Search results for: navier-stokes equations in a rotating frame of refence

Authors: Robert S. Giachetti, Emanuele Grossi

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Loosening of bolted joints in rotating machines can adversely affect their performance, cause mechanical damage, and lead to injuries. In this paper, two potential loosening phenomena in rotating applications are discussed. First, ‘precession,’ is governed by thread/nut contact forces, while the second is based on inertial effects of the fastened assembly. These mechanisms are reviewed within the context of historical usage of left-handed fasteners in rotating machines which appears absent in the literature and common machine design texts. Historically, to prevent loosening of wheel nuts, vehicle manufacturers have used right-handed and left-handed threads on different sides of the vehicle, but most modern vehicles have abandoned this custom and only use right-handed, tapered lug nuts on all sides of the vehicle. Other classical machines such as the bicycle continue to use different handed threads on each side while other machines such as, bench grinders, circular saws and brush cutters still use left-handed threads to fasten rotating components. Despite the continued use of left-handed fasteners, the rationale and analysis of left-handed threads to mitigate self-loosening of fasteners in rotating applications is not commonly, if at all, discussed in the literature or design textbooks. Without scientific literature to support these design selections, these implementations may be the result of experimental findings or aged institutional knowledge. Based on a review of rotating applications, historical documents and mechanical design references, a formal study of the paradoxical nature of left-handed threads in various applications is merited.

Keywords: rotating machinery, self-loosening fasteners, wheel fastening, vibration loosening

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Authors: S. Ben Brahim, T. H. Vuong, J. David, R. Bouallegue, M. Pietrzak-David

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Electrical machine monitoring is important to protect motor from unexpected problems. Today, using wireless communication for electrical machines is interesting for both real time monitoring and diagnostic purposes. In this paper, we propose a system based on wireless communication IEEE 802.11 to control electrical machine. IEEE 802.11 standard is recommended for this type of applications because it provides a faster connection, better range from the base station, and better security. Therefore, our contribution is to study a new technique to control and monitor the rotating electrical machines (motors, generators) using wireless communication. The reliability of radio channel inside rotating electrical machine is also discussed. Then, the communication protocol, software and hardware design used for the proposed system are presented in detail and the experimental results of our system are illustrated.

Keywords: control, DFIM machine, electromagnetic field, EMC, IEEE 802.11, monitoring, rotating electrical machines, wireless communication

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Authors: B. Mahfoud, A. Bendjagloli

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The effect of an axial magnetic field on the flow produced by co-rotation of the top and bottom disks in a vertical cylindrical heated from below is numerically analyzed. The governing Navier-Stokes, energy, and potential equations are solved by using the finite-volume method. It was observed that the Reynolds number is increased, the axisymmetric basic state loses stability to circular patterns of axisymmetric vortices and spiral waves. In mixed convection case the axisymmetric mode disappears giving an asymmetric mode m=1. It was also found that the primary thresholds Recr corresponding to the modes m=1and 2, increase with increasing of the Hartmann number (Ha). Finally, stability diagrams have been established according to the numerical results of this investigation. These diagrams giving the evolution of the primary thresholds as a function of the Hartmann number for various values of the Richardson number.

Keywords: bifurcation, co-rotating end disks, magnetic field, stability diagrams, vortices

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Authors: H. İmrek, O. Corumluoglu, B. Akdemir, I. Sanlioglu

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It is important to be able to determine the heading direction of a moving vehicle with respect to a distant location. Additionally, it is important to be able to direct a rotating platform on a moving vehicle towards a distant position or location on the earth surface, especially for applications such as determination of the Kaaba direction for daily Muslim prayers. GNNS offers some reasonable solutions. In this study, a functional model of such a directing system supported by GNNS is discussed, and an appropriate system is designed for these purposes. An application for directing system is done by using RTK and DGNSS. Accuracy estimations are given for this system.

