Wire antenna model of the vertical grounding electrode
|
|
- Spencer Casey
- 5 years ago
- Views:
Transcription
1 Boundary Elements and Other Mesh Reduction Methods XXXV 13 Wire antenna model of the vertical roundin electrode D. Poljak & S. Sesnic University of Split, FESB, Split, Croatia Abstract A straiht wire antenna model of the vertical roundin electrode has been presented in the paper. The formulation is based on the homoeneous interal equation of Pocklinton type for half-space problems. The influence of a finitely conductin half-space is taken into account via the correspondin reflection coicients. The Pocklinton equation is solved both numerically and analytically. The numerical solution is carried out via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Some illustrative computational examples are presented at the end. Keywords: vertical roundin electrode, antenna model, Pocklinton interal equation, boundary element method, analytical solution. 1 Introduction Vertical roundin electrode is considered to be one of the key components of practical roundin systems, particularly for the protection of wind turbines [1] as they are extremely vulnerable to lihtnin strikes due to their special shape and isolated locations, mainly in hih altitude areas. A typical realistic roundin system for wind turbines is rather complex and usually composed from rins, horizontal and vertical electrodes, respectively [1]. A frequency domain numerical/analytical antenna theory model of horizontal electrodes and rin electrodes as individual elements, has been carried out in [] (Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM) + analytical solution) and [3] (GB-IBEM), respectively. Vertical electrode, on the other hand, has not been analyzed as an individual element, to a reater extent, usin antenna model and related numerical and analytical solution procedures. doi:1.495/bem1311
2 14 Boundary Elements and Other Mesh Reduction Methods XXXV Thouh an electromanetic transient analysis of complex roundin systems for wind turbines has been already reported elsewhere, e.. in [1] where a combination of the rin, vertical rods and horizontal electrodes is considered, a detailed study of vertical electrode behavior, as an individual element, still remains rather important. Thus, of particular importance is the analytical analysis, as the complex practical confiurations consistin of straiht electrodes and rin incorporated in concrete blocks are rather difficult to deal with. Therefore, an analytical solution at least for the part of such eometry is of enineerin interest. Moreover, a trade-off between analytical and numerical approach clearly stressin out strenth and weaknesses of both approaches is necessary. The key parameter of the wire model is the current distribution induced alon the electrode bein excited by the equivalent current enerator. The wire antenna model of the electrode is based on the homoeneous Pocklinton interodifferential equation. The scattered voltae alon the electrode is obtained by interatin the scattered electric field enerated by the induced current. The impact of a round-air interface is taken into account via the correspondin Fresnel reflection coicient (within the numerical solution approach) and simplified reflection coicient approach arisin from the modified imae theory (within the analytical solution approach) [4]. The intero-differential relationships arisin from the proposed wire antenna model are numerically treated by means of the GB-IBEM and analytically. The scattered voltae alon the electrode is obtained by interatin the current derivative alon the electrode [5, 6]. Formulation Vertical roundin electrode of lenth L and radius a, buried in a lossy medium at depth d and excited by an equivalent current source is shown in Fi 1. Fiure 1: Vertical roundin electrode excited by the current source.
3 Boundary Elements and Other Mesh Reduction Methods XXXV 15 The overnin equations for the current and scattered voltae induced alon the vertical electrode can be readily derived from Maxwell s equations by enforcin the continuity conditions for the tanential components of the electric field alon the wire in the very similar manner as it was undertaken for the case of vertical electrode in [5] and horizontal electrode in [6]. A riorous approach to account for the influence of lossy medium to the frequency response of the roundin electrode is related to the solution of Sommerfeld interals, which is considered to be rather demandin and computationally expensive task [4 9]..1 Interal equation for the current alon the electrode The related homoeneous intero-differential equation of the Pocklinton type for the current distribution induced alon the electrode is iven by µ jω I ( z ) ( z, z ) dz 4 π L ( ) 1 I z ( z, z ) dz + Zs ( z) I ( z) = j4πω z z L (1) where the complex permittivity of the lossy round is iven by σ = r + () jω with r and σ bein the soil permittivity and conductivity, respectively. Furthermore, the Green function is of the form while ( ), and (, ) i (, ') (, ') (, ') zz = zz Γ zz (3) zz denotes the lossy medium Green function ( zz, ') zz is, accordin to the imae theory, iven by i ( zz, ') The propaation constant of the lossy round is ref γ jωµσ ω µ r 1 i γ R 1 e = (4) R γ R e = (5) R = (6) and R 1, R are the distances from the source and the imae to the observation point, respectively.
