Search results for: Nonlinear vibrations

Authors: T.C. Manjunath, Student Member, B. Bandyopadhyay

Abstract:

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

Keywords: Smart structure, Timoshenko beam theory, Discretesliding mode control, Bartoszewicz law, Finite Element Method, State space model, Vibration control, Mathematical model, SISO.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Mihai Caramihai, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control

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Authors: R. Oonsivilai, M. Oonsivilai, J. Sanguemrum, N. Thumsirirat, A. Oonsivilai

Abstract:

Chaiyaphum Starch Co. Ltd. is one of many starch manufacturers that has introduced machinery to aid in manufacturing. Even though machinery has replaced many elements and is now a significant part in manufacturing processes, problems that must be solved with respect to current process flow to increase efficiency still exist. The paper-s aim is to increase productivity while maintaining desired quality of starch, by redesigning the flipping machine-s mechanical control system which has grossly low functional lifetime. Such problems stem from the mechanical control system-s bearings, as fluids and humidity can access into said bearing directly, in tandem with vibrations from the machine-s function itself. The wheel which is used to sense starch thickness occasionally falls from its shaft, due to high speed rotation during operation, while the shaft may bend from impact when processing dried bread. Redesigning its mechanical control system has increased its efficiency, allowing quality thickness measurement while increasing functional lifetime an additional 62 days.

Keywords: Control system, Machinery, Measurement, Potato starch

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Authors: Annamária Käferné Rácz, Bence Jáger, Balázs Kövesdi, László Dunai

Abstract:

Due to the numerous advantages of steel corrugated web girders, its application field is growing for bridges as well as for buildings. The global stability behavior of such girders is significantly larger than those of conventional I-girders with flat web, thus the application of the structural steel material can be significantly reduced. Design codes and specifications do not provide clear and complete rules or recommendations for the determination of the lateral torsional buckling (LTB) resistance of corrugated web girders. Therefore, the authors made a thorough investigation regarding the LTB resistance of the corrugated web girders. Finite element (FE) simulations have been performed to develop new design formulas for the determination of the LTB resistance of trapezoidally corrugated web girders. FE model is developed considering geometrical and material nonlinear analysis using equivalent geometric imperfections (GMNI analysis). The equivalent geometric imperfections involve the initial geometric imperfections and residual stresses coming from rolling, welding and flame cutting. Imperfection sensitivity analysis was performed to determine the necessary magnitudes regarding only the first eigenmodes shape imperfections. By the help of the validated FE model, an extended parametric study is carried out to investigate the LTB resistance for different trapezoidal corrugation profiles. First, the critical moment of a specific girder was calculated by FE model. The critical moments from the FE calculations are compared to the previous analytical calculation proposals. Then, nonlinear analysis was carried out to determine the ultimate resistance. Due to the numerical investigations, new proposals are developed for the determination of the LTB resistance of trapezoidally corrugated web girders through a modification factor on the design method related to the conventional flat web girders.

Keywords: Critical moment, FE modeling, lateral torsional buckling, trapezoidally corrugated web girders.

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Authors: Mihai Caramihai Ana A Chirvase, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control.

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Authors: Ibrahim Abdul Razak, Suhana Arshad, Nur Rafikah Razali, Azhar Abdul Rahman, Mohd Sukeri Mohd Yusof

Abstract:

Theoretical investigations are performed by DFT method of B3LYP/6-31G+(2d,p) and B3LYP/6-311G+(2d,p) basis sets for three carbonyl thiourea compounds, namely N-[(2,6-Diethylphenyl)carbamothioyl]-2,2-diphenylacetamide (Compound I), N-[(3-Ethylphenyl)carbamothioyl]-2,2-diphenylacetamide (Compound II) and 2,2-Diphenyl-N-{[2-(trifluoromethyl)phenyl]carbamothioyl}acetamide (Compound III). Theoretical calculations for bond parameters, harmonic vibration frequencies and isotropic chemical shifts are in good agreement with the experimental results. The calculated molecular vibrations show good correlation values, which are 0.998 and 0.999 with the experimental data. The energy gap for compounds I, II and III calculated at B3LYP/6-31G+(2d,p) basis set are 4.455866117, 4.297495791 and 4.313550514 eV respectively, while for B3LYP/6-311G+(2d,p) basis set the energy gap obtained are 4.453689205 (Compound I), 4.311373603 (Compound II) and 4.315727426 (Compound III) eV.

