Search results for: numerical visualization

Authors: M. C. Lin, C. W. Su

Abstract:

The paper investigates the optimization analysis to the heat exchanger design, mainly with response surface method and genetic algorithm to explore the relationship between optimal fluid flow velocity and temperature of the heat exchanger using field synergy principle. First, finite volume method is proposed to calculate the flow temperature and flow rate distribution for numerical analysis. We identify the most suitable simulation equations by response surface methodology. Furthermore, a genetic algorithm approach is applied to optimize the relationship between fluid flow velocity and flow temperature of the heat exchanger. The results show that the field synergy angle plays vital role in the performance of a true heat exchanger.

Keywords: optimization analysis, field synergy, heat exchanger, genetic algorithm

Procedia PDF Downloads 307

Authors: Wen Liang Chang

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In this study, the optimal replacement time and number of preventive maintenance (PM) actions were investigated for a second-hand device. Suppose that a user intends to use a second-hand device for manufacturing products, and that the device is replaced with a new one. Any device failure is rectified through minimal repair, thereby incurring a fixed repair cost to the user. If the new device fails within the FRW period, minimal repair is performed at no cost to the user. After the FRW expires, a failed device is repaired and the cost of repair is incurred by the user. In this study, two profit models were developed, and the optimal replacement time and number of PM actions were determined to maximize profits. Finally, the influence of the optimal replacement time and number of PM actions were elaborated on, using numerical examples.

Keywords: second-hand device, preventive maintenance, replacement time, device failure

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Authors: Nurudeen Oluwasola Lasisi

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The COVID-19 is an infection caused by coronavirus, which has been designated as a pandemic in the world. In this paper, we proposed a model to study the effect of distancing and wearing masks on the transmission of COVID-19 infection dynamics. The invariant region of the model is established. The COVID-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using the linearization technique method and Lyapunov method. It was found that COVID-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R₀ < 1 and globally asymptomatically stable if R₀ < 1, otherwise unstable if R₀ > 1. More so, numerical analysis and simulations of the dynamics of the COVID-19 infection are presented.

Keywords: distancing, reproduction number, wearing of mask, local and global stability, modelling, transmission

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Authors: N. M. M. Ammar, S. M. Mustaqim, N. M. Nadzir

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The most important problem occurs on oil spills in sea water is to reduce the oil spills size. This study deals with the development of high pressurized nozzle using dispersion method for oil leakage in offshore. 3D numerical simulation results were obtained using ANSYS Fluent 13.0 code and correlate with the experimental data for validation. This paper studies the contribution of the process on flow speed and pressure of the flow from two different geometrical designs of nozzles and to generate a spray pattern suitable for dispersant application. Factor of size distribution of droplets generated by the nozzle is calculated using pressures ranging from 2 to 6 bars. Results obtain from both analyses shows a significant spray pattern and flow distribution as well as distance. Results also show a significant contribution on the effect of oil leakage in terms of the diameter of the oil spills break up.

Keywords: arc nozzle, CFD simulation, droplets, oil spills

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Authors: Krzysztof Pomorski

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In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

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Authors: Sagir M. Yusuf, Chris Baber

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In this paper, we describe how to achieve knowledge understanding and prediction (Situation Awareness (SA)) for multiple-agents conducting searching activity using Bayesian inferential reasoning and learning. Bayesian Belief Network was used to monitor agents' knowledge about their environment, and cases are recorded for the network training using expectation-maximisation or gradient descent algorithm. The well trained network will be used for decision making and environmental situation prediction. Forest fire searching by multiple UAVs was the use case. UAVs are tasked to explore a forest and find a fire for urgent actions by the fire wardens. The paper focused on two problems: (i) effective agents’ path planning strategy and (ii) knowledge understanding and prediction (SA). The path planning problem by inspiring animal mode of foraging using Lévy distribution augmented with Bayesian reasoning was fully described in this paper. Results proof that the Lévy flight strategy performs better than the previous fixed-pattern (e.g., parallel sweeps) approaches in terms of energy and time utilisation. We also introduced a waypoint assessment strategy called k-previous waypoints assessment. It improves the performance of the ordinary levy flight by saving agent’s resources and mission time through redundant search avoidance. The agents (UAVs) are to report their mission knowledge at the central server for interpretation and prediction purposes. Bayesian reasoning and learning were used for the SA and results proof effectiveness in different environments scenario in terms of prediction and effective knowledge representation. The prediction accuracy was measured using learning error rate, logarithm loss, and Brier score and the result proves that little agents mission that can be used for prediction within the same or different environment. Finally, we described a situation-based knowledge visualization and prediction technique for heterogeneous multi-UAV mission. While this paper proves linkage of Bayesian reasoning and learning with SA and effective searching strategy, future works is focusing on simplifying the architecture.