4 16 Boundary Elements and Other Mesh Reduction Methods XXXV The alternative approach, on the other hand, is related to the approximate reflection coicient approach [7, 8], which is used in this paper as well. Within the numerical solution the Fresnel reflection coicient (RC) is used [] 1 1 cosθ sin θ MIT n n x x Γ ref = ; θ = arct ; n = 1 1 d cosθ + sin θ n n (7) Furthermore, a simplified reflection coicient arisin from modified imae theory is used within the analytical solution [ 4] Γ MIT ref = + (8) The electrode is excited via an equivalent ideal current source with one terminal connected to the electrode and the other one rounded at infinity, as presented in Fi 1. This current source is incorporated into the Pocklinton equation formulation via the followin conditions at the electrode ends [5] ( ) ( ) I d = I, I L = (9) where I denotes the impressed unit current source. It is worth emphasizin that the knowlede of the electrode current provides the assessment of the scattered voltae.. The scattered voltae alon the electrode The scattered voltae alon the vertical electrode is defined by a line interal of the horizontal component of the scattered field (normal to the electrode and tanential to the round-air interface) from the remote soil to the electrode surface [5] a sct sct V ( z) Ex ( x, z) dx = (1) As the horizontal field component can be expressed in terms of the scalar potential radient sct E x φ = (11) x the scattered voltae alon the electrode can be written as follows a a ϕ (, ) ϕ (, ) (1) sct xz d V ( z) = dx = x z dx x dz
5 Boundary Elements and Other Mesh Reduction Methods XXXV 17 where ( xz, ) ϕ is defined by the followin particular interal 1 ϕ ( z) = q ( z ') ( z, z ') dz ' 4π (13) L and the chare density is linked to current distribution throuh the continuity equation [4] Substitutin continuity equation (14) into (13) yields 1 di q = jω dz (14) ( ') 1 I z ϕ ( z) = ( z, z ') dz ' j4 πω (15) z' L Insertin (15) into (1) and assumin the scalar potential in the remote soil to be zero [1], ives the scattered voltae alon the electrode ( ) sct 1 I z V ( z) = ( z, z ) dz j4πω (16) z L Note that the tedious interation from infinity to the electrode surface is avoided by takin the advantae of the very definition of voltae alon the electrode (1). 3 Solution The Pocklinton equation (1) is solved numerically and analytically, respectively. The numerical solution is undertaken via the GB-IBEM [4]. 3.1 Numerical solution The unknown current I e (z ) alon the straiht wire sement can be written as follows T ( ') { } { } e I z = f I (17) Assemblin the contributions from each sement, the Pocklinton equation (1) is transferred into the matrix equation M [ Z ] { I} =, and j = 1,,..., M (18) ji i j= 1 where M is the total number of sements and [Z] ji iven by
6 18 Boundary Elements and Other Mesh Reduction Methods XXXV T T Fr [ ] = { } { } ( ) { } { } ref i ( ) ji j + Γ i j i Z D D ' z, z ' dz ' D D ' z, z ' dz ' + γ lj li lj li T { } { } ( ) j i lj f f z, z ' dz ' dz li (19) is the mutual impedance matrix representin the interaction of the i-th source with the j-th observation sement, respectively. The matrices {f} and {f } contain the shape functions while {D} and {D } contain their derivatives, and l i, l j are the widths of i-th and j-th boundary elements. A linear approximation over a wire sement is used in this work, as it was shown to be optimal in various EMC problems includin thin wire confiurations. More details on the method can be found elsewhere, e.. in [4]. 3. Analytical solution The Pocklinton equation (1) can be solved analytically under certain conditions. It is convenient to write (1) in a followin way ( ') I z, ( ) ( ) () 1 γ ( z z ) dz + Zs z I z = j4πω z z L The first step in the analytical solution of () is to write the interal on the left-hand side of (1) as follows I( z' ) ( z, z' ) dz' = I( z) ( z, z' ) dz' + I( z' ) I( z) ( z, z' ) dz' (1) L L L The interal on the left hand side of (1) is now approximated by the first term on the riht hand side of (1), i.e. the second interal on the riht hand side of (1) is nelected. Furthermore, the solution of characteristic interal from (1) is L L L h+ h+ h+ jkr jkr e e L L ψ =, ' ' = ' +Γ ' = ln Γ ln R R a d i MIT MIT ( z z ) dz dz dz () ref ref L L L i h h h Consequently, the Pocklinton equation () simplifies into the partial differential equation of the form z γ I( z) = (3) The analytical solution of (3) is sh γ eq ( d + L z) I( z) = I (4) sh γ L ( eq )
