Search results for: fast nonlinear analysis

Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Alessandro Marzucchini, Yie Sue Chua, Andrew Lian, Richard Shonn Mills

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A unique, fast and easy installed inter-module connection named Candle-Loc was developed and applied in several high-rise steel and reinforced concrete modular buildings in Singapore and Hong Kong, China. However, its effect on the global behaviour of modular buildings in high seismic zones was not studied. Therefore, the design concept and the structural performance of each component in this connection was investigated through analytical approach. Response spectrum, linear time-history, and nonlinear time-history analyses were conducted to investigate the effects of the different joint models of the Candle-Loc in the global analysis of high-rise buildings under high seismic loads. It is found that it is important to assess the level of plasticity developed in the inter-module connection under high seismic loads. The ductility of the lateral force resisting system influences the amount of load taken by the inter-module connections.

Keywords: high-rise, inter-module connection, nonlinear, seismic, time-history analysis

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Authors: Minas Balyan

Abstract:

In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

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In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover

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Authors: V. Tabrizi, A. Vali, R. GHasemi, V. Behnamgol

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In this article, a nonlinear model of an under actuated six degrees of freedom (6 DOF) quadrotor UAV is derived on the basis of the Newton-Euler formula. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The robust nonlinear control strategy includes a smooth second order non-singular terminal sliding mode control which is applied to stabilizing this model. The control method is on the basis of super twisting algorithm for removing the chattering and producing smooth control signal. Also, nonsingular terminal sliding mode idea is used for introducing a nonlinear sliding variable that guarantees the finite time convergence in sliding phase. Simulation results show that the proposed algorithm is robust against uncertainty or disturbance and guarantees a fast and precise control signal.

Keywords: quadrotor UAV, nonsingular terminal sliding mode, second order sliding mode t, electronics, control, signal processing

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Authors: E. Feulefack Songong, A. Zingoni

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A vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Although vibrations can be linear or nonlinear depending on the basic components of the system, the interest is mostly pointed towards nonlinear vibrations. This is because most structures around us are to some extent nonlinear and also because we need more accurate values in an analysis. The goal of this research is the integration of nonlinearities in the development and validation of structural models and to ameliorate the resistance of structures when subjected to loads. Although there exist many types of nonlinearities, this thesis will mostly focus on the vibration of free and undamped systems incorporating nonlinearity due to stiffness. Nonlinear stiffness has been a concern to many engineers in general and Civil engineers in particular because it is an important factor that can bring a good modification and amelioration to the response of structures when subjected to loads. The analysis of systems will be done analytically and then numerically to validate the analytical results. We will first show the benefit and importance of stiffness nonlinearity when it is implemented in the structure. Secondly, We will show how its integration in the structure can improve not only the structure’s performance but also its response when subjected to loads. The results of this study will be valuable to practicing engineers as well as industry practitioners in developing better designs and tools for their structures and mechanical devices. They will also serve to engineers to design lighter and stronger structures and to give good predictions as for the behavior of structures when subjected to external loads.

Keywords: elastic foundation, nonlinear, plates, stiffness, structures, vibration

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Authors: Juliana A. Knocikova

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Methods of nonlinear signal analysis are based on finding that random behavior can arise in deterministic nonlinear systems with a few degrees of freedom. Considering the dynamical systems, entropy is usually understood as a rate of information production. Changes in temporal dynamics of physiological data are indicating evolving of system in time, thus a level of new signal pattern generation. During last decades, many algorithms were introduced to assess some patterns of physiological responses to external stimulus. However, the reflex responses are usually characterized by short periods of time. This characteristic represents a great limitation for usual methods of nonlinear analysis. To solve the problems of short recordings, parameter of approximate entropy has been introduced as a measure of system complexity. Low value of this parameter is reflecting regularity and predictability in analyzed time series. On the other side, increasing of this parameter means unpredictability and a random behavior, hence a higher system complexity. Reduced neurophysiological data complexity has been observed repeatedly when analyzing electroneurogram and electromyogram activities during defence reflex responses. Quantitative phrenic neurogram changes are also obvious during severe hypoxia, as well as during airway reflex episodes. Concluding, the approximate entropy parameter serves as a convenient tool for analysis of reflex behavior characterized by short lasting time series.