Keywords: Levy flight, distributed constraint optimization problem, multi-agent system, multi-robot coordination, autonomous system, swarm intelligence

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Authors: Tarek A. Mekail, Walid M. A. Elmagid

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Many researches have concentrated on improving the aerodynamic performance of wind turbine blade through testing and theoretical studies. A small wind turbine blade is designed, fabricated and tested. The power performance of small horizontal axis wind turbines is simulated in details using Computational Fluid Dynamic (CFD). The three-dimensional CFD models are presented using ANSYS-CFX v13 software for predicting the performance of a small horizontal axis wind turbine. The simulation results are compared with the experimental data measured from a small wind turbine model, which designed according to a vehicle-based test system. The analysis of wake effect and aerodynamic of the blade can be carried out when the rotational effect was simulated. Finally, comparison between experimental, numerical and analytical performance has been done. The comparison is fairly good.

Keywords: small wind turbine, CFD of wind turbine, CFD, performance of wind turbine, test of small wind turbine, wind turbine aerodynamic, 3D model

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Authors: Gennady M. Kulikov, Svetlana V. Plotnikova

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This paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and piezoelectric shells. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS formulation can be applied efficiently to 3D solutions for FG piezoelectric laminated shells, which asymptotically approach the exact solutions of piezoelectricity as the number of SaS In goes to infinity.

Keywords: electroelasticity, functionally graded material, laminated piezoelectric shell, sampling surfaces method

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

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This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: Sabri Arik

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In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Woo Young Jung, Bu Seog Ju

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This study described the seismic performance evaluation of bridge structures, located near Daegu metropolitan city in Korea. The structural design code or regulatory guidelines is focusing on the protection of brittle failure or collapse in bridges’ lifetime during an earthquake. This paper illustrated the procedure in terms of the safety evaluation of bridges using simple linear elastic 3D Finite Element (FE) model in ABAQUS platform. The design response spectra based on KBC 2009 were then developed, in order to understand the seismic behavior of bridge structures. Besides, the multiple directional earthquakes were applied and it revealed that the most dominated earthquake direction was transverse direction of the bridge. Also, the bridge structure under the compressive stress was more fragile than the tensile stress and the vertical direction of seismic ground motions was not significantly affected to the structural system.

Keywords: seismic, bridge, FEM, evaluation, numerical analysis

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Authors: Mohsen Ziaee

Abstract:

Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: K. B. Ghazaryan, R. A. Ghazaryan

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Based on the constitutive model and anti-plane equations of anisotropic elastic body of monoclinic symmetry we consider the problem of shear wave propagation in multi-layered disordered composite structure with point defect. Using transfer matrix method the analytic expression is obtained providing solutions of shear Floquet wave propagation in periodic disordered anisotropic structure. The usefulness of the obtained analytical expression was discussed also in reflection and refraction problems from multi-layered reflector as well as in vibration problem of multi-layered waveguides. Numerical results are presented highlighting the effects arising in disordered periodic structure due to defects of multi-layered structure.

Keywords: shear elastic waves, monoclinic anisotropic media, periodic structure, disordered multilayer laminae, multi-layered waveguide

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Swee Kun Yap, Sachin Jangam, Suraj Vasudevan

Abstract:

Experiential learning is dubbed as a highly effective way to enhance learning. Virtual reality (VR) is thus a helpful tool in providing a safe, memorable, and interactive learning environment. A class of 49 fluid mechanics students participated in starting up a pump, one of the most used equipment in the chemical industry, in VR. They experience the process in VR to familiarize themselves with the safety training and the standard operating procedure (SOP) in guided mode. Students subsequently observe their peers (in groups of 4 to 5) complete the same training. The training first brings each user through the personal protection equipment (PPE) selection, before guiding the user through a series of steps for pump startup. One of the most common feedback given by industries include the weakness of our graduates in pump design and operation. Traditional fluid mechanics is a highly theoretical module loaded with engineering equations, providing limited opportunity for visualization and operation. With VR pump, students can now learn to startup, shutdown, troubleshoot and observe the intricacies of a centrifugal pump in a safe and controlled environment, thereby bridging the gap between theory and practical application. Following the completion of the guided mode operation, students then individually complete the VR assessment for pump startup on the same day, which requires students to complete the same series of steps, without any cues given in VR to test their recollection rate. While most students miss out a few minor steps such as the checking of lubrication oil and the closing of minor drain valves before pump priming, all the students scored full marks in the PPE selection, and over 80% of the students were able to complete all the critical steps that are required to startup a pump safely. The students were subsequently tested for their recollection rate by means of an online quiz 3 weeks later, and it is again found that over 80% of the students were able to complete the critical steps in the correct order. In the survey conducted, students reported that the VR experience has been enjoyable and enriching, and 79.5% of the students voted to include VR as a positive supplementary exercise in addition to traditional teaching methods. One of the more notable feedback is the higher ease of noticing and learning from mistakes as an observer rather than as a VR participant. Thus, the cycling between being a VR participant and an observer has helped tremendously in their knowledge retention. This reinforces the positive impact VR has on learning.