7 Boundary Elements and Other Mesh Reduction Methods XXXV 19 where = + Z (5) γ eq γ j4πω ψ Furthermore, the scattered voltae alon the electrode (16) is iven by ( γ eq ) ( ) sct 1 I z V ( z) = ( z, z ) dz j4πω z L γ eq I = chγ eq ( d + L z) ( z, z ) dz ' j4πω sh L L and can be evaluated by means of numerical interation procedures. 4 Results s (6) The first set of the results is related to the absolute value of spatial distribution of induced current computed numerically and analytically, while the second set deals with the results for the scattered voltae induced alon the electrode and computed via both approaches, as well. The results are obtained for the followin parameters of the electrode: L=1 m, d=.3 m, a=5 mm. The excitation is the ideal current source I =1 A. Ground permittivity is r =1. All Fiures show the absolute value of the current distribution alon the electrode. Fiure shows the current distribution alon the electrode at the operatin frequency f=1 MHz for the round conductivity σ=.1 S/m. The results computed analytically and via GB-IBEM aree rather satisfactorily. Fiure : Current distribution (absolute value) alon the vertical electrode for f=1 MHz and σ=.1 S/m.
8 11 Boundary Elements and Other Mesh Reduction Methods XXXV Fiure 3 shows the current distribution alon the same electrode at the frequency f=1 MHz for the round conductivity σ=.1 S/m. The waveforms obtained via different approaches are still alike. However for the lower value of conductivity (σ=.1 S/m) differences in the results for the current distribution are slihtly hiher. Fiures 4 and 5 show the distribution of the scattered voltae induced alon the same electrode for different values of round conductivity at f=1 MHz. Fiure 3: Current distribution (absolute value) alon the vertical electrode for f=1 MHz and σ=.1 S/m. Fiure 4: Scattered voltae distribution (absolute value) alon the vertical electrode for f=1 MHz and σ=.1 S/m.
9 Boundary Elements and Other Mesh Reduction Methods XXXV 111 Fiure 5: Scattered voltae distribution (absolute value) alon the vertical electrode for f=1 MHz and σ=.1 S/m. A satisfactory areement between analytical and numerical results is achieved. Aain, certain differences are noticeable at f=1 MHz for lower value of round conductivity. It is worth notin that the problem of the vertical electrode transient response in principle does not have a solution in the closed form. Consequently, the numerical solution is considered to be exact one, or at least more realistic in this case contrary to the usual cases (if analytical solution is available) where the oal of comparin numerical with analytical solutions is to show converence of the numerical towards analytical results. 5 Conclusion The paper deals with an analysis of vertical roundin electrode by means of straiht wire antenna model featurin both numerical and analytical approach, respectively. The formulation is based on the solution of the homoeneous Pocklinton intero-differential equation for half-space problems in the frequency domain. The presence of a lossy round is taken into account via correspondin reflection coicients. The numerical solution is carried out via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB- IBEM). The same problem is also treated via the approximate analytical solution. Some illustrative computational examples are iven in the paper.