Keywords: GNNS, orientation of rotating platform, vehicle orientation, prayer aid device

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Authors: Daniel Y. Abebe, Jaehyouk Choi

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The objective of this paper is to investigate, through an analytical study, the behavior of both stiffened and un-stiffened removable shear link with perforated web considering different number and size of web openings. Removable shear link with perforated web is a novel shear link beam proposed to be used in eccentrically braced frame (EBF). The proposed link overcomes the difficulties during construction slab due to less cross-sectional areas of the link to control the plastic deformation on the conventional EBF with removable shear link. Finite element analyses were conducted under both cyclic and monotonic loading and from the results obtained design equations are developed.

Keywords: eccentrically braced frame, removable shear link, perforated web, non-linear FE analysis

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Assma Azeroual, Karim Afdel, Mohamed El Hajji, Hassan Douzi

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Key frame extraction methods select the most representative frames of a video, which can be used in different areas of video processing such as video retrieval, video summary, and video indexing. In this paper we present a novel approach for extracting key frames from video sequences. The frame is characterized uniquely by his contours which are represented by the dominant blocks. These dominant blocks are located on the contours and its near textures. When the video frames have a noticeable changement, its dominant blocks changed, then we can extracte a key frame. The dominant blocks of every frame is computed, and then feature vectors are extracted from the dominant blocks image of each frame and arranged in a feature matrix. Singular Value Decomposition is used to calculate sliding windows ranks of those matrices. Finally the computed ranks are traced and then we are able to extract key frames of a video. Experimental results show that the proposed approach is robust against a large range of digital effects used during shot transition.

Keywords: FSDWT, key frame extraction, shot detection, singular value decomposition

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Authors: N. H. Hamid, M. S. Syaref, M. I. Adiyanto, M. Mohamed

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A one-half scale of single-bay two-storey RC frame together with foundation beam and mass concrete block is investigated. Moment resisting RC frame was designed using EC8 by including the provision for seismic loading and detailing of its connection. The objective of the experimental work is to determine seismic behaviour RC frame under in-plane lateral cyclic loading using displacement control method. A double actuator is placed at centre of the mass concrete block at top of frame to represent the seismic load. The percentage drifts are starting from ±0.01% until ±2.25% with increment of ±0.25% drift. The ultimate lateral load of 158.48 kN was recorded at +2.25% drift in pushing and -126.09 kN in pulling direction. From the experimental hysteresis loops, the parameters such as lateral strength capacity, stiffness, ductility and equivalent viscous damping can be obtained. RC frame behaves in the elastic manner followed by inelastic behaviour after reaches the yield limit. The ductility value for this type frame is 4 which lies between the limit 3 and 6. Therefore, it is recommended to build this RC frame for moderate seismic regions under Ductility Class Medium (DCM) such as in Sabah, East Malaysia.

Keywords: single bay, moment resisting RC frame, ductility class medium, inelastic behavior, seismic load

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Authors: Daniel Y. Abebe, Jaehyouk Choi

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From the past earthquake events, many people get hurt at the exit while they are trying to go out of the buildings because of the exit doors are unable to be opened. The door is not opened because it deviates from its the original position. The aim of this research is to develop and evaluate a new type safety door that keeps the door frame in its original position or keeps its edge angles perpendicular during and post-earthquake. The proposed door is composed of three components: outer frame joined to the wall, inner frame (door frame) and circular hollow section connected to the inner and outer frame which is used as seismic energy dissipating device.

Keywords: safety-door, earthquake disaster, low yield point steel, passive energy dissipating device, FE analysis

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Authors: Ayman Abd-Elhamed, Sayed Mahmoud

