, Krzysztof Kecik, Michal Augustyniak

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This paper presents a numerical and experimental research of a nonlinear two degrees of freedom system. The tested system consists of a mechanical oscillator (the primary subsystem) with the attached pendulum (the secondary subsystem). The oscillator is suspended on a linear (or nonlinear) coil spring and a nonlinear magnetorheorogical damper and it is excited kinematically. Added pendulum can be used to reduce vibration of a primary subsystem or to energy harvesting. The numerical and experimental investigations showed that the pendulum can perform several types of motion, for example: chaotic motion, constant position in lower or upper (stable inverted pendulum), rotation, symmetrical or asymmetrical swinging vibrations. The main objective of this study is to determine an influence of system parameters for increasing the zone when the pendulum rotates. As a final effect a semi-active control method to change the pendulum solution on the rotation is proposed. To the implementation of this method the magnetorheorogical damper is applied. Continuous rotation of the pendulum is desirable for recovery of energy. The work is financed by Grant no. 0234/IP2/2011/71 from the Polish Ministry of Science and Higher Education in years 2012-2014.

Keywords: autoparametric vibrations, chaos and rotation control, magnetorheological damper

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Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

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Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

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Authors: Merrimi El Bekkaye, El Bikri Khalid, Benamar Rhali

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In the present paper, the problem of geometrically non-linear free vibration of symmetrically and asymmetrically laminated composite beams (LCB) resting on nonlinear Pasternak elastic Foundation with immovable ends is studied. A homogenization procedure has been performed to reduce the problem under consideration to that of the isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the LCB has been studied. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Keywords: large vibration amplitudes, laminated composite beam, Pasternak foundation, composite beams

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Authors: K. B. Rajasekarababu, J. Karthik, G. Vinayagamurthy

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This paper is intended to explain the influence of major axis on aerodynamic characteristics of elliptical section. Many engineering applications such as off shore structures, bridge piers, civil structures and pipelines can be modelled as a circular cylinder but flow over complex bodies like, submarines, Elliptical wing, fuselage, missiles, and rotor blades, in which the parameters such as axis ratio can influence the flow characteristics of the wake and nature of separation. Influence of Major axis in Flow characteristics of elliptical sections are examined both experimentally and computationally in this study. For this research, four elliptical models with varying major axis [*AR=1, 4, 6, 10] are analysed. Experimental works have been conducted in a subsonic wind tunnel. Furthermore, flow characteristics on elliptical model are predicted from k-ε turbulence model using the commercial CFD packages by pressure based transient solver with Standard wall conditions.The analysis can be extended to estimation and comparison of Drag coefficient and Fatigue analysis of elliptical sections.

Keywords: elliptical section, major axis, aerodynamic characteristics, k-ε turbulence model

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability

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Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Fouad Berrabeh, Sabir Messalti

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The performances of the photovoltaic systems are very dependent on different conditions, such as solar irradiation, temperature, etc. Therefore, it is very important to provide detailed studies for different cases in order to provide continuously power, so the photovoltaic system must be properly sized. This paper presents the modelling and simulation of the photovoltaic cell using single diode model. I-V characteristics and P-V characteristics are presented and it verified at different conditions (irradiance effect, temperature effect, series resistance effect).

Keywords: photovoltaic cell, BP SX 150 BP solar photovoltaic module, irradiance effect, temperature effect, series resistance effect, I–V characteristics, P–V characteristics

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Authors: Jianjia Wang, Tong Yu, Haoran Zhu, Kun Liu, Jinwei Hao

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The underlying pattern in the modern city is agglomeration. To some degree, the distribution of urban spatial density can be used to describe the status of this assemblage. There are three intrinsic characteristics to measure urban spatial density, namely, Floor Area Ratio (FAR), Building Coverage Ratio (BCR), and Average Storeys (AS). But the underlying mechanism that contributes to these quantities is still vague in the statistical urban study. In this paper, we explore the corresponding extrinsic factors related to spatial density. These factors can further provide the potential influence on the intrinsic quantities. Here, we take Shanghai Inner Ring Area and Manhattan in New York as examples to analyse the potential impacts on urban spatial density with six selected extrinsic elements. Ebery single factor presents the correlation to the spatial distribution, but the overall global impact of all is still implicit. To handle this issue, we attempt to develop the Boltzmann statistical model to explicitly explain the mechanism behind that. We derive a corresponding novel quantity, called capacity, to measure the global effects of all other extrinsic factors to the three intrinsic characteristics. The distribution of capacity presents a similar pattern to real measurements. This reveals the nonlinear influence on the multi-factor relations to the urban spatial density in agglomeration.