Keywords: approximate entropy, neurophysiological data, nonlinear dynamics, reflex

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

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In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT) and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect non-linear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub

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Authors: A. Ras, I. Nait Zerrad, N. Benmouna, N. Boumechra

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Use of base isolators in the seismic design of structures has attracted considerable attention in recent years. The major concern in the design of these structures is to have enough lateral stability to resist wind and seismic forces. There are different systems providing such isolation, among them there are friction- pendulum base isolation systems (FPS) which are rather widely applied nowadays involving to both affordable cost and high fundamental periods. These devices are characterised by a stiff resistance against wind loads and to be flexible to the seismic tremors, which make them suitable for different situations. In this paper, a 3D numerical investigation is done considering the seismic response of a twelve-storey steel building retrofitted with a FPS. Fast nonlinear time history analysis (FNA) of Boumerdes earthquake (Algeria, May 2003) is considered for analysis and carried out using SAP2000 software. Comparisons between fixed base, bearing base isolated and braced structures are shown in a tabulated and graphical format. The results of the various alternatives studies to compare the structural response without and with this device of dissipation energy thus obtained were discussed and the conclusions showed the interesting potential of the FPS isolator. This system may to improve the dissipative capacities of the structure without increasing its rigidity in a significant way which contributes to optimize the quantity of steel necessary for its general stability.

Keywords: energy dissipation, friction-pendulum system, nonlinear analysis, steel structure

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Authors: Ines Elouedi, Atef Hammouda

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This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

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Authors: Widari

Abstract:

This study aims to determine the relationship of fast food consumption preferences with macro and micro nutrient adequacy students of SMP Negeri 5 Padang. This study used a cross sectional study conducted on 100 students of SMP Negeri 5 Padang. The variables studied were fast food preferences, nutrition adequacy macronutrients (carbohydrate, protein, fat, fiber) and micro nutrients (sodium, calcium, iron). Confounding factor in this study was the physical activity level because it was considered quite affecting food consumption of students. Data collected by using a questionnaire food recall as many as 2 x 24 hours to see the history of the respondents eat at school day and on holidays. Then, data processed using software Nutrisurvey and Microsoft Excel 2010. The analysis was performed on samples that have low and medium category on physical activity. The physical activity was not analyzed with another variable to see the strength of the relationship between independent and dependent variables. So that, do restrictions on physical activity variables in an attempt to get rid of confounding in design. Univariate and bivariate analyzes performed using SPSS 16.0 for Windows with Kolmogrov-Smirnov statistical tests, confidence level = 95% (α = 0,05). Results of univariate analysis showed that more than 70% of respondents liked fast food. On average, respondents were malnourished macro; malnourished fiber (100%), carbohydrates (72%), and protein (56%), whereas for fat, excess intake of the respondents (41%). Furthermor, many respondents who have micronutrient deficiencies; 98% for sodium, 96% for iron, and 91% for calcium. The results of the bivariate analysis showed no significant association between fast food consumption preferences with macro and micro nutrient adequacy (p > 0,05). This happens because in the fact not all students who have a preference for fast food actually eat them. To study better in the future, it is expected sampling really like and eat fast food in order to obtain better analysis results.

Keywords: fast food, nutritional adequacy, preferences, students

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: N. H. Adenan, M. S. M. Noorani

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River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to developed an efficient water management system to optimize the allocation water resources.

Keywords: river flow, nonlinear prediction method, phase space, local linear approximation

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: E. Menga, S. Hernandez

Abstract:

Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Ijeoma Chinyere Ukonu

Abstract:

This research seeks to investigate how the globalisation of fast food has affected students’ food choice. A mixed method approach was used in this research; basically involving quantitative and qualitative methods. The quantitative method uses a self-completion questionnaire to randomly sample one hundred and four students; while the qualitative method uses a semi structured interview technique to survey four students on their knowledge and choice to consume fast food. A cross tabulation of variables and the Kruskal Wallis nonparametric test were used to analyse the quantitative data; while the qualitative data was analysed through deduction of themes, and trends from the interview transcribe. The findings revealed that globalisation has amplified the evolution of fast food, popularising it among students. Its global presence has affected students’ food choice and preference. Price, convenience, taste, and peer influence are some of the major factors affecting students’ choice of fast food. Though, students are familiar with the health effect of fast food and the significance of using food information labels for healthy choice making, their preference of fast food is more than homemade food.