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The present research work investigates the seismic response of reinforced concrete (RC) frame building considering the effect of modeling masonry infill (MI) walls. The seismic behavior of a residential 6-storey RC frame building, considering and ignoring the effect of masonry, is numerically investigated using response spectrum (RS) analysis. The considered herein building is designed as a moment resisting frame (MRF) system following the Egyptian code (EC) requirements. Two developed models in terms of bare frame and infill walls frame are used in the study. Equivalent diagonal strut methodology is used to represent the behavior of infill walls, whilst the well-known software package ETABS is used for implementing all frame models and performing the analysis. The results of the numerical simulations such as base shear, displacements, and internal forces for the bare frame as well as the infill wall frame are presented in a comparative way. The results of the study indicate that the interaction between infill walls and frames significantly change the responses of buildings during earthquakes compared to the results of bare frame building model. Specifically, the seismic analysis of RC bare frame structure leads to underestimation of base shear and consequently damage or even collapse of buildings may occur under strong shaking. On the other hand, considering infill walls significantly decrease the peak floor displacements and drifts in both X and Y-directions.

Keywords: masonry infill, bare frame, response spectrum, seismic response

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Authors: Ibrahim Beldjilali, Adel Ghenaiet

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The contra-rotating axial machine is a promising solution for several applications, where high pressure and efficiencies are needed. Also, they allow reducing the speed of rotation, the radial spacing and a better flexibility of use. However, this requires a better understanding of their operation, including the influence of second rotor on the overall aerodynamic performances. This work consisted of both experimental and numerical studies to characterize this counter-rotating fan, especially the analysis of the effects of the blades stagger angle and the inter-distance between the rotors. The experimental study served to validate the computational fluid dynamics model (CFD) used in the simulations. The numerical study permitted to cover a wider range of parameter and deeper investigation on flow structures details, including the effects of blade stagger angle and inter-distance, associated with the interaction between the rotors. As a result, there is a clear improvement in aerodynamic performance compared with a conventional machine.

Keywords: aerodynamic performance, axial fan, counter rotating rotors, CFD, experimental study

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Authors: Rupinder Kaur, Harjot Kaur

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The objective of this paper is to present the study of the effect of varying thickness on rotating composite disks made from Al-SiC_P having different particle sizes. Mathematical modeling is used to calculate the effect of varying thickness with different particle sizes on rotating composite disks in radial as well as tangential directions with thermal gradients. In comparison to various particle sizes with varied thicknesses, long-term deformation occurs. The results are displayed visually, demonstrating how creep deformation decreases with changing particle size and thickness.

Keywords: creep, varying thickness, particle size, stresses and strain rates

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Authors: Dang HuynhMinhTam, Kuang-Cong Lu, Yi-Hung Chen, Zhung-Yu Lin, Cheng-Siang Cheng

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Carbon capture, utilization, and storage (CCUS) technology become a predominant technique to mitigate carbon dioxide and achieve net-zero emissions goals. This research targets to continuously capture the low concentration CO₂ from the tail gas of the regenerative thermal oxidizer (RTO) in the high technology industry. A rotating packed bed (RPB) reactor is investigated to capture the efficiency of CO₂ using a mixture of NaOH/Na₂CO₃ solutions to simulate the real absorbed solution. On a lab scale, semi-batch experiments of continuous gas flow and circulating absorbent solution are conducted to find the optimal parameters and are then examined in a continuous operation. In the semi-batch tests, the carbon capture efficiency and pH variation in the conditions of a low concentration CO₂ (about 1.13 vol%), the NaOH concentration of 1 wt% or 2 wt% mixed with 14 wt% Na₂CO₃, the rotating speed (600, 900, 1200 rpm), the gas-liquid ratio (100, 200, and 400), and the temperature of absorbent solution of 40 ºC are studied. The CO₂ capture efficiency significantly increases with higher rotating speed and smaller gas-liquid ratio, respectively, while the difference between the NaOH concentration of 1 wt% and 2 wt% is relatively small. The maximum capture efficiency is close to 80% in the conditions of the NaOH concentration of 1 wt%, the G/L ratio of 100, and the rotating speed of 1200 rpm within the first 5 minutes. Furthermore, the continuous operation based on similar conditions also demonstrates the steady efficiency of the carbon capture of around 80%.