10 11 Boundary Elements and Other Mesh Reduction Methods XXXV References [1] D. Cavka, D. Poljak, V. Doric, R. Goic, Transient Analysis of Wind Turbines, Renewable Enery 43, pp , 1. [] D. Poljak, S. Sesnic, and R. Goic, Analytical versus boundary element modellin of horizontal round electrode, Enineerin Analysis with Boundary Elements, 34, pp , 1. [3] D. Cavka, D. Poljak, R. Goic, Transient Analysis of Rin Shaped Groundin Electrode usin Isoparametric Quadratic Elements, Proc. ICLP 1. [4] D. Poljak, Advanced Modelin in Computational Electromanetic Compatibility. New Jersey, USA: Wiley-Interscience, 7. [5] D. Poljak, V. Doric, Wire antenna Model for Transient Analysis of Simple Groundin systems, Part I: The Vertical Groundin Electrode, Proress in Electromanetics Research, PIER 64, pp , 6. [6] D. Poljak, V. Doric, Wire antenna Model for Transient Analysis of Simple Groundin systems, Part II: The Horizontal Groundin Electrode, Proress in Electromanetics Research, PIER 64, pp , 6. [7] E. K. Miller, A. J. Poio, G. J. Burke, and E. S. Selden, Analysis of wire Antennas in the Presence of a Conductin Half-Space. Part I. The Vertical Antenna in Free Space, Canadian Journal of Physics, 5, pp , 197. [8] E. K. Miller, A. J. Poio, G. J. Burke, and E. S. Selden, Analysis of wire Antennas in the Presence of a Conductin Half-Space. Part II. The Horizontal Antenna in Free Space, Canadian Journal of Physics, 5, pp , 197. [9] R. G. Olsen, M. C. Willis, A Comparison of Exact and Quasi-static Methods for Evaluatin Groundin Systems at Hih Frequencies, IEEE Trans. Power Delivery, 11 (), pp , April [1] F. M. Tesche, M. Ianoz, and T. Karlsson, EMC Analysis Methods and Computational Models. New York, USA: John Wiley & Sons, Inc., 1997.
Lightning Transients on Branched Distribution Lines Considering Frequency-Dependent Ground Parameters
214 International Conference on Lihtnin Protection (ICLP), Shanhai, China Lihtnin Transients on Branched Distribution Lines Considerin Frequency-Dependent Ground Parameters Alberto De Conti LRC Lihtnin
More informationTWINS II ANNA ŠUŠNJARA, VICKO DORIĆ & DRAGAN POLJAK
TWINS II ANNA ŠUŠNJARA, VICKO DORIĆ & DRAGAN POLJAK Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture University of Split, Croatia Training School on Ground Penetrating Radar
More informationAnalysis of log-periodic dipole arrays with boundary elements
Boundary Elements and Other Mesh Reduction Methods XXX 75 Analysis of log-periodic dipole arrays with boundary elements D. Poljak 1, V. Doric 1, M. Birkic 2 & D. Kosor 3 1 Department of Electronics, University
More informationWIRE ANTENNA MODEL FOR TRANSIENT ANALYSIS OF SIMPLE GROUNDINGSYSTEMS, PART I: THE VERTICAL GROUNDING ELECTRODE
Progress In Electromagnetics Research, PIER 64, 149 166, 2006 WIRE ANTENNA MODEL FOR TRANSIENT ANALYSIS OF SIMPLE GROUNDINGSYSTEMS, PART I: THE VERTICAL GROUNDING ELECTRODE D. Poljak and V. Doric Department
More informationEfficient method for obtaining parameters of stable pulse in grating compensated dispersion-managed communication systems
3 Conference on Information Sciences and Systems, The Johns Hopkins University, March 12 14, 3 Efficient method for obtainin parameters of stable pulse in ratin compensated dispersion-manaed communication
More informationMODELING A METAL HYDRIDE HYDROGEN STORAGE SYSTEM. Apurba Sakti EGEE 520, Mathematical Modeling of EGEE systems Spring 2007
MODELING A METAL HYDRIDE HYDROGEN STORAGE SYSTEM Apurba Sakti EGEE 520, Mathematical Modelin of EGEE systems Sprin 2007 Table of Contents Abstract Introduction Governin Equations Enery balance Momentum
More information2.3. PBL Equations for Mean Flow and Their Applications
.3. PBL Equations for Mean Flow and Their Applications Read Holton Section 5.3!.3.1. The PBL Momentum Equations We have derived the Reynolds averaed equations in the previous section, and they describe
More informationDesign of Chevron Gusset Plates
017 SEAOC CONENTION PROCEEDINGS Desin of Chevron Gusset Plates Rafael Sali, Director of Seismic Desin Walter P Moore San Francisco, California Leih Arber, Senior Enineer American Institute of Steel Construction
More informationStochastic collocation analysis of the transient current induced along the wire buried in a lossy medium
