Search results for: method of integral equations

Authors: Wayan Widhiada, Cok Indra Partha, Gusti Ngurah Nitya Santhiarsa

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The purpose of this paper is to investigate the sophistication of the use of Proportional Integral and Derivative Control to control the kinematic motion of the mobile robot manipulator. Simulation and experimental methods will be used to investigate the sophistication of PID control to control the mobile robot arm in the collection and placement of several kinds of objects quickly, accurately and correctly. Mathematical modeling will be done by utilizing the integration of Solidworks and MATLAB / Simmechanics software. This method works by converting the physical model file into the xml file. This method is easy, fast and accurate done in modeling and design robotics. The automatic control design of this robot manipulator will be validated in simulations and experimental in control labs as evidence that the mobile robot manipulator gripper control design can achieve the best performance such as the error signal is lower than 5%, small overshoot and get steady signal response as quickly.

Keywords: control analysis, kinematics motion, mobile robot manipulator, performance

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Authors: Prathmesh Vikas Patil, Yashaswini Lomte Patil

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Laminated composite materials have considerable attention in various engineering applications due to their exceptional strength-to-weight ratio and mechanical properties. The analysis of laminated composite plates in three-dimensional (3D) elasticity is a complex problem, as it requires accounting for the orthotropic anisotropic nature of the material and the interactions between multiple layers. Conventional approaches, such as the classical plate theory, provide simplified solutions but are limited in performing exact analysis of the plate. To address such a challenge, the state space method emerges as a powerful numerical technique for modeling the behavior of laminated composites in 3D. The state-space method involves transforming the governing equations of elasticity into a state-space representation, enabling the analysis of complex structural systems in a systematic manner. Here, an effort is made to perform a 3D elasticity analysis of plates with cross-ply and angle-ply laminates using the state space approach. The state space approach is used in this study as it is a mixed formulation technique that gives the displacements and stresses simultaneously with the same level of accuracy.

Keywords: cross ply laminates, angle ply laminates, state space method, three-dimensional elasticity analysis

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

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108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in the Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in the Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of a general theory of relativity was obscure and incorrect, but they did not give a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not yet been successfully completed, although former scholars have thought of it and tried to do it. In order to solve the problems, it is necessary to explore the obscure and incorrect problems in a general theory of relativity based on the physical laws and to find out the methodology for solving the problems. Therefore, as the first step toward achieving this purpose, the right solution of the geodesic equation in the Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: Shafiullah Soomro

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Active contour is one of the image segmentation techniques and its goal is to capture required object boundaries within an image. In this paper, we propose a novel image segmentation method by using an active contour method based on anisotropic diffusion feature enhancement technique. The traditional active contour methods use only pixel information to perform segmentation, which produces inaccurate results when an image has some noise or complex background. We use Perona and Malik diffusion scheme for feature enhancement, which sharpens the object boundaries and blurs the background variations. Our main contribution is the formulation of a new SPF (signed pressure force) function, which uses global intensity information across the regions. By minimizing an energy function using partial differential framework the proposed method captures semantically meaningful boundaries instead of catching uninterested regions. Finally, we use a Gaussian kernel which eliminates the problem of reinitialization in level set function. We use several synthetic and real images from different modalities to validate the performance of the proposed method. In the experimental section, we have found the proposed method performance is better qualitatively and quantitatively and yield results with higher accuracy compared to other state-of-the-art methods.

Keywords: active contours, anisotropic diffusion, level-set, partial differential equations

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: model predictive control, optimal control, process control, crystal growth

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

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The analytical bright two soliton solution of the 3-coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: optical soliton, soliton interaction, soliton switching, WDM

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: Arash Ghahraman, Gyula Bene

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The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

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Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

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This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

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Authors: Malorzata Kmiotek, Anna Kucaba-Pietal, Robert Smusz