Keywords: carbon dioxide capture, regenerative thermal oxidizer, rotating packed bed, sodium hydroxide

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Authors: A. Giniatoulline

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We consider the internal oscillations of the ocean which are caused by the gravity force and the Coriolis force, for different models with changeable density, heat transfer, and salinity. Traditionally, the mathematical description of the resonance effect is related to the growing amplitude as a result of input vibrations. We offer a different approach: the study of the relation between the spectrum of the internal oscillations and the properties of the limiting amplitude of the solution for the harmonic input vibrations of the external forces. Using the results of the spectral theory of self-adjoint operators in Hilbert functional spaces, we prove that there exists an explicit relation between the localization of the frequency of the external input vibrations with respect to the essential spectrum of proper inner oscillations and the non-uniqueness of the limiting amplitude. The results may find their application in various problems concerning mathematical modeling of turbulent flows in the ocean.

Keywords: computational fluid dynamics, essential spectrum, limiting amplitude, rotating fluid, spectral theory, stratified fluid, the uniqueness of solutions of PDE equations

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Huang Bingling, Jia Yuhong, Liu Yanhui

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As an important part of aircraft, landing gears are responsible for taking-off and landing function. In recent years, big airplane's structural quality increases a lot. As a result, landing gears have stricter technical requirements than ever before such as structure strength and etc. If the structural strength of the landing gear is enhanced through traditional methods like increasing structural quality, the negative impacts on the landing gear's function would be very serious and even counteract the positive effects. Thus, in order to solve this problem, the impact of pre-rotating of landing gears on performance of landing gears is studied from the theoretical and experimental verification in this paper. By increasing the pre-rotating speed of the wheel, it can improve the performance of the landing gear and reduce the structural quality, the force of joint parts and other properties. In addition, the pre-rotating of the wheels also has other advantages, such as reduce the friction between wheels and ground and extend the life of the wheel. In this paper, the impact of the pre-rotating speed on landing gears and the connecting between landing gears performance and pre-rotating speed would be researched in detail. This paper is divided into three parts. In the first part, large airplane landing gear model is built by CATIA and LMS. As most general landing gear type in big plane, four-wheel landing gear is picked as model. The second part is to simulate the process of landing in LMS motion, and study the impact of pre-rotating of wheels on the aircraft`s properties, including the buffer stroke, efficiency, power; friction, displacement and relative speed between piston and sleeve; force and load distribution of tires. The simulation results show that the characteristics of the different pre-rotation speed are understood. The third part is conclusion. Through the data of the previous simulation and the relationship between the pre-rotation speed of the aircraft wheels and the performance of the aircraft, recommended speed interval is proposed. This paper is of great theoretical value to improve the performance of large airplane. It is a very effective method to improve the performance of aircraft by setting wheel pre-rotating speed. Do not need to increase the structural quality too much, eliminating the negative effects of traditional methods.

Keywords: large airplane, landing gear, pre-rotating, simulation

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Authors: P. Ravinder Reddy, Chaitanya Vishal Nalli, B. Tulja Lal, Anusha Kankanala

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The chassis frame of an automobile with different sections have been considered for different loads. The orthotropic materials are selected to get the stability by varying fiber angle, fiber thickness, laminates, fiber properties, matrix properties and elastic ratios. The geometric model of chassis frame is carried out with parametric modelling approach. The analysis of chassis frame is carried out with ANSYS FEA software. The static and dynamic analysis of chassis frame is carried out by varying geometric parameters, orthotropic properties, materials and various sections. The static and dynamic response is discussed in detail in different sections.

Keywords: chassis frame, dynamic response, geometric model, orthotropic materials

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Authors: Chi Zhang, Jun Jiang

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Constitutive equations are very important in finite element (FE) modeling, and the accuracy of the material constants in the equations have significant effects on the accuracy of the FE models. A wide range of constitutive equations are available; however, fitting the material constants in the constitutive equations could be complex and time-consuming due to the strong non-linearity and relationship between the constants. This work will focus on the development of a set of unified MATLAB programs for fitting the material constants in the constitutive equations efficiently. Users will only need to supply experimental data in the required format and run the program without modifying functions or precisely guessing the initial values, or finding the parameters in previous works and will be able to fit the material constants efficiently.