Computational Methods and Experimental Measurements XVII 47 Stochastic collocation analysis of the transient current induced along the wire buried in a lossy medium S. Šesnić 1, S. Lalléchère, D. Poljak
More information2.2 Differentiation and Integration of Vector-Valued Functions
.. DIFFERENTIATION AND INTEGRATION OF VECTOR-VALUED FUNCTIONS133. Differentiation and Interation of Vector-Valued Functions Simply put, we differentiate and interate vector functions by differentiatin
More informationA Mathematical Model for the Fire-extinguishing Rocket Flight in a Turbulent Atmosphere
A Mathematical Model for the Fire-extinuishin Rocket Fliht in a Turbulent Atmosphere CRISTINA MIHAILESCU Electromecanica Ploiesti SA Soseaua Ploiesti-Tiroviste, Km 8 ROMANIA crismihailescu@yahoo.com http://www.elmec.ro
More informationParametric Equations
Parametric Equations Suppose a cricket jumps off of the round with an initial velocity v 0 at an anle θ. If we take his initial position as the oriin, his horizontal and vertical positions follow the equations:
More informationModeling for control of a three degrees-of-freedom Magnetic. Levitation System
Modelin for control of a three derees-of-freedom Manetic evitation System Rafael Becerril-Arreola Dept. of Electrical and Computer En. University of Toronto Manfredi Maiore Dept. of Electrical and Computer
More informationCode_Aster. Element CABLE_GAINE
Titre : Élément CABLE_GAINE Date : 28/07/2015 Pae : 1/12 Element CABLE_GAINE Summary: The element CABLE_GAINE presented in this document is to model cables of prestressin bein able to rub or slip into
More information(a) 1m s -2 (b) 2 m s -2 (c) zero (d) -1 m s -2
11 th Physics - Unit 2 Kinematics Solutions for the Textbook Problems One Marks 1. Which one of the followin Cartesian coordinate system is not followed in physics? 5. If a particle has neative velocity
More informationFE Magnetic Field Analysis Simulation Models based Design, Development, Control and Testing of An Axial Flux Permanent Magnet Linear Oscillating Motor
Proceedins of the World Conress on Enineerin 9 Vol I WCE 9, July 1-3, 9, London, U.K. FE Manetic Field Analysis Simulation Models based Desin, Development, Control and Testin of An Axial Flux Permanent
More informationCornell s ERL User Area Shielding Considerations
Cornell s ERL User Area Shieldin Considerations Kyle Ausfeld Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627 (Dated: Auust 7, 2009) The proposed Enery Recovery Linac
More informationONLINE: MATHEMATICS EXTENSION 2 Topic 6 MECHANICS 6.3 HARMONIC MOTION
ONINE: MATHEMATICS EXTENSION Topic 6 MECHANICS 6.3 HARMONIC MOTION Vibrations or oscillations are motions that repeated more or less reularly in time. The topic is very broad and diverse and covers phenomena
More informationTHE IMPACT OF ELEVATED MASTS ON LIGHTNING INCIDENCE AT THE RADIO-BASE-STATION VICINITIES
X International Symosium on Lihtnin Protection 9 th -13 th November, 9 Curitiba, Brazil THE IMPACT OF ELEVATED MASTS ON LIGHTNING INCIDENCE AT THE RADIO-BASE-STATION VICINITIES Rosilene Nietzsch Dias 1,
More informationCourse , General Circulation of the Earth's Atmosphere Prof. Peter Stone Section 8: Lorenz Energy Cycle
Course.8, General Circulation of the Earth's Atmosphere Prof. Peter Stone Section 8: Lorenz Enery Cycle Enery Forms: As we saw in our discussion of the heat budet, the enery content of the atmosphere per
More information11. Excitons in Nanowires and Nanotubes
Excitons in Nanowires and Nanotubes We have seen that confinement in quantum wells leads to enhanced excitonic effects in the optical response of semiconductors The bindin enery of the stronest bound excitons
More informationANALYSIS OF POWER EFFICIENCY FOR FOUR-PHASE POSITIVE CHARGE PUMPS
ANALYSS OF POWER EFFCENCY FOR FOUR-PHASE POSTVE CHARGE PUMPS Chien-pin Hsu and Honchin Lin Department of Electrical Enineerin National Chun-Hsin University, Taichun, Taiwan e-mail:hclin@draon.nchu.edu.tw
More informationMathematical Analysis of Efficiencies in Hydraulic Pumps for Automatic Transmissions
TECHNICAL PAPER Mathematical Analysis of Efficiencies in Hydraulic Pumps for Automatic Transmissions N. YOSHIDA Y. INAGUMA This paper deals with a mathematical analysis of pump effi ciencies in an internal
More informationJ.L. Kirtley Jr. September 4, 2010