Keywords: urban spatial density, Boltzmann statistics, multi-factor correlation, spatial distribution

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Ga Ye Kim, Hee Sun Kim, Yeong Soo Shin

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Many studies have been done on the repair and strengthening method of concrete structure, so far. The traditional retrofit method was to attach fiber sheet such as CFRP (Carbon Fiber Reinforced Polymer), GFRP (Glass Fiber Reinforced Polymer) and AFRP (Aramid Fiber Reinforced Polymer) on the concrete structure. However, this method had many downsides in that there are a risk of debonding and an increase in displacement by a shortage of structure section. Therefore, it is effective way to enlarge the structural member with polymer mortar or Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) as a means of strengthening concrete structure. This paper intends to investigate structural performance of reinforced concrete (RC) beams enlarged with polymer mortar and compare the experimental results with analytical results. Nonlinear finite element analyses were conducted to compare the experimental results and predict structural behavior of retrofitted RC beams accurately without cost consuming experimental process. In addition, this study aims at comparing differences of retrofit material between commonly used material (polymer mortar) and recently used material (UHPFRC) by conducting nonlinear finite element analyses. In the first part of this paper, the RC beams having different cover type were fabricated for the experiment and the size of RC beams was 250 millimeters in depth, 150 millimeters in width and 2800 millimeters in length. To verify the experiment, nonlinear finite element models were generated using commercial software ABAQUS 6.10-3. From this study, both experimental and analytical results demonstrated good strengthening effect on RC beam and showed similar tendency. For the future, the proposed analytical method can be used to predict the effect of strengthened RC beam. In the second part of the study, the main parameters were type of retrofit materials. The same nonlinear finite element models were generated to compare the polymer mortar with UHPFRCC. Two types of retrofit material were evaluated and retrofit effect was verified by analytical results.

Keywords: retrofit material, polymer mortar, UHPFRC, nonlinear finite element analysis

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Authors: Ehsan Sadie

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The use of steel braces in concrete structures has been considered by researchers in recent decades due to its easy implementation, economics and the ability to create skylights in braced openings compared to shear wall openings as well as strengthening weak concrete structures to earthquakes. The purpose of this article is to improve and strengthen concrete structures with steel bracing. In addition, cases such as different numbers of steel braces in different openings of concrete structures and interaction between concrete frames and metal braces have been studied. In this paper, by performing static nonlinear analysis and examining ductility, the relative displacement of floors, examining the performance of samples, and determining the coefficient of behavior of composite frames (concrete frames with metal bracing), the behavior of reinforced concrete frames is compared with frame without bracing. The results of analyzes and studies show that the addition of metal bracing increases the strength and stiffness of the frame and reduces the ductility and lateral displacement of the structure. In general, the behavior of the structure against earthquakes will be improved.

Keywords: behavior coefficient, bracing, concrete structure, convergent bracing, earthquake, linear static analysis, nonlinear analysis, pushover curve

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Rahisham Abd Rahman

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In this paper, a nonlinear pollution model has been proposed to compute electric field distribution over the polymeric insulator surface under wet contaminated conditions. A 2D axial-symmetric insulator geometry, energized with 11kV was developed and analysed using Finite Element Method (FEM). A field-dependent conductivity with simplified assumptions was established to characterize the electrical properties of the pollution layer. Comparative field studies showed that simulation of dynamic pollution model results in a more realistic field profile, offering better understanding on how the electric field behaves under wet polluted conditions.

Keywords: electric field distributions, pollution layer, dynamic model, polymeric outdoor insulators, finite element method (FEM)

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Authors: Andreas Rudisch, Ralf Lampert, Andreas Kolbitsch

