Search results for: nonlinear exponential model
7829 Prediction of Nonlinear Torsional Behavior of High Strength RC Beams
Authors: Woo-Young Jung, Minho Kwon
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Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both the strength and ductility is needed to analyze reinforced concrete (RC) structures under such event. A three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC members. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC members are performed to validate the proposed model. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results.
Keywords: Torsion, non-linear analysis, three-dimensional lattice, high-strength concrete.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22677828 Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design
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In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17857827 A First Course in Numerical Methods with “Mathematica“
Authors: Andrei A. Kolyshkin
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In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.Keywords: Numerical methods, "Mathematica", e-learning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36527826 An Optimized Method for Calculating the Linear and Nonlinear Response of SDOF System Subjected to an Arbitrary Base Excitation
Authors: Hossein Kabir, Mojtaba Sadeghi
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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.
Keywords: Single-degree-of-freedom system, linear acceleration method, nonlinear excited system, equivalent displacement method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10947825 Design of a Non-linear Observer for VSI Fed Synchronous Motor
Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar
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This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18527824 Strengthening of RC Beams with Large Openings in Shear by CFRP Laminates: 2D Nonlinear FE Analysis
Authors: S.C. Chin, N. Shafiq, M.F. Nuruddin
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To date, theoretical studies concerning the Carbon Fiber Reinforced Polymer (CFRP) strengthening of RC beams with openings have been rather limited. In addition, various numerical analyses presented so far have effectively simulated the behaviour of solid beam strengthened by FRP material. In this paper, a two dimensional nonlinear finite element analysis is presented to validate against the laboratory test results of six RC beams. All beams had the same rectangular cross-section geometry and were loaded under four point bending. The crack pattern results of the finite element model show good agreement with the crack pattern of the experimental beams. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption used between the concrete and steel reinforcement.Keywords: CFRP, large opening, RC beam, strengthening
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17957823 Time Series Forecasting Using a Hybrid RBF Neural Network and AR Model Based On Binomial Smoothing
Authors: Fengxia Zheng, Shouming Zhong
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ANNARIMA that combines both autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models. This paper provides a hybrid methodology that combines both radial basis function (RBF) neural network and auto regression (AR) model based on binomial smoothing (BS) technique which is efficient in data processing, which is called BSRBFAR. This method is examined by using the data of Canadian Lynx data. Empirical results indicate that the over-fitting problem can be eased using RBF neural network based on binomial smoothing which is called BS-RBF, and the hybrid model–BS-RBFAR can be an effective way to improve forecasting accuracy achieved by BSRBF used separately.
Keywords: Binomial smoothing (BS), hybrid, Canadian Lynx data, forecasting accuracy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36707822 Basic Tendency Model in Complete Factor Synergetics of Complex Systems
Authors: Li Zong-Cheng
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The deviation between the target state variable and the practical state variable should be used to form the state tending factor of complex systems, which can reflect the process for the complex system to tend rationalization. Relating to the system of basic equations of complete factor synergetics consisting of twenty nonlinear stochastic differential equations, the two new models are considered to set, which should be called respectively the rationalizing tendency model and the non- rationalizing tendency model. Therefore we can extend the theory of programming with the objective function & constraint condition suitable only for the realm of man-s activities into the new analysis with the tendency function & constraint condition suitable for all the field of complex system.Keywords: complex system, complete factor synergetics, basicequation, rationalizing tendency model, non-rationalizing tendencymodel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13277821 Performance Comparison between Sliding Mode Control (SMC) and PD-PID Controllers for a Nonlinear Inverted Pendulum System
Authors: A. N. K. Nasir, R. M. T. Raja Ismail, M. A. Ahmad
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The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.Keywords: SMC, PID, Inverted Pendulum System.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 47817820 Analysis of Nonlinear Pulse Propagation Characteristics in Semiconductor Optical Amplifier for Different Input Pulse Shapes
Authors: Suchi Barua, Narottam Das, Sven Nordholm, Mohammad Razaghi
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23627819 Numerical Model of Low Cost Rubber Isolators for Masonry Housing in High Seismic Regions
Authors: Ahmad B. Habieb, Gabriele Milani, Tavio Tavio, Federico Milani