Keywords: Crystallization, DFT studies, Spectroscopic Analysis, Thiourea.

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Authors: S. Meziane, H. I. Faraoun, C. Esling

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Transition metal dichalcogenides have potential applications in power generation devices that convert waste heat into electric current by the so-called Seebeck and Hall effects thus providing an alternative energy technology to reduce the dependence on traditional fossil fuels. In this study, the thermoelectric properties of 1T and 2HTaX2 (X= S or Se) dichalcogenide superconductors have been computed using the semi-classical Boltzmann theory. Technologically, the task is to fabricate suitable materials with high efficiency. It is found that 2HTaS2 possesses the largest value of figure of merit ZT= 1.27 at 175 K. From a scientific point of view, we aim to model the underlying materials properties and in particular the transport phenomena as mediated by electrons and lattice vibrations responsible for superconductivity, Charge Density Waves (CDW) and metal/insulator transitions as function of temperature. The goal of the present work is to develop an understanding of the superconductivity of these selected materials using the transport properties at the fundamental level.

Keywords: Ab initio, high efficiency, power generation devices, transition metal dichalcogenides.

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Authors: S. Barabas, F. Sarbu, B. Barabas, A. Fota

Abstract:

Main objective of this paper is to establish a link between inertial forces of the bearings used in construction of wind power plant and its behavior. Using bearings with lower inertial forces has the immediate effect of decreasing inertia rotor system, with significant results in increased energy efficiency, due to decreased friction forces between rollers and raceways. The F.E.M. analysis shows the appearance of uniform contact stress at the ends of the rollers, demonstrated the necessity of production of low mass bearings. Favorable results are expected in the economic field, by reducing material consumption and by increasing the durability of bearings. Using low mass bearings with hollow rollers instead of solid rollers has an impact on working temperature, on vibrations and noise which decrease. Implementation of types of hollow rollers of cylindrical tubular type, instead of expensive rollers with logarithmic profile, will bring significant inertial forces decrease with large benefits in behavior of wind power plant.

Keywords: Inertial forces, Von Mises stress, hollow rollers.

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Authors: Nikhil Ramaswamy, S.N.Omkar, Kashyap.H.Nathwani, Anil.M.Vanjare

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In this present work, the development of an avionics system for flight data collection of a Raptor 30 V2 is carried out. For the data acquisition both onground and onboard avionics systems are developed for testing of a small-scale Unmanned Aerial Vehicle (UAV) helicopter. The onboard avionics record the helicopter state outputs namely accelerations, angular rates and Euler angles, in real time, and the on ground avionics system record the inputs given to the radio controlled helicopter through a transmitter, in real time. The avionic systems are designed and developed taking into consideration low weight, small size, anti-vibration, low power consumption, and easy interfacing. To mitigate the medium frequency vibrations embedded on the UAV helicopter during flight, a damper is designed and its performance is evaluated. A number of flight tests are carried out and the data obtained is then analyzed for accuracy and repeatability and conclusions are inferred.

Keywords: Data collection, Flight Testing, Onground and Onboard Avionics, UAV helicopter

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.

Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.

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Authors: A. Elakkary, A. Echchatbi, N. Elalami

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In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands.

The DTC of SRM is analyzed by two methods. In one method, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: Direct Toque Control, Simplified Torque Equation, Finite Element Analysis, Torque Ripple.

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Authors: Farshad Mehrabi, Ali kheirodin, Mohsen Gerami

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Ambiguities in effects of earthquake on various structures in all earthquake codes would necessitate more study and research concerning influential factors on dynamic behavior. Previous studies which were done on different features in different buildings play a major role in the type of response a structure makes to lateral vibrations. Diagnosing each of these irregularities can help structure designers in choosing appropriate setbacks for decreasing possible damages. Therefore vertical setback is one of the irregularity factors in the height of the building where can be seen in skyscrapers and hotels. Previous researches reveal notable changes in the place of these setbacks showing dynamic response of the structure. Consequently analyzing 48 models of concrete frames for 3, 6 and 9 stories heights with three different bays in general shape of a surface decline by height have been constructed in ETABS2000 software, and then the shape effect of each and every one of these frames in period scale has been discussed. The result of this study reveals that not only mass, stiffness and height but also shape of the frame is influential.