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It is a well-known fact among the engineering community that earthquakes with comparatively low magnitudes can cause serious damage to nonstructural components (NSCs) of buildings, even when the supporting structure performs relatively well. Past research works focused mainly on NSCs of nuclear power plants and industrial plants. Particular attention should also be given to architectural façade elements of old masonry buildings (e.g. ornamental figures, balustrades, vases), which are very vulnerable under seismic excitation. Large numbers of these historical nonstructural components (HiNSCs) can be found in highly frequented historical city centers and in the event of failure, they pose a significant danger to persons. In order to estimate the vulnerability of acceleration sensitive HiNSCs, the peak horizontal floor acceleration (PHFA) is used. The PHFA depends on the dynamic characteristics of the building, the ground excitation, and induced nonlinearities. Consequently, the PHFA can not be generalized as a simple function of height. In the present research work, an extensive case study was conducted to investigate the influence of induced nonlinearity on the PHFA for old masonry buildings. Probabilistic nonlinear FE time-history analyses considering three different hazard levels were performed. A set of eighteen synthetically generated ground motions was used as input to the structure models. An elastoplastic macro-model (multiPlas) for nonlinear homogenized continuum FE-calculation was calibrated to multiple scales and applied, taking specific failure mechanisms of masonry into account. The macro-model was calibrated according to the results of specific laboratory and cyclic in situ shear tests. The nonlinear macro-model is based on the concept of multi-surface rate-independent plasticity. Material damage or crack formation are detected by reducing the initial strength after failure due to shear or tensile stress. As a result, shear forces can only be transmitted to a limited extent by friction when the cracking begins. The tensile strength is reduced to zero. The first goal of the calibration was the consistency of the load-displacement curves between experiment and simulation. The calibrated macro-model matches well with regard to the initial stiffness and the maximum horizontal load. Another goal was the correct reproduction of the observed crack image and the plastic strain activities. Again the macro-model proved to work well in this case and shows very good correlation. The results of the case study show that there is significant scatter in the absolute distribution of the PHFA between the applied ground excitations. An absolute distribution along the normalized building height was determined in the framework of probability theory. It can be observed that the extent of nonlinear behavior varies for the three hazard levels. Due to the detailed scope of the present research work, a robust comparison with code-recommendations and simplified PHFA distributions are possible. The chosen methodology offers a chance to determine the distribution of PHFA along the building height of old masonry structures. This permits a proper hazard assessment of HiNSCs under seismic loads.

Keywords: nonlinear macro-model, nonstructural components, time-history analysis, unreinforced masonry

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Raj Nandkeolyar, Precious Sibanda

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The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

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Authors: Jelena R. Pejović, Nina N. Serdar

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This paper presents an analysis of the “Performance-Based” seismic design method, in order to overcome the perceived disadvantages and limitations of the existing seismic design approach based on force, in engineering practice. Bearing in mind, the specificity of the earthquake as a load and the fact that the seismic resistance of the structures solely depends on its behaviour in the nonlinear field, traditional seismic design approach based on force and linear analysis is not adequate. “Performance-Based” seismic design method is based on nonlinear analysis and can be used in everyday engineering practice. This paper presents the application of this method to eight-story high reinforced concrete building with combined structural system (reinforced concrete frame structural system in one direction and reinforced concrete ductile wall system in other direction). The nonlinear time-history analysis is performed on the spatial model of the structure using program Perform 3D, where the structure is exposed to forty real earthquake records. For considered building, large number of results were obtained. It was concluded that using this method we could, with a high degree of reliability, evaluate structural behavior under earthquake. It is obtained significant differences in the response of structures to various earthquake records. Also analysis showed that frame structural system had not performed well at the effect of earthquake records on soil like sand and gravel, while a ductile wall system had a satisfactory behavior on different types of soils.

Keywords: ductile wall, frame system, nonlinear time-history analysis, performance-based methodology, RC building

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Authors: Leila Graini

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In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: all-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

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Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: artificial immune system, breast cancer diagnosis, Euclidean function, Gaussian function

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Priyanka Kumari Gupta, Punya Prasanna Paltani, Shrivishal Tripathi