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Due to the miniaturisation process, in many technical devices, microchannels are used in cooling systems. Because of the small size of microchannels, the flow inside is laminar, which caused a slow heat exchange. In order to intensify the heat exchange, the flow must be disturbed, for example, by introducing obstacles. We present results on the influence of a thin obstacle, placed on microchannel wall, on the fluid and heat flow in the aspect of their use by constructors of heat exchangers. The obstacle is called 'thin' when its geometrical parameter (o=w/h, w- width, h - height of the obstacle) satisfies inequality: o < 0.5. In this work, we report numerical results on heat and mass transfer in the microchannels of 400 micrometer height (H - height of the microchannel), where thin obstacles are immersed on the walls, to disturb the flow. The Reynolds number of the flow in microchannel varies between 20 and 200 and is typical for the flow in micro heat exchangers. The equations describing the fluid and heat flows in microchannels were solved numerically by using the finite element method with an application of CFD&FSI package of ADINA R&D, Inc. 9.4 solver. In the case of flows in the microchannels with sequences of thin rectangular obstacles placed on the bottom and the top wall of a microchannel, the influence of distances s (s is the distance between two thin obstacles) and heights of obstacles on the fluid and heat transfer was investigated. Thermal and flow conditions of the application area of microchannels in electronic cooling systems, i.e., wall temperature of 60 °C, the fluid temperature of 20°C were used to solve equations. Additionally, the distance s between the thin obstacles in microchannels as a multiple of the amount of the channel height was determined. Results show that placing thin obstacles on microchannel walls increase the length of recirculation zones of the flow and improves the heat transfer.

Keywords: Finite Element Method, heat transfer, mechanical engineering, microchannel

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Authors: T. Watanabe

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Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: analysis, combustion, droplet, sodium

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Authors: Jin Hwa Yang, Hwang Bae, Sung Uk Ryu, Byong Guk Jeon, Sung Jae Yi, Hyun Sik Park

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Experimental studies using a large-scale thermal-hydraulic integral test facility, System–integrated Modular Advanced Reactor Integral Test Loop (SMART-ITL), have been carried out to validate the performance of the prototype, SMART. After Fukushima accident, the passive safety systems have been dealt as important designs for retaining of nuclear safety. One of the concerned scenarios for evaluating the passive safety system is a Complete Loss of Coolant Flow (CLOF). The flowrate of coolant in the primary system is maintained by Reactor Coolant Pump (RCP). When the supply of electric power of RCP is shut off, the flowrate of coolant decreases sharply, and the temperature of the coolant increases rapidly. Therefore, the reactor trip signal is activated to prevent the over-heating of the core. In this situation, Passive Residual Heat Removal System (PRHRS) plays a significant role to assure the soundness of the SMART. The PRHRS using a two-phase natural circulation is a passive safety system in the SMART to eliminate the heat of steam generator in the secondary system with heat exchanger submarined in the Emergency Cooling Tank (ECT). As the RCPs continue to coast down, inherent natural circulation in the primary system transfers heat to the secondary system. The transferred heat is removed by PRHRS in the secondary system. In this paper, the progress of the CLOF accident is described with experimental data of transient condition performed by SMART-ITL. Finally, the capability of passive safety system and inherent natural circulation will be evaluated.

Keywords: CLOF, natural circulation, PRHRS, SMART-ITL

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Authors: Jinghua Zhang

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Shaft-tunnel junction is a typical case of the structural nonuniformity in underground structures. The shaft and the tunnel possess greatly different structural features. Even under uniform excitations, they tend to behave discrepantly. Studies on shaft-tunnel junctions are mainly performed numerically. Shaking table tests are also conducted. Although many numerical and experimental data are obtained, an analytical solution still has great merits of gaining more insights into the shaft-tunnel problem. This paper will try to remedy the situation. Since the seismic responses of shaft-tunnel junctions are very related to directions of the excitations, they are studied in two scenarios: the longitudinal-excitation scenario and the transverse-excitation scenario. The former scenario will be addressed in this paper. Given that responses of the tunnel are highly dependent on the shaft, the analytical solutions would be developed firstly for the vertical shaft. Then, the seismic responses of the tunnel would be discussed. Since vertical shafts bear a resemblance to rigid caissons, the solution proposed in this paper is derived by introducing terms of shaft-tunnel and soil-tunnel interactions into equations originally developed for rigid caissons. The validity of the solution is examined by a validation model computed by finite element method. The mutual influence between the shaft and the tunnel is introduced. The soil-structure interactions are discussed parametrically based on the proposed equations. The shaft-tunnel relative displacement and the soil-tunnel relative stiffness are found to be the most important parameters affecting the magnitudes and distributions of the internal forces of the tunnel. A hinge-joint at the shaft-tunnel junction could significantly reduce the degree of stress concentration compared with a rigid joint.