Keywords: period, concrete frame, irregularity in height, decrease in plan surface, dynamic behavior

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Authors: Devdutt, M. L. Aggarwal

Abstract:

The development of vehicles having best ride comfort and safety of travelling passengers is of great interest for automotive manufacturers. The effect of transmitted vibrations from car body to passenger seat is required to be controlled for achieving the same. The application of magneto-rheological (MR) shock absorber in suspension system has been considered to achieve significant benefits in this regard. This paper introduces a secondary suspension controlled semi-active quarter car system using MR shock absorber for effective vibration control. Fuzzy logic control system is used for design of controller for actual damping force generation by MR shock absorber. Performance evaluations are done related to passenger seat acceleration and displacement in time and frequency domains, in order to see the effectiveness of the proposed semi-active suspension system. Simulation results show that the semi-active suspension system provides better results compared to passive suspension system in terms of passenger ride comfort improvement.

Keywords: Fuzzy logic control, MR shock absorber, Quarter car model, Semi-active suspension system.

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Authors: Ren Jian-min, Wu Si-wei, Jin Wei

Abstract:

CTMA-bentonite and BTEA-Bentonite prepared by Na-bentonite cation exchanged with cetyltrimethylammonium(CTMA) and benzyltriethylammonium (BTEA). Products were characterized by XRD and IR techniques.The d001 spacing value of CTMA-bentonite and BTEA-bentonite are 7.54Å and 3.50Å larger than that of Na-bentonite at 100% cation exchange capacity, respectively. The IR spectrum showed that the intensities of OH stretching and bending vibrations of the two organoclays decreased greatly comparing to untreated Na-bentonite. Batch experiments were carried out at 303 K, 318 K and 333 K to obtain the sorption isotherms of Crystal violet onto the two organoclays. The results show that the sorption isothermal data could be well described by Freundlich model. The dynamical data for the two organoclays fit well with pseudo-second-order kinetic model. The adsorption capacity of CTMA-bentonite was found higher than that of BTEA-Bentonite. Thermodynamic parameters such as changes in the free energy (ΔG°), the enthalpy (ΔH°) and the entropy (ΔS°) were also evaluated. The overall adsorption process of Crystal violet onto the two organoclays were spontaneous, endothermic physisorption. The CTMA-bentonite and BTEA-Bentonite could be employed as low-cost alternatives to activated carbon in wastewater treatment for the removal of color which comes from textile dyes.

Keywords: Characterization, Adsorption, Crystal violet, Bentonite, BTEA, CTMA

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.

Keywords: Population model, Stability, Hopf bifurcation, Delay, Global Hopf bifurcation.

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Authors: Indah Kurniawaty, Yoki Yulizar, Haryo Satrya Oktaviano, Adam Kusuma Rianto

Abstract:

Magnesium oxide nanoparticles (MgO NP) were successfully synthesized in this study using a one-pot green synthesis mediated by Calliandra calothyrsus leaf extract (CLE). CLE was prepared by maceration of the leaf using methanol with a ratio of 1:5 for 7 days. Secondary metabolites in CLE, such as alkaloids and flavonoids, served as a weak base provider and capping agent in the formation of MgO NP. CLE Fourier Transform Infra-Red (FTIR) spectra peak at 3255 cm-1, 1600 cm-1, 1384 cm-1, 1205 cm-1, 1041 cm-1, and 667 cm-1 showing the presence of vibrations O-H stretching, N-H bending, C-C stretching, C-N stretching and N-H wagging. During the experiment, different CLE volumes and calcined temperatures were used, resulting in a variety of structures. Energy Dispersive X-ray Spectrometer (EDS) and FTIR were used to characterize metal oxide particles. MgO diffraction patterns at 2θ of 36.9°; 42.9°; 62.2°; 74.6°; and 78.5° can be assigned to crystal planes (111), (200), (220), (311), and (222), respectively. Scanning Electron Microscopy (SEM) was used to characterize the surface morphology. The morphology ranged from sphere to flower-like resulting in crystallite sizes of 28 nm, 23 nm, 12 nm, and 9 nm.