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This paper proposes a nonlinear photonic crystal ring resonator-based all-optical 2 × 2 switch. The nonlinear Kerr effect is used to evaluate the essential 2 x 2 components of the photonic crystal-based optical switch, including the bar and cross states. The photonic crystal comprises a two-dimensional square lattice of dielectric rods in an air background. In the background air, two different dielectric materials are used for this comparison study separately. Initially with chalcogenide glass rods, then with GaAs rods. For both materials, the operating wavelength, bandgap diagram, operating power intensities, and performance parameters, such as the extinction ratio, insertion loss, and cross-talk of an optical switch, have also been estimated using the plane wave expansion and the finite-difference time-domain method. The chalcogenide glass material (Ag20As32Se48) has a high refractive index of 3.1 which is highly suitable for switching operations. This dielectric material is immersed in an air background with a nonlinear Kerr coefficient of 9.1 x 10-17 m2/W. The resonance wavelength is at 1552 nm, with the operating power intensities at the cross-state and bar state around 60 W/μm2 and 690 W/μm2. The extinction ratio, insertion loss, and cross-talk value for the chalcogenide glass at the cross-state are 17.19 dB, 0.051 dB, and -17.14 dB, and the bar state, the values are 11.32 dB, 0.025 dB, and -11.35 dB respectively. The gallium arsenide (GaAs) dielectric material has a high refractive index of 3.4, a direct bandgap semiconductor material highly preferred nowadays for switching operations. This dielectric material is immersed in an air background with a nonlinear Kerr coefficient of 3.1 x 10-16 m2/W. The resonance wavelength is at 1558 nm, with the operating power intensities at the cross-state and bar state around 110 W/μm2 and 200 W/μm2. The extinction ratio, insertion loss, and cross-talk value for the chalcogenide glass at the cross-state are found to be 3.36.19 dB, 2.436 dB, and -5.8 dB, and for the bar state, the values are 15.60 dB, 0.985 dB, and -16.59 dB respectively. This paper proposes an all-optical 2 × 2 switch based on a nonlinear photonic crystal using a ring resonator. The two-dimensional photonic crystal comprises a square lattice of dielectric rods in an air background. The resonance wavelength is in the range of photonic bandgap. Later, another widely used material, GaAs, is also considered, and its performance is compared with the chalcogenide glass. Our presented structure can be potentially applicable in optical integration circuits and information processing.

Keywords: photonic crystal, FDTD, ring resonator, optical switch

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Authors: Gram Y. Rivas Sanchez

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The seismic design codes in the world allow the analysis of structures considering an elastic-linear behavior; however, against earthquakes, the structures exhibit non-linear behaviors that induce damage to their elements. For this reason, it is necessary to use non-linear methods to analyze these structures, being the dynamic methods that provide more reliable results but require a lot of computational costs; on the other hand, non-linear static methods do not have this disadvantage and are being used more and more. In the present work, the nonlinear static analysis (pushover) of RC frame buildings of three, five, and seven stories is carried out considering models of concentrated plasticity using plastic hinges; and the seismic performance points are determined using ATC-40, FEMA 356, and FEMA 440 guidelines. Using this last standard, the highest inelastic displacements and basal shears are obtained, providing designs that are more conservative.

Keywords: pushover, nonlinear, RC building, FEMA 440, ATC 40

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Chi-Yan Chu, Kai-Chi Chuang, Huang-Chung Cheng

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In this study, the RRAM devices with the TiN/Ti/HfO_x/TiN structure were fabricated, then the electrical characteristics of the devices without annealing and after 400 °C and 500 °C of the furnace annealing (FA) temperature processes were compared. The RRAM devices after the FA’s 400 °C showed the lower forming, set and reset voltages than the other devices without annealing. However, the RRAM devices after the FA’s 500 °C did not show any electrical characteristics because the TiN/Ti/HfO_x/TiN device was oxidized, as shown in the XPS analysis. From these results, the RRAM devices after the FA’s 400 °C showed the best electrical characteristics.

Keywords: RRAM, furnace annealing (FA), forming, set and reset voltages, XPS

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Issam Aouari, Abdelmalek Abdelhamid

Abstract:

For seismologists, the characterization of seismic demand should include the amplitude and duration of strong shaking in the system. The duration of ground shaking is one of the key parameters in earthquake resistant design of structures. This paper proposes a nonlinear statistical model to estimate earthquake ground motion duration in soft soils using multiple seismicity indicators. Three definitions of ground motion duration proposed by literature have been applied. With a comparative study, we select the most significant definition to use for predict the duration. A stochastic model is presented for the McCann and Shah Method using nonlinear regression analysis based on a data set for moment magnitude, source to site distance and site conditions. The data set applied is taken from PEER strong motion databank and contains shallow earthquakes from different regions in the world; America, Turkey, London, China, Italy, Chili, Mexico...etc. Main emphasis is placed on soft site condition. The predictive relationship has been developed based on 600 records and three input indicators. Results have been compared with others published models. It has been found that the proposed model can predict earthquake ground motion duration in soft soils for different regions and sites conditions.

Keywords: duration, earthquake, prediction, regression, soft soil

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