Search results for: nonlinear mathematical model

Authors: I. Khabbazi, R. Ghasemi

Abstract:

This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Nina Philipova

Abstract:

The influence of the geometric parameters of trapezoidal labyrinth channel on the pressure losses along the labyrinth length is investigated in this work. The impact of the dentate height is studied at fixed values of the dentate angle and the dentate spacing. The objective of the work presented in this paper is to derive a mathematical model of the pressure losses along the labyrinth length depending on the dentate height. The numerical simulations of the water flow movement are performed by using Commercial codes ANSYS GAMBIT and FLUENT. Dripper inlet pressure is set up to be 1 bar. As a result, the mathematical model of the pressure losses is determined as a second-order polynomial by means Commercial code STATISTIKA. Bi-objective optimization is performed by using the mean algebraic function of utility. The optimum value of the dentate height is defined at fixed values of the dentate angle and the dentate spacing. The derived model of the pressure losses and the optimum value of the dentate height are used as a basis for a more successful emitter design.

Keywords: drip irrigation, labyrinth channel hydrodynamics, numerical simulations, Reynolds stress model

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Authors: Shewangizaw Tesfaye Wolde

Abstract:

The current engineering community has developed a method called performance based seismic design in which we design structures based on predefined performance levels set by the parties. Since we design our structures economically for the maximum actions expected in the life of structures they go beyond their elastic limit, in need of nonlinear analysis. In this paper conventional pushover analysis (nonlinear static analysis) is used for the performance assessment of the case study Reinforced Concrete (RC) Frame building located in Addis Ababa City, Ethiopia where proposed peak ground acceleration value by RADIUS 1999 project and others is more than twice as of EBCS-8:1995 (RADIUS 1999 project) by taking critical planar frame. Fiber beam-column model is used to control material nonlinearity with tension stiffening effect. The reliability of the fiber model and validation of software outputs are checked under verification chapter. Therefore, the aim of this paper is to propose a way for structural performance assessment of existing reinforced concrete frame buildings as well as design check.

Keywords: seismic, performance, fiber model, tension stiffening, reinforced concrete

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Authors: Hari Pulapaka

Abstract:

This paper defines and develops the notion of a traceability index for food and may be used by any consumer (restaurant, distributor, average consumer etc.). The concept is then extended to a region's food system as a way to measure how well a regional food system utilizes its own bounty or at least, is connected to its food sources. With increasing emphases on the sustainability of aspects of regional and ultimately, the global food system, it is reasonable to accept that if we know how close (in relative terms) an end-user of a set of ingredients (as they traverse through the maze of supply chains) is from the sources, we may be better equipped to evaluate the quality of the set as measured by any number of qualitative and quantitative criteria. We propose a mathematical model which may be adapted to a number of contexts and sizes. Two hypothetical cases of different scope are presented which highlight how the model works as an evaluator of steps between an end-user and the source(s) of the ingredients they consume. The variables in the model are flexible enough to be adapted to other applications beyond food systems.

Keywords: food, traceability, supply chain, mathematical model

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Authors: Joao Fialho

Abstract:

The mathematical modelling of idiopathic scoliosis has been studied throughout the years. The models presented on those papers are based on the orthotic stabilization of the idiopathic scoliosis, which are based on a transversal force being applied to the human spine on a continuous form. When considering the ATT (Antalgic-Trak Technology) device, the existent models cannot be used, as the type of forces applied are no longer transversal nor applied in a continuous manner. In this device, vertical traction is applied. In this study we propose to model the idiopathic scoliosis, using the ATT (Antalgic-Trak Technology) device, and with the parameters obtained from the mathematical modeling, set up a case-by-case individualized therapy plan, for each patient.

Keywords: idiopathic scoliosis, mathematical modelling, human spine, Antalgic-Trak technology

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Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

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Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.

Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mostafa Sefidgar, Sohrab Zendehboudi, Hossein Bazmara, Madjid Soltani

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Based on findings from clinical applications, most drug treatments fail to eliminate malignant tumors completely even though drug delivery through systemic administration may inhibit their growth. Therefore, better understanding of tumor formation is crucial in developing more effective therapeutics. For this purpose, nowadays, solid tumor modeling and simulation results are used to predict how therapeutic drugs are transported to tumor cells by blood flow through capillaries and tissues. A solid tumor is investigated as a porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multi scale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. In this work, the mathematical model in our previous studies is developed by considering two model of momentum equation for porous media: Darcy and Brinkman. The mathematical method involves processes such as fluid flow through solid tumor as porous media, extravasation of blood flow from vessels, blood flow through vessels and solute diffusion, convective transport in extracellular matrix. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model does.