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Housings in developing countries have often inadequate seismic protection, particularly for masonry. People choose this type of structure since the cost and application are relatively cheap. Seismic protection of masonry remains an interesting issue among researchers. In this study, we develop a low-cost seismic isolation system for masonry using fiber reinforced elastomeric isolators. The elastomer proposed consists of few layers of rubber pads and fiber lamina, making it lower in cost comparing to the conventional isolators. We present a finite element (FE) analysis to predict the behavior of the low cost rubber isolators undergoing moderate deformations. The FE model of the elastomer involves a hyperelastic material property for the rubber pad. We adopt a Yeoh hyperelasticity model and estimate its coefficients through the available experimental data. Having the shear behavior of the elastomers, we apply that isolation system onto small masonry housing. To attach the isolators on the building, we model the shear behavior of the isolation system by means of a damped nonlinear spring model. By this attempt, the FE analysis becomes computationally inexpensive. Several ground motion data are applied to observe its sensitivity. Roof acceleration and tensile damage of walls become the parameters to evaluate the performance of the isolators. In this study, a concrete damage plasticity model is used to model masonry in the nonlinear range. This tool is available in the standard package of Abaqus FE software. Finally, the results show that the low-cost isolators proposed are capable of reducing roof acceleration and damage level of masonry housing. Through this study, we are also capable of monitoring the shear deformation of isolators during seismic motion. It is useful to determine whether the isolator is applicable. According to the results, the deformations of isolators on the benchmark one story building are relatively small.Keywords: Masonry, low cost elastomeric isolator, finite element analysis, hyperelasticity, damped non-linear spring, concrete damage plasticity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11707818 New Moment Rotation Model of Single Web Angle Connections
Authors: Zhengyi Kong, Seung-Eock Kim
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Single angle connections, which are bolted to the beam web and the column flange, are studied to investigate their moment-rotation behavior. Elastic–perfectly plastic material behavior is assumed. ABAQUS software is used to analyze the nonlinear behavior of a single angle connection. The identical geometric and material conditions with Lipson’s test are used for verifying finite element models. Since Kishi and Chen’s Power model and Lee and Moon’s Log model are accurate only for a limited range of mechanism, simpler and more accurate hyperbolic function models are proposed.Keywords: Single-web angle connections, finite element method, moment and rotation, hyperbolic function models.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22827817 Empirical Statistical Modeling of Rainfall Prediction over Myanmar
Authors: Wint Thida Zaw, Thinn Thu Naing
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One of the essential sectors of Myanmar economy is agriculture which is sensitive to climate variation. The most important climatic element which impacts on agriculture sector is rainfall. Thus rainfall prediction becomes an important issue in agriculture country. Multi variables polynomial regression (MPR) provides an effective way to describe complex nonlinear input output relationships so that an outcome variable can be predicted from the other or others. In this paper, the modeling of monthly rainfall prediction over Myanmar is described in detail by applying the polynomial regression equation. The proposed model results are compared to the results produced by multiple linear regression model (MLR). Experiments indicate that the prediction model based on MPR has higher accuracy than using MLR.Keywords: Polynomial Regression, Rainfall Forecasting, Statistical forecasting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26197816 Speed Control of a Permanent Magnet Synchronous Machine (PMSM) Fed by an Inverter Voltage Fuzzy Control Approach
Authors: Jamel Khedri, Mohamed Chaabane, Mansour Souissi, Driss Mehdi
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This paper deals with the synthesis of fuzzy controller applied to a permanent magnet synchronous machine (PMSM) with a guaranteed H∞ performance. To design this fuzzy controller, nonlinear model of the PMSM is approximated by Takagi-Sugeno fuzzy model (T-S fuzzy model), then the so-called parallel distributed compensation (PDC) is employed. Next, we derive the property of the H∞ norm. The latter is cast in terms of linear matrix inequalities (LMI-s) while minimizing the H∞ norm of the transfer function between the disturbance and the error ( ) ev T . The experimental and simulations results were conducted on a permanent magnet synchronous machine to illustrate the effects of the fuzzy modelling and the controller design via the PDC.Keywords: Feedback controller, Takagi-Sugeno fuzzy model, Linear Matrix Inequality (LMI), PMSM, H∞ performance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23197815 Comparison of Prognostic Models in Different Scenarios of Shoreline Position on Ponta Negra Beach in Northeastern Brazil
Authors: Débora V. Busman, Venerando E. Amaro, Mattheus da C. Prudêncio
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Prognostic studies of the shoreline are of utmost importance for Ponta Negra Beach, located in Natal, Northeastern Brazil, where the infrastructure recently built along the shoreline is severely affected by flooding and erosion. This study compares shoreline predictions using three linear regression methods (LMS, LRR and WLR) and tries to discern the best method for different shoreline position scenarios. The methods have shown erosion on the beach in each of the scenarios tested, even in less intense dynamic conditions. The WLA_A with confidence interval of 95% was the well-adjusted model and calculated a retreat of -1.25 m/yr to -2.0 m/yr in hot spot areas. The change of the shoreline on Ponta Negra Beach can be measured as a negative exponential curve. Analysis of these methods has shown a correlation with the morphodynamic stage of the beach.
