Boundary Partial Stabilization of a Coupled Wave Equations on an Exterior Bounded Obstacle

We consider a boundary partial measure stabilization problem for a coupled wave equations on an exterior of bounded domain \({\Omega }=\mathbb {R}^{d}\setminus \overline {{\mathcal O}}\). With the theory of defect measure, we prove a uniformly result (exponential or polynomial) of stability in the energy space, under a geometrical control condition (BLR).     

Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type

In this paper, we study the stabilization of solutions of an axially moving string of kirchhoff type by a viscoelastic boundary control. We prove that the dissipation produced by the viscoelastic term is sufficient to suppress the transversal vibrations that occur during the axial motion of the string, and we also show that the string displacement decays in an arbitrary rate. When comparing with immobile strings, we conclude that the movement of the string itself produces enough extra damping ensuring the stabilization.     

Oscillation of Linear Ordinary Differential Equations: On a Theorem of A. Grigoriev

We give a simplified proof and an improvement of a recent theorem of A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions of systems of linear equations with polynomial or rational coefficients. To Yulij Sergeevich Ilyashenko on his 60th birthday. 2000 Mathematics Subject Classification. 34C08, 34C10, 34M10. Gershon Kekst professorial chair in Mathematics.     

Optimal Heating Control of Thermosensitive Rectangular Domain under Restrictions on Stresses in a Plastic Zone

A numerical algorithm to solve the problem on optimal heating control for a long isotropic homogeneous rectangular parallelepiped under plane strain has been proposed. The control (the surrounding temperature at one of the boundary surfaces of a parallelepiped) which in a minimal time, carries the body from the initial thermal state to the final one characterized by the given mean-integral temperature has been determined. In addition, restrictions both to the control function and to the maximal tangential stress intensity have been considered. The case of elastoplastic deformation of the material has been studied in the framework of the theory of the body element deformation along small curvature paths.     

Optimal Boundary Control of Thermal Stresses in a Plate Based on Time-Fractional Heat Conduction Equation

This article presents an optimal control problem for a fractional heat conduction equation that describes a temperature field. The main purpose of the research was to find the boundary temperature that takes the thermal stress under control. The fractional derivative is defined in terms of the Caputo operator. The Laplace and finite Fourier sine transforms were applied to obtain the exact solution. Linear approximation is used to get the numerical results. The dependence of the solution on the order of fractional derivative and on the nondimensional time is analyzed.     

Study on synchronization phenomena of fixed speed wind turbines with an induction generator in a wind farm

Synchronization of rotor angles of fixed speed wind energy converters with an induction generator has been reported in several wind farms. In terms of impacts on a power system, the synchronization could worsen the voltage flicker problems. Although many articles have examined this synchronization, there remains considerable room in the physical interpretation of the phenomena. This article discusses the physical context of the synchronization phenomena of wind turbines in a wind farm. After analysing interaction among electric power output, voltage, generator slip and rotor angle, differential equations describing the phenomena are presented. The synchronization phenomena are examined through a study on equilibria of the equations and their stability. Fundamental characteristics of the phenomena such as pull‐in force, speed of synchronization and the impact of discrepancies among generator characteristics are discussed for two‐ and three‐machine systems. The results show that synchronization tends to occur in wind energy converters with large 3p components and a low power factor, which are interconnected into a grid with large short‐circuit impedance of high X/R ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

The Influence of Graded Coatings on the Thermal Stress Intensity Factors of an Oblique Crack in a Semi-Infinite Substrate Subjected to Local Heating on the Boundary

Thermally induced singular behavior of an arbitrarily oriented crack in a homogeneous substrate overlaid with a functionally graded coating is considered, within the framework of linear plane thermoelasticity. It is assumed that the graded coating/substrate system is subjected to steady-state thermal loading applied over a finite region at the coating surface and the crack in the substrate is thermally insulated, disturbing the prescribed heat flow. Based on the method of Fourier integral transform and the coordinate transformations of basic field variables in thermoelasticity equations, formulation of the crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stresses in the coated medium. In the numerical results, the main emphasis is placed on the investigation of influences of loading, geometric, and material parameters of the coated system on the variations of mixed-mode thermal stress intensity factors. Further addressed are the probable cleavage angles for the incipient growth of the original crack and the corresponding values of effective tensile-mode stress intensity factors.     

Analytical solution of natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature by means of HAM

In this paper, fluid flow and heat transfer of vertical full cone embedded in porous media have been studied. Similarity solution for full cone subjected to wall temperature boundary conditions gives us a nonlinear ordinary differential equation which the obtained nonlinear ODE has been solved through homotopy analysis method (HAM). The obtained analytical solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region. By the way we also calculate Nusselt number that is an important parameter in heat transfer by obtained analytical solution by HAM.     

用渐近分析法研究蜂窝蓄热体温度分布

1前言在冶金、机械和石化工业锻造炉、均热炉、连续加热炉、热处理炉、钢包烘烤炉、辐射管和熔铝炉上应用的高温空气燃烧(High Temperature Air Combustion,Hi-TAC)[1],具有热效率高、低NOx排放和燃烧放热均匀等特点。大多数的HiTAC应用了蜂窝蓄热系统[2]。温度变化和温度效率(     

采用扩展温度振荡法测量超临界CO_2管内对流换热特性

提出了考虑小通道内流体温度变化时测量管内对流换热系数的扩展温度振荡法模型,该法可用于测量各种光滑表面通道内流动的局部对流换热系数。实测了典型压力温度条件下2mm内径不锈钢圆管内超临界CO2对流换热系数。     

A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.