Keywords: Calliandra calothyrsus, green-synthesis, magnesium oxide, nanoparticle.

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Authors: Devdutt

Abstract:

An active quarter car model with three degrees of freedom is presented for vibration reduction of passenger seat. The designed Fuzzy Logic Controller (FLC) and Self-Tuning Fuzzy Logic Controller (STFLC) are applied in seat suspension. Vibration control performance of active and passive quarter car systems are determined using simulation work. Simulation results in terms of passenger seat acceleration and displacement responses are compared for controlled and uncontrolled cases. Simulation results showed the improved results of both FLC and STFLC controllers in improving passenger ride comfort compared to uncontrolled case. Furthermore, the best performance in simulation studies is achieved by STFLC controlled suspension system compared to FLC controlled and uncontrolled cases.

Keywords: Active suspension system, quarter car model, passenger ride comfort, self-tuning fuzzy logic controller.

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Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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Authors: Asmir Gogic, Aljo Mujcic, Sandra Ibric, Nermin Suljanovic

Abstract:

Ubiquity of natural disasters during last few decades have risen serious questions towards the prediction of such events and human safety. Every disaster regardless its proportion has a precursor which is manifested as a disruption of some environmental parameter such as temperature, humidity, pressure, vibrations and etc. In order to anticipate and monitor those changes, in this paper we propose an overall system for disaster prediction and monitoring, based on wireless sensor network (WSN). Furthermore, we introduce a modified and simplified WSN routing protocol built on the top of the trickle routing algorithm. Routing algorithm was deployed using the bluetooth low energy protocol in order to achieve low power consumption. Performance of the WSN network was analyzed using a real life system implementation. Estimates of the WSN parameters such as battery life time, network size and packet delay are determined. Based on the performance of the WSN network, proposed system can be utilized for disaster monitoring and prediction due to its low power profile and mesh routing feature.

Keywords: Bluetooth low energy, disaster prediction, mesh routing protocols, wireless sensor networks.

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Authors: S. Ghorbani, N. I. Polushin

Abstract:

Chatter vibrations, occurring during cutting process, cause vibration between the cutting tool and workpiece, which deteriorates surface roughness and reduces tool life. The purpose of this study is to investigate the influence of cutting parameters and tool construction on surface roughness and vibration in turning of aluminum alloy AA2024. A new design of cutting tool is proposed, which is filled up with epoxy granite in order to improve damping capacity of the tool. Experiments were performed at the lathe using carbide cutting insert coated with TiC and two different cutting tools made of AISI 5140 steel. Taguchi L9 orthogonal array was applied to design of experiment and to optimize cutting conditions. By the help of signal-to-noise ratio and analysis of variance the optimal cutting condition and the effect of the cutting parameters on surface roughness and vibration were determined. Effectiveness of Taguchi method was verified by confirmation test. It was revealed that new cutting tool with epoxy granite has reduced vibration and surface roughness due to high damping properties of epoxy granite in toolholder.

Keywords: ANOVA, damping capacity, surface roughness, Taguchi method, vibration.

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Authors: G. M. Ozkan, H. Akilli

Abstract:

The aim of present study is to control the unsteady flow structure downstream of a circular cylinder by use of attached permeable plates. Particle image velocimetry (PIV) technique and dye visualization experiments were performed in deep water and the flow characteristics were evaluated by means of time-averaged streamlines, Reynolds Shear Stress and Turbulent Kinetic Energy concentrations. The permeable plate was made of a chrome-nickel screen having a porosity value of β=0.6 and it was attached on the cylinder surface along its midspan. Five different angles were given to the plate (θ=0^o, 15^o, 30^o, 45^o, 60^o) with respect to the centerline of the cylinder in order to examine its effect on the flow control. It was shown that the permeable plate is effective on elongating the vortex formation length and reducing the fluctuations in the wake region. Compared to the plain cylinder, the reductions in the values of maximum Reynolds shear stress and Turbulent Kinetic Energy were evaluated as 72.5% and 66%, respectively for the plate angles of θ=45^oand 60^o which were also found to be suggested for applications concerning the vortex shedding and consequent Vortex-Induced Vibrations.