Keywords: Coastal Erosion, Prognostic Model, DSAS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25697814 Radiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction
Authors: Motahar Reza, Rajni Chahal, Neha Sharma
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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.
Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17717813 Nonlinear Equations with N-dimensional Telegraph Operator Iterated K-times
Authors: Jessada Tariboon
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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.
Keywords: Telegraph operator, Elementary solution, Distribution kernel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11867812 Numerical Analysis of Cold-Formed Steel Shear Wall Panels Subjected to Cyclic Loading
Authors: H. Meddah, M. Berediaf-Bourahla, B. El-Djouzi, N. Bourahla
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Shear walls made of cold formed steel are used as lateral force resisting components in residential and low-rise commercial and industrial constructions. The seismic design analysis of such structures is often complex due to the slenderness of members and their instability prevalence. In this context, a simplified modeling technique across the panel is proposed by using the finite element method. The approach is based on idealizing the whole panel by a nonlinear shear link element which reflects its shear behavior connected to rigid body elements which transmit the forces to the end elements (studs) that resist the tension and the compression. The numerical model of the shear wall panel was subjected to cyclic loads in order to evaluate the seismic performance of the structure in terms of lateral displacement and energy dissipation capacity. In order to validate this model, the numerical results were compared with those from literature tests. This modeling technique is particularly useful for the design of cold formed steel structures where the shear forces in each panel and the axial forces in the studs can be obtained using spectrum analysis.
Keywords: Cold-formed steel, cyclic loading, modeling technique, nonlinear analysis, shear wall panel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12517811 Evaluation of Linear and Geometrically Nonlinear Static and Dynamic Analysis of Thin Shells by Flat Shell Finite Elements
Authors: Djamel Boutagouga, Kamel Djeghaba
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The choice of finite element to use in order to predict nonlinear static or dynamic response of complex structures becomes an important factor. Then, the main goal of this research work is to focus a study on the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements. In this purpose: First, simple triangular and quadrilateral flat shell finite elements are implemented in an incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear analysis. The triangular element is a combination of DKT and CST elements, while the quadrilateral is a combination of DKQ and the bilinear quadrilateral membrane element. In both elements, the sixth degree of freedom is handled via introducing fictitious stiffness. Secondly, in the same code, the sixth degrees of freedom in these elements is handled differently where the in-plane rotational d.o.f is considered as an effective d.o.f in the in-plane filed interpolation. Our goal is to compare resulting shell elements. Third, the analysis is enlarged to dynamic linear analysis by direct integration using Newmark-s implicit method. Finally, the linear dynamic analysis is extended to geometrically nonlinear dynamic analysis where Newmark-s method is used to integrate equations of motion and the Newton-Raphson method is employed for iterating within each time step increment until equilibrium is achieved. The obtained results demonstrate the effectiveness and robustness of the interpolation of the in-plane rotational d.o.f. and present deficiencies of using fictitious stiffness in dynamic linear and nonlinear analysis.Keywords: Flat shell, dynamic analysis, nonlinear, Newmark, drilling rotation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29067810 Power Series Solution to Sliding Velocity in Three-Dimensional Multibody Systems with Impact and Friction
Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat
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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19007809 Ion- Acoustic Solitary Waves in a Self- Gravitating Dusty Plasma Having Two-Temperature Electrons
Authors: S.N.Paul, G.Pakira, B.Paul, B.Ghosh
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Nonlinear propagation of ion-acoustic waves in a selfgravitating dusty plasma consisting of warm positive ions, isothermal two-temperature electrons and negatively charged dust particles having charge fluctuations is studied using the reductive perturbation method. It is shown that the nonlinear propagation of ion-acoustic waves in such plasma can be described by an uncoupled third order partial differential equation which is a modified form of the usual Korteweg-deVries (KdV) equation. From this nonlinear equation, a new type of solution for the ion-acoustic wave is obtained. The effects of two-temperature electrons, gravity and dust charge fluctuations on the ion-acoustic solitary waves are discussed with possible applications.Keywords: Charge fluctuations, gravitating dusty plasma, Ionacoustic solitary wave, Two-temperature electrons
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20357808 'Performance-Based' Seismic Methodology and Its Application in Seismic Design of Reinforced Concrete Structures
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14847807 The Role of the Studs Configuration in the Structural Response of Composite Bridges
Authors: M. M. Mohammadi Dehnavi, A. De Angelis, M. R. Pecce
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This paper deals with the role of studs in structural response for steel-concrete composite beams. A tri-linear slip-shear strength law is assumed according to literature and codes provisions for developing a finite element (FE) model of a case study of a composite deck. The variation of the strength and ductility of the connection is implemented in the numerical model carrying out nonlinear analyses. The results confirm the utility of the model to evaluate the importance of the studs capacity, ductility and strength, on the global response (ductility and strength) of the structures but also to analyse the trend of slip and shear at interface along the beams.