Keywords: analytical solution, longitudinal excitation, numerical validation , shaft-tunnel junction

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Authors: Loïc Chrislin Nguedjio, S. Jerome Afoutou, Rostand Moutou Pitti, Benoit Blaysat, Frédéric Dubois, Naman Recho, Pierre Kisito Talla

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The safety and durability of structures remain challenging fields that continue to draw the attention of designers. One widely adopted approach is fracture mechanics, which provides methods to evaluate crack stability in complex geometries and under diverse loading conditions. The global energy approach is particularly comprehensive, as it calculates the energy release rate required for crack initiation and propagation using path-independent integrals. This study aims to extend these invariant integrals to include path-independent integrals, with the goal of enhancing the accuracy of failure predictions. The ultimate objective is to create more robust materials while optimizing structural safety and durability. By integrating the real and virtual field method with the virtual crack closure technique, a new formulation of the M-integral is introduced. This formulation establishes a direct relationship between local stresses on the crack faces and the opening displacements, allowing for an accurate calculation of fracture energy. The analytical calculations are grounded in the assumption that the energy needed to close a crack virtually is equal to the energy released during its opening. This novel integral is implemented in a finite element code using Cast3M to simulate cracking criteria within a wood material context. Initially, the numerical calculations are focused on plane strain conditions, but they are later extended to three-dimensional environments, taking into account the orthotropic nature of wood.

Keywords: energy release rate, path-independent integrals, virtual crack closure, orthotropic material

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Authors: Jagdish Prasad Maurya, Sanjay Kumar Pandey

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Inadequate understanding of the complex nature of flow features in tornado vortex is a major problem in modelling tornadoes. Tornadoes are violent atmospheric phenomenon that appear all over the world. Modelling tornadoes aim to reduce the loss of the human lives and material damage caused by the tornadoes. Dynamics of tornado is investigated by a numerical technique, the improved version of the projection method. In this paper, authors solve the problem for axisymmetric tornado vortex by the said method that uses a finite difference approach for getting an accurate and stable solution. The conclusions drawn are that large radial inflow velocity occurs near the ground that leads to increase the tangential velocity. The increased velocity phenomenon occurs close to the boundary and absolute maximum wind is obtained near the vortex core. The results validate previous numerical and theoretical models.

Keywords: computational fluid dynamics, mathematical model, Navier-Stokes equations, tornado

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Authors: Isa Ahmadi, Ramin Khamedi

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In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C1 continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: cyclic loading, finite element analysis, Prager kinematic hardening model, torsion of shaft

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Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Abera Kotu, Girma Tesema, Mitiku Tadesse

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This study investigated ACE supported instruction and pre-service mathematics teachers’ mental construction in solving equations and inequalities. A mixed approach with concurrent parallel design was employed. It was conducted on two intact groups of regular first-year pre-service mathematics teachers at Fiche College of Teachers’ Education in which one group was assigned as an intervention group and the other group as a comparison group using the lottery method. There were 33 participants in the intervention and 32 participants in the comparison. Six pre-service mathematics teachers were selected for interview using purposive sampling based on pre-test results. An instruction supported with ACE cycle was given to the intervention group for two weeks duration of time. Written tasks, interviews, and observations were used to collect data. Data collected from written tasks were analyzed quantitatively using independent samples t-test and effect size. Data collected from interviews and observations were analyzed narratively. The findings of the study uncovered that ACE-supported instruction has a moderate effect on Pre-service Mathematics Teachers’ levels of conceptualizations of action, process, object, ad schema. Moreover, the ACE supported group out scored and performed better than the usual traditional method supported groups across the levels of conceptualization. The majority of pre-service mathematics teachers’ levels of conceptualizations were at action and process levels and their levels of conceptualization were linked with genetic decomposition more at action and object levels than object and schema. The use of ACE supported instruction is recommended to improve pre-service mathematics teachers’ mental construction.

Keywords: ACE teaching cycle, APOS theory, mental construction, genetic composition

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

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On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: Ali Reza Tahavvor‚ Saeed Hosseini, Behnam Amiri

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Concentric and eccentric annulus is used frequently in technical and industrial applications such as nuclear reactors, thermal storage system and etc. In this paper, computational fluid dynamics (CFD) is used to investigate two dimensional free convection of laminar flow in annulus with isotherm cylinders surface and cooler inner surface. Problem studied in thirty different cases. Due to natural convection continuity and momentum equations are coupled and must be solved simultaneously. Finite volume method is used for solving governing equations. The purpose was to obtain the eccentricity effect on Nusselt number in different Rayleight numbers, so streamlines and temperature fields must be determined. Results shown that the highest Nusselt number values occurs in degree of eccentricity equal to 0.5 upward for inner cylinder and degree of eccentricity equal to 0.3 upward for outer cylinder. Side eccentricity reduces the outer cylinder Nusselt number but increases inner cylinder Nusselt number. The trend in variation of Nusselt number with respect to eccentricity remain similar in different Rayleight numbers. Correlations are included to calculate the Nusselt number of the cylinders.