Keywords: Bluff body, flow control, permeable plate, PIV, VIV, vortex shedding.

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Authors: Helle Hein, Ülo Lepik

Abstract:

A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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Authors: K.L. Verma

Abstract:

Analysis for the generalized thermoelastic Lamb waves, which propagates in anisotropic thin plates in generalized thermoelasticity, is presented employing normal mode expansion method. The displacement and temperature fields are expressed by a summation of the symmetric and antisymmetric thermoelastic modes in the surface thermal stresses and thermal gradient free orthotropic plate, therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin anisotropic plates. The transient waveforms excited by the thermoelastic expansion are analyzed for an orthotropic thin plate. The obtained results show that the theory provides a quantitative analysis to characterize anisotropic thermoelastic stiffness properties of plates by wave detection. Finally numerical calculations have been presented for a NaF crystal, and the dispersion curves for the lowest modes of the symmetric and antisymmetric vibrations are represented graphically at different values of thermal relaxation time. However, the methods can be used for other materials as well

Keywords: Anisotropic, dispersion, frequency, normal, thermoelasticity, wave modes.

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.

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Authors: Mohammad Aminnia, Mahmood Hosseini

Abstract:

Environmental and functional conditions, sometimes, necessitate the architectural plan of the building to be asymmetric, and this result in an asymmetric structure. In such cases finding an optimal pattern for locating the components of lateral load bearing system, including shear walls, in the building’s plan is desired. In case of shear wall in addition to the location the shape of the wall cross-section is also an effective factor. Various types of shear walls and their proper layout might come effective in better stiffness distribution and more appropriate seismic response of the building. Several studies have been conducted in the context of analysis and design of shear walls; however, few studies have been performed on making decisions for the location and form of shear walls in multistory buildings, especially those with irregular plan. In this study, an attempt has been made to obtain the most reliable seismic behavior of multi-story reinforced concrete vertically chamfered buildings by using more appropriate shear walls form and arrangement in 7-, 10-, 12-, and 15-stoy buildings. The considered forms and arrangements include common rectangular walls and L-, T-, U- and Z-shaped plan, located as the core or in the outer frames of the building structure. Comparison of seismic behaviors of the buildings, including maximum roof displacement and particularly formation of plastic hinges and their distribution in the buildings’ structures, have been done based on the results of a series of nonlinear time history analyses, by using a set of selected earthquake records. Results show that shear walls with U-shaped cross-section, placed as the building central core, and also walls with Z-shaped cross-section, placed at the corners give the building more reliable seismic behavior.

Keywords: Vertically chamfered buildings, non-linear time history analyses, L-, T-, U- and Z-shaped plan walls.

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Authors: Ahmed M. Farag, Wael F. Mohamed, Atef A. Ata, Burhamy M. Burhamy

Abstract:

The main objective of the present paper is to derive an easy numerical technique for the analysis of the free vibration through the stepped regions of plates. Based on the utilities of the step by step integration initial values IV and Finite differences FD methods, the present improved Initial Value Finite Differences (IVFD) technique is achieved. The first initial conditions are formulated in convenient forms for the step by step integrations while the upper and lower edge conditions are expressed in finite difference modes. Also compatibility conditions are created due to the sudden variation of plate thickness. The present method (IVFD) is applied to solve the fourth order partial differential equation of motion for stepped plate across two different panels under the sudden step compatibility in addition to different types of end conditions. The obtained results are examined and the validity of the present method is proved showing excellent efficiency and rapid convergence.

Keywords: Vibrations, Step by Step Integration, Stepped plate, Boundary.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

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In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: Maharavo Randrianarivony

Abstract:

The length  of a given rational B'ezier curve is efficiently estimated. Since a rational B'ezier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation n is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis of the rate of convergence of n to  is given. The required number of subdivisions to attain a prescribed accuracy is also analyzed. An application to CAD parametrization is briefly described. Numerical results are reported to supplement the theory.

Keywords: Adaptivity, Length, Parametrization, Rational Bezier

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