Keywords: experiential learning, learning by doing, pump, unit operations, virtual reality

Procedia PDF Downloads 138

Authors: H. Samadiyeh, R. Khajavi

Abstract:

A new FD-based procedure, modal finite difference method (MFDM), is proposed for seismic wave propagation modeling, in which simulation is dealt with in the modal space. The method employs eigenvalues of a characteristic matrix formed by appropriate time-space FD stencils. Since MFD runs for different modes are totally independent of each other, MFDM can easily be parallelized while considerable simplicity in parallel-algorithm is also achieved. There is no requirement to any domain-decomposition procedure and inter-core data exchange. More important is the possibility to skip processing of less-significant modes, which enables one to adjust the procedure up to the level of accuracy needed. Thus, in addition to considerable ease of parallel programming, computation and storage costs are significantly reduced. The method is qualified for its efficiency by some numerical examples.

Keywords: Finite Difference Method, Graphics Processing Unit (GPU), Message Passing Interface (MPI), Modal, Wave propagation

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Authors: Prashant S. Humnabad

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The objective of this work is to carry out a thermal heat transfer analysis to obtain the time dependent temperature field in welding process friction stir welded dissimilar materials with different preheating temperature. A series of joints were made on four mm thick aluminum and steel plates. The temperature used was 100ºC, 150ºC and 200ºC. The welding operation was performed with different rotational speeds and traverse speed (1000, 1400 and 2000 rmp and 16, 20 and 25 mm/min..). In numerical model, the welded plate was modeled as the weld line is the symmetric line. The work-piece has dimensions of 100x100x4 mm. The obtained result was compared with experimental result, which shows good agreement and within the acceptable limit. The peak temperature at the weld zone increases significantly with respect to increase in process time.

Keywords: FEA, thermal analysis, preheating, friction stir welding

Procedia PDF Downloads 189

Authors: Alireza Mehdizadeh, Ghanbarali Sheikhzadeh

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In this paper the pressure loss of drilling fluid flow in the annulus is investigated. On this purpose the domains between two concentric and two eccentric cylinders are considered as computational domains. In this research foam is used as drilling fluid. Firstly simulation results for laminar flow and non Newtonian fluid and different density like 100, 200, 300 kg/m3 and different inner cylinder rotational velocity like 100, 200, 300 RPM is presented. These results are compared and matched with references results. The power law and Herschel Bulkly methods are used for non Newtonian fluid modeling. After that computations are repeated with turbulence flow considering. K- Model is used for turbulence modeling. Results show that in laminar flow Herschel bulkly model has best result in comparison with power law model. And pressure loss in turbulence flow is higher than laminar flow.

Keywords: simulation, concentric cylinders, drilling, non Newtonian

Procedia PDF Downloads 566

Authors: Elsayed M. A. Elbashbeshy, T. G. Emam, M. S. El-Azab, K. M. Abdelgaber

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The effect of thermal radiation on flow, heat and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder embedded in a porous medium with suction/injection is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.

Keywords: laminar flow, boundary layer, stretching horizontal cylinder, thermal radiation, suction/injection, nanofluid

Procedia PDF Downloads 382

Authors: M. H. Alhajeri, Hamad M. Alhajeri, A. H. Alenezi

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Computational fluid dynamics (CFD) investigation of heat transfer in U-duct with turbulators is presented in this paper. The duct passages used to cool internally the blades in gas turbine. The study is focused in the flow behavior and the Nusselt number (Nu) distributions. The model of the u-duct contains two square legs that are connected by 180* turn. Four turbulators are located in each surface of the leg and distributed in a staggered arrangement. The turbulator height and width are equal to 0.1 of the duct width, and the turbulator height is 0.1 of the distance between the turbulators. The Reynolds number (Re) used in this study is 95000 and the inlet velocity is 10 m/s. It was noticed that, after the flow resettles from the interruptions generated by the first turbulator or the turn, the flow construct two eddies, one large and the other is small after and before the turbulator, respectively. The maximum values of the Nu are found at a distance of approximately one turbulator width w before of the flow reattachment point.

Keywords: computational fluid dynamics, CFD, rib, heat transfer, blade

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Authors: Nan Tang, Bin Wu, Cunfu He

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The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

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Authors: Hyun-Kyu Cho, Jun-Su Kim, Choon-Geun Huh, Geon Lee Young-Chul Park

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In this study, the relationship between flow properties and fluid projection distance look into connection for shape variations of foam monitor. A numerical analysis technique for fluid analysis of a foam monitor was developed for the prediction. Shape of foam monitor the flow path of fluid flow according to the shape, The fluid losses were calculated from flow analysis result.. The modified model used the length increase model of the flow path, and straight line of the model. Inlet pressure was 7 [bar] and external was atmosphere codition. am. The results showed that the length increase model of the flow path and straight line of the model was improved in the nozzle projection distance.