Keywords: natural convection, concentric, eccentric, Nusselt number, annulus

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Authors: Oveis Abedinia, Noradin Ghadimi, Nasser Mikaeilvand, Roza Poursoleiman, Asghar Poorfaraj

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In this paper a robust Fuzzy Proportional Integral Differential (PID) controller is applied to multi-machine power system based on Modified Shuffled Frog Leaping (MSFL) algorithm. This newly proposed controller is more efficient because it copes with oscillations and different operating points. In this strategy the gains of the PID controller is optimized using the proposed technique. The nonlinear problem is formulated as an optimization problem for wide ranges of operating conditions using the MSFL algorithm. The simulation results demonstrate the effectiveness, good robustness and validity of the proposed method through some performance indices such as ITAE and FD under wide ranges operating conditions in comparison with TS and GSA techniques. The single-machine infinite bus system and New England 10-unit 39-bus standard power system are employed to illustrate the performance of the proposed method.

Keywords: fuzzy PID, MSFL, multi-machine, low frequency oscillation

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Authors: Zineddine Bouyahiaoui, Rabah Haoui

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The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.

Keywords: blunt body, finite volume, hypersonic flow, viscous flow

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Authors: N. Ben-Mahmoud, M. Elfandi, A. Shallof

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This paper presents a methodology to design multivariable PID controllers for multi-input and multi-output systems. The proposed control strategy, which is centralized, combines of PID controllers. The proportional gains in the P controllers act as tuning parameters of (SISO) in order to modify the behavior of the loops almost independently. The design procedure consists of three steps: first, an ideal decoupler including integral action is determined. Second, the decoupler is approximated with PID controllers. Third, the proportional gains are tuned to achieve the specified performance. The proposed method is applied to representative processes.

Keywords: boiler turbine, MIMO, PID controller, control by decoupling, anti wind-up techniques

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Saleh Elawgali

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Current spectrums of a four pole-pair, 400 kW induction machine were calculated for the cases of full symmetry and static eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. Zooms of the current spectrums, around the 50 Hz fundamental harmonic as well as of the main slot harmonic zone, were included. The spectrums included refer to both calculated and measured currents.

Keywords: diagnostic, harmonic, induction machine, spectrum

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Authors: Gonzalez Carlos, Martinez Fransisco

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There are various types of analysis that allow us to involve seismic phenomena that cause strong requirements for structures that are designed by society; one of them is a probabilistic analysis which works from prediction equations that have been created based on metadata seismic compiled in different regions. These equations form models that are used to describe the 5% damped pseudo spectra response for the various zones considering some easily known input parameters. The biggest problem for the creation of these models requires data with great robust statistics that support the results, and there are several places where this type of information is not available, for which the use of alternative methodologies helps to achieve adjustments to different models of seismic prediction.

Keywords: GMPM, 5% damped pseudo-response spectra, models of seismic prediction, PSHA

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Authors: Nosakhare Enoma, Alphose Zingoni

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The requirements for various toroidal shell forms are increasing due to new applications, available storage space and the consideration of appearance. Because of the complexity of some of these structural forms, the finite element method is nowadays mainly used for their analysis, even for simple static studies. This paper presents an easy-to-use analytical algorithm for pressurized multi-segmented toroidal shells of revolution. The membrane solution, which acts as a particular solution of the bending-theory equations, is developed based on membrane theory of shells, and a general approach is formulated for quantifying discontinuity effects at the shell junctions using the well-known Geckeler’s approximation. On superimposing these effects, and applying the ensuing solution to the problem of the pressurized toroid with four segments, closed-form stress results are obtained for the entire toroid. A numerical example is carried out using the developed method. The analytical results obtained show excellent agreement with those from the finite element method, indicating that the proposed method can be also used for complementing and verifying FEM results, and providing insights on other related problems.

Keywords: bending theory of shells, membrane hypothesis, pressurized toroid, segmented toroidal vessel, shell analysis

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Authors: Yue-Tzu Yang, Shu-Ching Liao

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This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm2 ≦ ≦ 40W/cm2. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.

Keywords: microchannel heat sinks, conjugate heat transfer, optimization, genetic algorithm method

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