Keywords: solid tumor, porous media, Darcy model, Brinkman model, drug delivery

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Authors: Endrik Mifta Shaiful, Firman Riyudha

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Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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Authors: Benaliouche Hana, Abdessemed Djamal, Meniai Abdessalem, Lesage Geoffroy, Heran Marc

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This paper presents a dynamic mathematical model of activated sludge which is able to predict the formation and degradation kinetics of SMP (Soluble microbial products) in membrane bioreactor systems. The model is based on a calibrated version of ASM1 with the theory of production and degradation of SMP. The model was calibrated on the experimental data from MBR (Mathematical modeling Membrane bioreactor) pilot plant. Analytical expressions have been developed, describing the concentrations of the main state variables present in the sludge matrix, with the inclusion of only six additional linear differential equations. The objective is to present a new dynamic mathematical model of activated sludge capable of predicting the formation and degradation kinetics of SMP (UAP and BAP) from the submerged membrane bioreactor (BRMI), operating at low organic load (C / N = 3.5), for two sludge retention times (SRT) fixed at 40 days and 60 days, to study their impact on membrane fouling, The modeling study was carried out under the steady-state condition. Analytical expressions were then validated by comparing their results with those obtained by simulations using GPS-X-Hydromantis software. These equations made it possible, by means of modeling approaches (ASM1), to identify the operating and kinetic parameters and help to predict membrane fouling.

Keywords: Activated Sludge Model No. 1 (ASM1), mathematical modeling membrane bioreactor, soluble microbial products, UAP, BAP, Modeling SMP, MBR, heterotrophic biomass

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Authors: Zahid Ullah, Atlas Khan

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This abstract focuses on the advancements in mathematical modeling and optimization techniques that play a crucial role in enhancing the efficiency, reliability, and performance of these systems. In this era of rapidly evolving technology, mathematical modeling and optimization offer powerful tools to tackle the complex challenges faced by control, signal processing, and energy systems. This abstract presents the latest research and developments in mathematical methodologies, encompassing areas such as control theory, system identification, signal processing algorithms, and energy optimization. The abstract highlights the interdisciplinary nature of mathematical modeling and optimization, showcasing their applications in a wide range of domains, including power systems, communication networks, industrial automation, and renewable energy. It explores key mathematical techniques, such as linear and nonlinear programming, convex optimization, stochastic modeling, and numerical algorithms, that enable the design, analysis, and optimization of complex control and signal processing systems. Furthermore, the abstract emphasizes the importance of addressing real-world challenges in control, signal processing, and energy systems through innovative mathematical approaches. It discusses the integration of mathematical models with data-driven approaches, machine learning, and artificial intelligence to enhance system performance, adaptability, and decision-making capabilities. The abstract also underscores the significance of bridging the gap between theoretical advancements and practical applications. It recognizes the need for practical implementation of mathematical models and optimization algorithms in real-world systems, considering factors such as scalability, computational efficiency, and robustness. In summary, this abstract showcases the advancements in mathematical modeling and optimization techniques for control, signal processing, and energy systems. It highlights the interdisciplinary nature of these techniques, their applications across various domains, and their potential to address real-world challenges. The abstract emphasizes the importance of practical implementation and integration with emerging technologies to drive innovation and improve the performance of control, signal processing, and energy.

Keywords: mathematical modeling, optimization, control systems, signal processing, energy systems, interdisciplinary applications, system identification, numerical algorithms

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Authors: Wajahat Ali, Shakeel Javaid

Abstract:

In this study, we have developed a mathematical programming model for a solid transportation problem with three objective functions arranged in hierarchical order. The mathematical programming models with more than one objective function to be solved in hierarchical order is termed as a multi-level programming model. Our study explores a Multi-Level Solid Transportation Problem with Uncertain Parameters (MLSTPWU). The proposed MLSTPWU model consists of three objective functions, viz. minimization of transportation cost, minimization of total transportation time, and minimization of deterioration during transportation. These three objective functions are supposed to be solved by decision-makers at three consecutive levels. Three constraint functions are added to the model, restricting the total availability, total demand, and capacity of modes of transportation. All the parameters involved in the model are assumed to be uncertain in nature. A solution method based on fuzzy logic is also discussed to obtain the compromise solution for the proposed model. Further, a simulated numerical example is discussed to establish the efficiency and applicability of the proposed model.