Massachusetts Institute of Technoloy Department of Electrical Enineerin and Computer Science 6.007 Electromanetic Enery: From Motors to Lasers Supplemental Class Notes Manetic Circuit Analo to Electric
More informationSlip-Flow and Heat Transfer in Isoflux Rectangular Microchannels with Thermal Creep Effects
Journal of Applied Fluid Mechanics, Vol. 3, No. 2, pp. 33-4, 200. Available online at www.jafmonline.net, ISSN 735-3645. Slip-Flow and Heat Transfer in Isoflux Rectanular Microchannels with Thermal Creep
More informationMotion in Two Dimensions Sections Covered in the Text: Chapters 6 & 7, except 7.5 & 7.6
Motion in Two Dimensions Sections Covered in the Tet: Chapters 6 & 7, ecept 7.5 & 7.6 It is time to etend the definitions we developed in Note 03 to describe motion in 2D space. In doin so we shall find
More informationDynamical Diffraction
Dynamical versus Kinematical Di raction kinematical theory valid only for very thin crystals Dynamical Diffraction excitation error s 0 primary beam intensity I 0 intensity of other beams consider di racted
More informationGeneration of random waves in time-dependent extended mild-slope. equations using a source function method
Generation of random waves in time-dependent etended mild-slope equations usin a source function method Gunwoo Kim a, Chanhoon Lee b*, Kyun-Duck Suh c a School of Civil, Urban, and Geosystem Enineerin,
More informationAltitude measurement for model rocketry
Altitude measurement for model rocketry David A. Cauhey Sibley School of Mechanical Aerospace Enineerin, Cornell University, Ithaca, New York 14853 I. INTRODUCTION In his book, Rocket Boys, 1 Homer Hickam
More informationOpen boundary conditions for barotropic waves
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C5, 3168, doi:10.109/00jc00159, 003 Open boundary conditions for barotropic waves J. Nycander and K. Döös Department of Meteoroloy, Stockholm University,
More information11 Free vibrations: one degree of freedom
11 Free vibrations: one deree of freedom 11.1 A uniform riid disk of radius r and mass m rolls without slippin inside a circular track of radius R, as shown in the fiure. The centroidal moment of inertia
More informationPneumatic Conveying in Horizontal Pipes: Eulerian Modeling and Pressure Drop Characteristics
American Journal of Mathematical and Computational Sciences 08; (): 0-6 http://www.aascit.or/journal/ajmcs Pneumatic Conveyin in Horizontal Pipes: Eulerian Modelin and Pressure Drop Characteristics Pandaba
More informationAdvanced Methods Development for Equilibrium Cycle Calculations of the RBWR. Andrew Hall 11/7/2013
Advanced Methods Development for Equilibrium Cycle Calculations of the RBWR Andrew Hall 11/7/2013 Outline RBWR Motivation and Desin Why use Serpent Cross Sections? Modelin the RBWR Axial Discontinuity
More informationSchool of Nuclear Science and Engineering, North China Electric Power University, Beijing, China
Hindawi Publishin Corporation Science and Technoloy of Nuclear Installations Volume 06, Article ID 634065, paes http://dx.doi.or/0.55/06/634065 Research Article Development and Validation of a Three-Dimensional
More information1 CHAPTER 7 PROJECTILES. 7.1 No Air Resistance
CHAPTER 7 PROJECTILES 7 No Air Resistance We suppose that a particle is projected from a point O at the oriin of a coordinate system, the y-axis bein vertical and the x-axis directed alon the round The
More informationWindow energy rating systems
Window enery ratin systems Claus F. Jensen, MSc Svend Svendsen, Professor 1. INTRODUCTION Different window enery ratin systems are bein developed in Denmark and in Europe. The purpose of a controlled and
More informationLinearized optimal power flow
Linearized optimal power flow. Some introductory comments The advantae of the economic dispatch formulation to obtain minimum cost allocation of demand to the eneration units is that it is computationally
More informationAn eigen theory of waves in piezoelectric solids
Acta Mech Sin (010 6:41 46 DOI 10.1007/s10409-009-031-z RESEARCH PAPER An eien theory of waves in piezoelectric solids Shaohua Guo Received: 8 June 009 / Revised: 30 July 009 / Accepted: 3 September 009
More information(a) Find the function that describes the fraction of light bulbs failing by time t e (0.1)x dx = [ e (0.1)x ] t 0 = 1 e (0.1)t.