Keywords: constitutive equations, FE modelling, MATLAB program, non-linear curve fitting

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Authors: HyunSu Seo, HoYoung Son, Sungjin Kim, WooYoung Jung

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In order to understand the seismic behavior of steel frame structure with infill FRP composite panel, simple models for simulation on the steel frame with the panel systems were developed in this study. To achieve the simple design method of the steel framed structure with the damping panel system, 2-D finite element analysis with the springs and dashpots models was conducted in ABAQUS. Under various applied spring stiffness and dashpot coefficient, the expected hysteretic energy responses of the steel frame with damping panel systems we re investigated. Using the proposed simple design method which decides the stiffness and the damping, it is possible to decide the FRP and damping materials on a steel frame system.

Keywords: numerical analysis, FEM, infill, GFRP, damping

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Authors: A. Miloud

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In this work, the results of numerical simulations of the turbulent flow with 3D heat transfer are presented for the case of two U-shaped channels and rotating rectangular section. The purpose of this investigation was to study the effect of the corrugated walls of the heated portion on the improved cooling, in particular the influence of the wavelength. The calculations were performed for a Reynolds number ranging from 10 000 to 100 000, two values of the number of rotation (Ro = 0.0 to 0.14) and a ratio of the restricted density to 0.13. In these simulations, ANSYS FLUENT code was used to solve the Reynolds equations expressing relations between different fields averaged variables over time. Model performance k-omega SST model and RSM are evaluated through a comparison of the numerical results for each model and the experimental and numerical data available. In this work, detailed average temperature predictions, the scope of the secondary flow and distributions of local Nusselt are presented. It turns out that the corrugated configuration further urges the heat exchange provided to reduce the velocity of the coolant inside the channel.

Keywords: cooling blades, corrugated walls, model k-omega SST and RSM, fluent code, rotation effect

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Authors: Yu-Kai Ting, Jia-Ying Tu, Chung-Chun Hsiao

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New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.

Keywords: Galerkin method, Lorenz equations, Navier-Stokes equations, convectional motion

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Authors: Putul Haldar, Yogendra Singh, D. K. Paul

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Un-Reinforced Masonry (URM) infilled RC framed buildings are the most common construction practice for modern multi-storey buildings in India like many other parts of the world. Although the behavior and failure pattern of the global structure changes significantly due to infill-frame interaction, the general design practice is to treat them as non-structural elements and their stiffness, strength and interaction with frame is often ignored, as it is difficult to simulate. Indian Standard, like many other major national codes, does not provide any explicit guideline for modeling of infills. This paper takes a stock of controlling design provisions in some of the major national seismic design codes (BIS 2002; CEN 2004; NZS-4230 2004; ASCE-41 2007) to ensure the desired seismic performance of infilled frame. Most of the national codes on seismic design of buildings still lack in adequate guidelines on modeling and design of URM infilled frames results in variable assumption in analysis and design. This paper, using nonlinear pushover analysis, also presents the effect of one of such assumptions of conventional ‘simultaneous’ analysis procedure of infilled frame on the seismic performance of URM infilled RC frame buildings.

Keywords: URM infills, RC frame, seismic design codes, construction sequence of infilled frame

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Authors: Seong Do Kim, Woo Young Jung

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Recently, damages due to typhoons and strong wind are on the rise. Considering this issue, we evaluated the performance of soundproofing walls based on the strong wind fragility by means of numerical analysis. Among the components of the soundproof wall, aluminum frame was the most vulnerable member, thus we have considered different section of aluminum frame in the determination of wind fragility. Wind load was randomly generated using Monte Carlo Simulation method. Moreover, limit state was based on the test standard of road construction soundproofing wall. In this study, the strong wind fragility was determined by considering the influence factors of wind exposure category, soundproof wall’s installation position, and shape of aluminum frame section. Results of this study could be used to determine the section shape of the frame that has high resistance to the wind during construction of the soundproofing wall.