Keywords: solid transportation problem, multi-level programming, uncertain variable, uncertain environment

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Authors: Yunusa Aliyu Hadejia

Abstract:

Cholera is a gastrointestinal disease caused by a bacterium called Vibrio Cholerae which spread as a result of eating food or drinking water contaminated with feaces from an infected person. In this work we proposed and analyzed the impact of isolating infected people and give them therapeutic treatment, the specific objectives of the research was to formulate a mathematical model of cholera transmission incorporating treatment class, to make analysis on stability of equilibrium points of the model, positivity and boundedness was shown to ensure that the model has a biological meaning, the basic reproduction number was derived by next generation matrix approach. The result of stability analysis show that the Disease free equilibrium was both locally and globally asymptotically stable when R_0< 1 while endemic equilibrium has locally asymptotically stable when R_0> 1. Sensitivity analysis was perform to determine the contribution of each parameter to the basic reproduction number. Numerical simulation was carried out to show the impact of the model parameters using MAT Lab Software.

Keywords: mathematical model, treatment, stability, sensitivity

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Authors: Anna Avramenko, Heikki Haario

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This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

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Authors: Alina Fedossova, Jose Jorge Sierra Molina

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SIP problems are part of non-classical optimization. There are problems in which the number of variables is finite, and the number of constraints is infinite. These are semi-infinite programming problems. Most algorithms for semi-infinite programming problems reduce the semi-infinite problem to a finite one and solve it by classical methods of linear or nonlinear programming. Typically, any of the constraints or the objective function is nonlinear, so the problem often involves nonlinear programming. An investment portfolio is a set of instruments used to reach the specific purposes of investors. The risk of the entire portfolio may be less than the risks of individual investment of portfolio. For example, we could make an investment of M euros in N shares for a specified period. Let yi> 0, the return on money invested in stock i for each dollar since the end of the period (i = 1, ..., N). The logical goal here is to determine the amount xi to be invested in stock i, i = 1, ..., N, such that we maximize the period at the end of ytx value, where x = (x1, ..., xn) and y = (y1, ..., yn). For us the optimal portfolio means the best portfolio in the ratio "risk-return" to the investor portfolio that meets your goals and risk ways. Therefore, investment goals and risk appetite are the factors that influence the choice of appropriate portfolio of assets. The investment returns are uncertain. Thus we have a semi-infinite programming problem. We solve a semi-infinite optimization problem of portfolio selection using the outer approximations methods. This approach can be considered as a developed Eaves-Zangwill method applying the multi-start technique in all of the iterations for the search of relevant constraints' parameters. The stochastic outer approximations method, successfully applied previously for robotics problems, Chebyshev approximation problems, air pollution and others, is based on the optimal criteria of quasi-optimal functions. As a result we obtain mathematical model and the optimal investment portfolio when yields are not clear from the beginning. Finally, we apply this algorithm to a specific case of a Colombian bank.

Keywords: outer approximation methods, portfolio problem, semi-infinite programming, numerial solution

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Authors: Gareth Baxter

Abstract:

We use a mathematical model of language change to examine two recently observed patterns of language change: one in which most speakers change gradually, following the mean of the community change, and one in which most individuals use predominantly one variant or another, and change rapidly if they change at all. The model is based on Croft’s Utterance Selection account of language change, which views language change as an evolutionary process, in which different variants (different ‘ways of saying the same thing’) compete for usage in a population of speakers. Language change occurs when a new variant replaces an older one as the convention within a given population. The present model extends a previous simpler model to include effects related to speaker aging and interspeaker variation in behaviour. The two patterns of individual change (one more centralized and the other more polarized) were recently observed in historical language changes, and it was further observed that slower changes were more associated with the centralized pattern, while quicker changes were more polarized. Our model suggests that the two patterns of change can be explained by different balances between the preference of speakers to use one variant over another and the degree of accommodation to (propensity to adapt towards) other speakers. The correlation with the rate of change appears naturally in our model, and results from the fact that both differential weighting of variants and the degree of accommodation affect the time for change to occur, while also determining the patterns of change. This work represents part of an ongoing effort to examine phenomena in language change through the use of mathematical models. This offers another way to evaluate qualitative explanations that cannot be practically tested (or cannot be tested at all) in a real-world, large-scale speech community.

Keywords: agent based modeling, cultural evolution, language change, social behavior modeling, social influence

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Authors: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

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In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller.

Keywords: the Bouc-Wen hysteresis model, particle swarm optimization, Prandtl-Ishlinskii model, automation engineering

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Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Haowen Xi

Abstract:

We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Naila Nasreen, Dianchen Lu

Abstract:

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: A. A. Okafor, C. H. Achebe, J. L. Chukwuneke, C. G. Ozoegwu

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The performance of an engine whose basic design parameters are known can be predicted with the assistance of simulation programs into the less time, cost and near value of actual. This paper presents a comprehensive mathematical model of the performance parameters of four stroke spark ignition engine. The essence of this research work is to develop a mathematical model for the analysis of engine performance parameters of four stroke spark ignition engine before embarking on full scale construction, this will ensure that only optimal parameters are in the design and development of an engine and also allow to check and develop the design of the engine and it’s operation alternatives in an inexpensive way and less time, instead of using experimental method which requires costly research test beds. To achieve this, equations were derived which describe the performance parameters (sfc, thermal efficiency, mep and A/F). The equations were used to simulate and optimize the engine performance of the model for various engine speeds. The optimal values obtained for the developed bivariate mathematical models are: sfc is 0.2833kg/kwh, efficiency is 28.77% and a/f is 20.75.