1 M 13-Lecture March 8, 216 Contents: 1) Differential Equations 2) Unlimited Population Growth 3) Terminal velocity and stea states Voluntary Quiz: The probability density function of a liht bulb failin
More informationA Non Isothermal Two-Phase Model for the Air-Side Electrode of PEM Fuel Cells
A Non Isothermal Two-Phase Model for the Air-Side Electrode of PEM Fuel Cells M. Khakbaz Baboli 1 and M. J. Kermani 2 Department of Mechanical Enineerin Amirkabir University of technoloy (Tehran Polytechnic)
More informationFREQUENCY DEPENDENT CHARACTERISTICS OF GROUNDING SYSTEM BURIED IN MULTILAYERED EARTH MODEL BASED ON QUASI-STATIC ELECTRO- MAGNETIC FIELD THEORY
Progress In Electromagnetics Research M, Vol. 33, 169 183, 2013 FREQUENCY DEPENDENT CHARACTERISTICS OF GROUNDING SYSTEM BURIED IN MULTILAYERED EARTH MODEL BASED ON QUASI-STATIC ELECTRO- MAGNETIC FIELD
More informationEffect of Frequency and Moisture Variation on Dielectric Properties of Pearl Millet in Powder Form
J. Environ. Nanotechnol. Volume (013) 01-05 pp. ISSN (Print) : 79-0748 ISSN (Online) : 319-5541 Effect of Frequency and Moisture Variation on Dielectric Properties of Pearl Millet in Powder Form Nidhi
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science
Massachusetts nstitute of Technoloy Department of Electrical Enineerin and Computer Science 6.685 Electric Machines Class Notes 2 Manetic Circuit Basics September 5, 2005 c 2003 James L. Kirtley Jr. 1
More informationSTOCHASTICALLY GENERATED MULTIGROUP DIFFUSION COEFFICIENTS
STOCHASTICALLY GENERATED MULTIGROUP DIFFUSION COEFFICIENTS A Thesis Presented to The Academic Faculty by Justin M. Pounders In Partial Fulfillment of the Requirements for the Deree Master of Science in
More informationConical Pendulum: Part 2 A Detailed Theoretical and Computational Analysis of the Period, Tension and Centripetal Forces
European J of Physics Education Volume 8 Issue 1 1309-70 Dean onical Pendulum: Part A Detailed heoretical and omputational Analysis of the Period, ension and entripetal orces Kevin Dean Physics Department,
More informationFREE VIBRATION CHARACTERISTICS OF LAMINATED COMPOSITE JOINED CONICAL-CYLINDRICAL SHELLS
Journal of Sound and
More information[ ][ ] mg = R GM g = R GM = g R 2. Definition of G: From (1) we have, 2 NEWTON S LAW OF GRAVITATION:
NEWTON S LAW OF GAVITATION: Statement: Every particle in the universe attracts every other particle with a force which is directly proportional to the product of the masses and inversely proportional to
More informationUniversity of Thessaly Volos, Greece
th HSTAM International Conress on Mechanics Chania, Crete, Greece, 5 7 May, PRETWISTED BEAMS IN AXIA TENSION AND TORSION: AN ANAOGY WITH DIPOAR GRADIENT EASTICITY AND APPICATIONS TO TEXTIE MATERIAS Kordolemis
More informationHomework # 2. SOLUTION - We start writing Newton s second law for x and y components: F x = 0, (1) F y = mg (2) x (t) = 0 v x (t) = v 0x (3)
Physics 411 Homework # Due:..18 Mechanics I 1. A projectile is fired from the oriin of a coordinate system, in the x-y plane (x is the horizontal displacement; y, the vertical with initial velocity v =
More informationThermo-Mechanical Damage Modeling of Polymer Matrix Composite Structures in Fire