Keywords: injection performance, finite element method, foam monitor, Projection distance

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Authors: Samira Mohabbatdar, Abbas Ahmadi, Mohsen S. Sajadieh

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This paper deals with a two-level supply chain consisted of one manufacturer and one retailer for single-type product. The demand function of the customers depends on price. We consider an integrated production inventory system where the manufacturer processes raw materials in order to deliver finished product with imperfect quality to the retailer. Then retailer inspects the products and after that delivers perfect products to customers. The proposed model is based on the joint total profit of both the manufacturer and the retailer, and it determines the optimal ordering lot-size, number of shipment and selling price of the retailer. A numerical example is provided to analyse and illustrate the behaviour and application of the model. Finally, sensitivity analysis of the key parameters are presented to test feasibility of the model.

Keywords: supply chain, pricing policy, defective quality, joint economic lot sizing

Procedia PDF Downloads 337

Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Meriam Khelifa

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In recent years, many studies have focused on the harvesting of the vibrations energy to produce electrical energy using contact separation (CS) triboelectric nanogenerators (TENG). The simplest design for a TENG consists of a capacitor comprising a single moving electrode. The conversion efficiency of vibration energy into electrical energy can, in principle, reach 100%. But to actually achieve this objective, it is necessary to optimize the parameters of the TENG, such as the dielectric constant and the thickness of the insulator, the load resistance, etc. In particular, the use of a switch which is actioned at optimal times within the TENG cycle is essential. Using numerical modeling and experimental design, we applied a methodology to find the TENG parameters which optimize the energy transfer efficiency (ETE) to almost 100% for any vibration frequency and amplitude. The rather simple design of a TENG is promising as an environment friendly device. It opens the doors for harvesting acoustic vibrations from the environment and to design effective protection against environmental noise.

Keywords: vibrations, CS TENG, efficiency, design of experiments

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Authors: Dimitrios J. Dimitriou

Abstract:

It is widely recognised that the assets portfolio development is helping to enhance economic growth, productivity and competitiveness. While numerous studies and reports certify the positive effect of investments in large infrastructure investments on the local economy, still, the methodology to estimate the contribution in economic development is a challenging issue for researchers and economists. The key question is how to estimate those economic impacts in each economic system. This paper provides a compact and applicable methodological framework providing quantitative results in terms of the overall jobs and income generated into the project life cycle. According to a deterministic mathematical approach, the key variables and the modelling framework are presented. The numerical case study highlights key results for a new motorway project in Greece, which is experienced economic stress for many years, providing the opportunity for comparisons with similar cases.

Keywords: quantitative modelling, economic impact, large transport infrastructure, economic assessment

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Authors: Abouzar Kaboudian, Ravi Chaithanya Mysa, Boo Cheong Khoo, Rajeev Kumar Jaiman

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The vortex structures observed in the wake of a flexible cylinder can be significantly different from those of a traditional vibrating, spring mounted, rigid cylinder. These differences can significantly affect the VIV characteristics of the flow and subsequently the VIV response of the cylindrical structures. In this work, we present how the aspect ratio of a flexible cylinder can change the vortex structures in its wake. We will discuss different vortex dynamics which can be observed in the wake of the vibrating flexible cylinder, and how they can affect the vibrational response of the cylinder. Moreover, we will study the transition of these structures versus the aspect ratio of the flexible cylinder. We will discuss how these transitions affect the in-line and transverse forces on the structure. In the end, we will provide general guidelines on the minimum acceptable aspect ratio for the offshore riser studies which may have grave implications for future numerical and experimental works.

Keywords: aspect ratio, flexible cylinder, vortex-shedding, VIV

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Authors: Javad Shamsi Soosahab, Reza Ziaie Moayed

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The compressive and tensile bearing capacity of helical piles in sand is investigated by means of numerical modeling. The analyses are carried out using two-dimensional finite-element software, Optum G2. The load–displacement behavior under compression and tension is compared in different relative densities for constant and various elastic modulus. The criterion used to find the ultimate axial load is the load corresponding to 5% of the helical diameter. The results show that relative density of sand plays an essential role in the response of ultimate capacities towards various condition. Increase in elastic modulus with depth is found to play a relatively more significant role to the increase in ultimate compressive load capacities, however tension bearing capacity decreases.

Keywords: helical piles, Optum G2, relative density, constant and various elastic modulus

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Authors: Jixiang Zhang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, dynamics, Lagrange, parallel platform

Procedia PDF Downloads 345