Keywords: bivariate models, engine performance, injector engine, optimization, performance parameters, simulation, spark ignition

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Authors: Jun Tian, Yu Yang, Liping Zhang, Qianhua Kan

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Experimental results show that SA 508-3 steel exhibits temperature dependent cyclic softening characteristic and obvious ratcheting behaviors, and dynamic strain age was observed at temperature range of 200 ºC to 350 ºC. Based on these observations, a temperature dependent cyclic plastic constitutive model was proposed by introducing the nonlinear cyclic softening and kinematic hardening rules, and the dynamic strain age was also considered into the constitutive model. Comparisons between experiments and simulations were carried out to validate the proposed model at elevated temperature.

Keywords: constitutive model, elevated temperature, ratcheting, SA 508-3

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Authors: Alireza Toloei, Ahmad R. Saffary, Reza Ghasemi

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Due to the growing need for energy and limited fossil resources, the use of renewable energy, particularly wind is strongly favored. We all wind energy can’t be saved. Betz law, 59% of the total kinetic energy of the wind turbine is extracting. Therefore turbine control to achieve maximum performance and maintain stable conditions seem necessary. In this article, we plan for a horizontal axis wind turbine variable-speed variable-pitch nonlinear controller to obtain maximum output power. The model presented in this article, including a wide range of wind turbines are horizontal axis. However, the parameters used in this model is from Vestas V29 225 kW wind turbine. We designed second order sliding mode controller, which was robust in the face of changes in wind speed and it eliminated chattering by using of super twisting algorithm. Finally, using MATLAB software to simulate the results we considered the accuracy of the simulation results.

Keywords: non linear controller, robust, sliding mode, kinetic energy

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Morteza Shayan Arani, Mohammadamin Esmailzadehazimi, Mohammadreza Moeini, Mohammad Toorani, Aouni A. Lakis

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This paper investigates the nonlinear response of thin, incompressible, hyperelastic cylindrical shells in the presence of a time-varying temperature field while considering initial geometric imperfections. The governing equations of motion are derived using an improved Donnell's shallow shell theory. The hyperelastic material is modeled using the Mooney-Rivlin model with two parameters, incorporating temperature-dependent terms. The Lagrangian method is applied to obtain the equation of motion. The resulting governing equation is addressed through the Lindstedt-Poincaré and Multiple Scale methods. The linear and nonlinear models presented in this study are verified against existing open literature, demonstrating the accuracy and reliability of the presented model. The study focuses on understanding the influence of temperature variations and geometrical imperfections on the natural frequency and amplitude-frequency response of the systems. Notably, the investigation reveals the coexistence of hardening and softening peaks in the amplitude-frequency response, which vary in magnitude depending on these parameters. Additionally, resonance peaks exhibit changes as a result of temperature and geometric imperfections.

Keywords: hyperelastic material, cylindrical shell, geometrical nonlinearity, material naolinearity, initial geometric imperfection, temperature gradient, hardening and softening

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Authors: Hau-Wei Lee, Yu-Chi Liu, Chien-Hung Liu

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A mathematical model is presented for a system that measures rotational errors in a shaft using a ball lens. The geometric optical characteristics of the ball lens mounted on the shaft allows the measurement of rotation axis errors in both the radial and axial directions. The equipment used includes two quadrant detectors (QD), two laser diodes and a ball lens that is mounted on the rotating shaft to be evaluated. Rotational errors in the shaft cause changes in the optical geometry of the ball lens. The resulting deflection of the laser beams is detected by the QDs and their output signals are used to determine rotational errors. The radial and the axial rotational errors can be calculated as explained by the mathematical model. Results from system calibration show that the measurement error is within ±1 m and resolution is about 20 nm. Using a direct drive motor (DD motor) as an example, experimental results show a rotational error of less than 20 m. The most important features of this system are that it does not require the use of expensive optical components, it is small, very easy to set up, and measurements are highly accurate.

Keywords: ball lens, quadrant detector, axial error, radial error

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Authors: Bencheikh Abdellah

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In this paper, we present a mathematical model dedicated to the simulation breaks bars in a three-phase cage induction motor. This model is based on a mesh circuit representing the rotor cage. The tested simulation allowed us to demonstrate the effectiveness of this model to describe the behavior of the machine in a healthy state, failure.

Keywords: AC motors, squirrel cage, diagnostics, MATLAB, SIMULINK

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