Keywords: Shear Load, slip, steel-concrete composite bridge, stud connectors.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3637806 Digital Image Encryption Scheme using Chaotic Sequences with a Nonlinear Function
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In this study, a system of encryption based on chaotic sequences is described. The system is used for encrypting digital image data for the purpose of secure image transmission. An image secure communication scheme based on Logistic map chaotic sequences with a nonlinear function is proposed in this paper. Encryption and decryption keys are obtained by one-dimensional Logistic map that generates secret key for the input of the nonlinear function. Receiver can recover the information using the received signal and identical key sequences through the inverse system technique. The results of computer simulations indicate that the transmitted source image can be correctly and reliably recovered by using proposed scheme even under the noisy channel. The performance of the system will be discussed through evaluating the quality of recovered image with and without channel noise.Keywords: Digital image, Image encryption, Secure communication
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22257805 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm
Authors: U. C. Amadi, N. A. Udoh
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One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.
Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4337804 Effect of Concrete Nonlinear Parameters on the Seismic Response of Concrete Gravity Dams
Authors: Z. Heirany, M. Ghaemian
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Behavior of dams against the seismic loads has been studied by many researchers. Most of them proposed new numerical methods to investigate the dam safety. In this paper, to study the effect of nonlinear parameters of concrete in gravity dams, a twodimensional approach was used including the finite element method, staggered method and smeared crack approach. Effective parameters in the models are physical properties of concrete such as modulus of elasticity, tensile strength and specific fracture energy. Two different models were used in foundation (mass-less and massed) in order to determine the seismic response of concrete gravity dams. Results show that when the nonlinear analysis includes the dam- foundation interaction, the foundation-s mass, flexibility and radiation damping are important in gravity dam-s response.Keywords: Numerical methods; concrete gravity dams; finiteelement method; boundary condition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23237803 Stability Analysis of Impulsive BAM Fuzzy Cellular Neural Networks with Distributed Delays and Reaction-diffusion Terms
Authors: Xinhua Zhang, Kelin Li
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In this paper, a class of impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms is formulated and investigated. By employing the delay differential inequality and inequality technique developed by Xu et al., some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.
Keywords: Bi-directional associative memory, fuzzy cellular neuralnetworks, reaction-diffusion, delays, impulses, global exponentialstability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15277802 Analysis of EEG Signals Using Wavelet Entropy and Approximate Entropy: A Case Study on Depression Patients
Authors: Subha D. Puthankattil, Paul K. Joseph
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Analyzing brain signals of the patients suffering from the state of depression may lead to interesting observations in the signal parameters that is quite different from a normal control. The present study adopts two different methods: Time frequency domain and nonlinear method for the analysis of EEG signals acquired from depression patients and age and sex matched normal controls. The time frequency domain analysis is realized using wavelet entropy and approximate entropy is employed for the nonlinear method of analysis. The ability of the signal processing technique and the nonlinear method in differentiating the physiological aspects of the brain state are revealed using Wavelet entropy and Approximate entropy.
Keywords: EEG, Depression, Wavelet entropy, Approximate entropy, Relative Wavelet energy, Multiresolution decomposition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36257801 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.Keywords: p-Laplacian, cone, fixed point theorem, positive solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5827800 Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales
Authors: Xinli Zhang
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In this paper, we consider the nonlinear delay dynamic system xΔ(t) = p(t)f1(y(t)), yΔ(t) = −q(t)f2(x(t − τ )). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.
Keywords: Dynamic system, oscillation, time scales, two-dimensional.
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