Keywords: aluminum frame soundproofing wall, Monte Carlo simulation, numerical simulation, wind fragility

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Authors: V. K. Gupta, Tejeet Singh

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In many whisker reinforced composites, anisotropy may result due to material flow during processing operations such as forging, extrusion etc. The consequence of anisotropy, introduced during processing of disc material, has been investigated on the steady state creep deformations of the rotating disc. The disc material is assumed to undergo plastic deformations according to Hill’s anisotropic criterion. Steady state creep has been analyzed in a constant thickness rotating disc made of functionally graded 6061Al-SiCw (where the subscript ‘w’ stands for whisker) using Hill’s The content of reinforcement (SiCw) in the disc is assumed to decrease linearly from the inner to outer radius. The stresses and strain rates in the disc are estimated by solving the force equilibrium equation along with the constitutive equations describing multi-axial creep. The results obtained for anisotropic FGM disc have been compared with those estimated for isotropic FGM disc having the same average whisker content. The anisotropic constants, appearing in Hill’s yield criterion, have been obtained from the available experimental results. The results show that the presence of anisotropy reduces the tangential stress in the middle of the disc but near the inner and outer radii the tangential stress is higher when compared to isotropic disc. On the other hand, the steady state creep rates in the anisotropic disc are reduced significantly over the entire disc radius, with the maximum reduction observed at the inner radius. Further, in the presence of anisotropy the distribution of strain rate becomes relatively uniform over the entire disc, which may be responsible for reducing the extent of distortion in the disc.

Keywords: anisotropy, creep, functionally graded composite, rotating disc

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Authors: Ali Khaleel Kareem, Shian Gao, Ahmed Qasim Ahmed

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A numerical investigation of unsteady mixed convection heat transfer in a 3D moving top wall enclosure, which has a central rotating cylinder and uses either artificial roughness on the bottom hot plate or smooth bottom hot plate to study the heat transfer enhancement, is completed for fixed circular cylinder, and anticlockwise and clockwise rotational speeds, -1 ≤ Ω ≤ 1, at Reynolds number of 5000. The top lid-driven wall was cooled, while the other remaining walls that completed obstructed cubic were kept insulated and motionless. A standard k-ε model of Unsteady Reynolds-Averaged Navier-Stokes (URANS) method is involved to deal with turbulent flow. It has been clearly noted that artificial roughness can strongly control the thermal fields and fluid flow patterns. Ultimately, the heat transfer rate has been dramatically increased by involving artificial roughness on the heated bottom wall in the presence of rotating cylinder.

Keywords: artificial roughness, lid-driven cavity, mixed convection heat transfer, rotating cylinder, URANS method

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Authors: A. Kahil, A. Nekmouche, N. Khelil, I. Hamadou, M. Hamizi, Ne. Hannachi

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The objective of this work is to study the influence of the nonlinear behavior models of the concrete (concrete_BAEL and concrete_UNI) as well as the confinement brought by the transverse reinforcement on the seismic response of reinforced concrete frame (RC/frame). These models as well as the confinement are integrated in the Cast3m finite element calculation code. The consideration of confinement (TAC, taking into account the confinement) provided by the transverse reinforcement and the non-consideration of confinement (without consideration of containment, WCC) in the presence and absence of a vertical load is studied. The application was made on a reinforced concrete frame (RC/frame) with 3 levels and 2 spans. The results show that on the one hand, the concrete_BAEL model slightly underestimates the resistance of the RC/frame in the plastic field, whereas the concrete_uni model presents the best results compared to the simplified model "concrete_BAEL", on the other hand, for the concrete-uni model, taking into account the confinement has no influence on the behavior of the RC/frame under imposed displacement up to a vertical load of 500 KN.

Keywords: reinforced concrete, nonlinear calculation, behavior laws, fiber model confinement, numerical simulation

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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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: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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