Keywords: fast food, food choice, globalisation, students

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Authors: Felix Jr. Garde, Eric Augustus Tingatinga

Abstract:

Most analysis procedures of reinforced concrete (RC) slabs are based on elastic theory. When subjected to large forces, however, slabs deform beyond elastic range and the study of their behavior and performance require nonlinear analysis. This paper presents a numerical model to simulate nonlinear behavior of RC slabs using rigid body-spring discrete element method. The proposed slab model composed of rigid plate elements and nonlinear springs is based on the yield line theory which assumes that the nonlinear behavior of the RC slab subjected to transverse loads is contained in plastic or yield-lines. In this model, the displacement of the slab is completely described by the rigid elements and the deformation energy is concentrated in the flexural springs uniformly distributed at the potential yield lines. The spring parameters are determined from comparison of transverse displacements and stresses developed in the slab obtained using FEM and the proposed model with assumed homogeneous material. Numerical models of typical RC slabs with varying geometry, reinforcement, support conditions, and loading conditions, show reasonable agreement with available experimental data. The model was also shown to be useful in investigating dynamic behavior of slabs.

Keywords: RC slab, nonlinear behavior, yield line theory, rigid body-spring discrete element method

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Hyun-Woo Cho

Abstract:

Unexpected events may occur with serious impacts on industrial process. This work utilizes a data representation technique to model and to analyze process data pattern for the purpose of diagnosis. In this work, the use of triangular representation of process data is evaluated using simulation process. Furthermore, the effect of using different pre-treatment techniques based on such as linear or nonlinear reduced spaces was compared. This work extracted the fault pattern in the reduced space, not in the original data space. The results have shown that the non-linear technique based diagnosis method produced more reliable results and outperforms linear method.

Keywords: process monitoring, data analysis, pattern modeling, fault, nonlinear techniques

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Khaled Sandjak, Boualem Tiliouine

Abstract:

Structural analysis of flexible pavements has been and still is currently performed using multi-layer elastic theory. However, for thinly surfaced pavements subjected to low to medium volumes of traffics, the importance of non-linear stress-strain behaviour of unbound granular materials (UGM) requires the use of more sophisticated numerical models for structural design and performance of such pavements. In the present work, nonlinear unbound aggregates constitutive model is implemented within an axisymmetric finite element code developed to simulate the nonlinear behaviour of pavement structures including two local aggregates of different mineralogical nature, typically used in Algerian pavements. The performance of the mechanical model is examined about its capability of representing adequately, under various conditions, the granular material non-linearity in pavement analysis. In addition, deflection data collected by falling weight deflectometer (FWD) are incorporated into the analysis in order to assess the sensitivity of critical pavement design criteria and pavement design life to the constitutive model. Finally, conclusions of engineering significance are formulated.

Keywords: FWD backcalculations, finite element simulations, Nonlinear resilient behaviour, pavement response and performance, RLT test results, unbound granular materials

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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Authors: Suchi Barua, Narottam Das, Sven Nordholm, Mohammad Razaghi

Abstract:

This paper presents nonlinear pulse propagation characteristics for different input optical pulse shapes with various input pulse energy levels in semiconductor optical amplifiers. For simulation of nonlinear pulse propagation, finite-difference beam propagation method is used to solve the nonlinear Schrödinger equation. In this equation, gain spectrum dynamics, gain saturation are taken into account which depends on carrier depletion, carrier heating, spectral-hole burning, group velocity dispersion, self-phase modulation and two photon absorption. From this analysis, we obtained the output waveforms and spectra for different input pulse shapes as well as for different input energies. It shows clearly that the peak position of the output waveforms are shifted toward the leading edge which due to the gain saturation of the SOA for higher input pulse energies. We also analyzed and compared the normalized difference of full-width at half maximum for different input pulse shapes in the SOA.

Keywords: finite-difference beam propagation method, pulse shape, pulse propagation, semiconductor optical amplifier

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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