Thermo-Mechanical Damae Modelin of Polymer Matrix Composite Structures in Fire CHANGSONG LUO, and JIM LUA Global Enineerin and Materials, Inc. One Airport Place, Suite One Princeton, NJ 08540 USA ABSTRACT
More informationFOOTING FIXITY EFFECT ON PIER DEFLECTION
Southern Illinois University Carbondale OpenSIUC Publications Department of Civil and Environmental Enineerin Fall 9--04 FOOTING FIXITY EFFECT ON PIER DEFECTION Jen-kan Kent Hsiao Yunyi Jian Southern Illinois
More informationOn the falling (or not) of the folded inextensible string
On the fallin (or not) of the folded inextensible strin Tyler McMillen Proram in Applied and Computational Mathematics, Princeton University, Fine Hall, Princeton, NJ 8544-1 e-mail: mcmillen@princeton.edu
More informationExperiment 3 The Simple Pendulum
PHY191 Fall003 Experiment 3: The Simple Pendulum 10/7/004 Pae 1 Suested Readin for this lab Experiment 3 The Simple Pendulum Read Taylor chapter 5. (You can skip section 5.6.IV if you aren't comfortable
More informationTip-sample control using quartz tuning forks in near-field scanningoptical microscopes
1 Tip-sample control usin quartz tunin forks in near-field scanninoptical microscopes Contributed by Xi Chen and Zhaomin Zhu 1 Introduction In near-field scannin optical microscopy (NSOM), a subwavelenth
More informationChapter 8 Applications of Newton s Second Law
81 Force Laws 2 Chapter 8 Applications of Newton s Second Law 811 Hooke s Law 2 822 Principle of Equivalence: 6 823 Gravitational Force near the Surface of the Earth 7 824 Electric Chare and Coulomb s
More information7.2 Maximization of the Range of a Rocket
138 CHAPTER 7. SOME APPLICATIONS The counterintuitive answer that a supersonic aircraft must dive first in order to climb to a iven altitude in minimum time was first discovered by Walter Denham and Art
More informationv( t) g 2 v 0 sin θ ( ) ( ) g t ( ) = 0
PROJECTILE MOTION Velocity We seek to explore the velocity of the projectile, includin its final value as it hits the round, or a taret above the round. The anle made by the velocity vector with the local
More informationPI3CH400 4-Bit Bus Switch, Enable Low 1.8V/2.5V/3.3V, High-Bandwidth, Hot Plug
1.8V/2.5V/3.3V, Hih-Bandwidth, Hot Plu Features Near-Zero propaation delay 5-ohm switches connect inputs to outputs Hih sinal passin bandwidth (500 MHz) Beyond Rail-to-Rail switchin - 0 to 5V switchin
More informationExam 2A Solution. 1. A baseball is thrown vertically upward and feels no air resistance. As it is rising
Exam 2A Solution 1. A baseball is thrown vertically upward and feels no air resistance. As it is risin Solution: Possible answers: A) both its momentum and its mechanical enery are conserved - incorrect.
More informationV DD. M 1 M 2 V i2. V o2 R 1 R 2 C C
UNVERSTY OF CALFORNA Collee of Enineerin Department of Electrical Enineerin and Computer Sciences E. Alon Homework #3 Solutions EECS 40 P. Nuzzo Use the EECS40 90nm CMOS process in all home works and projects
More informationDielectric characteristics of glass fibre reinforced plastics and their components
Plasticheskie Massy, No. 11, 2004, pp. 20 22 Dielectric characteristics of lass fibre reinforced plastics and their components V. I. Sokolov, S. I. Shalunov, I. G. Gurtovnik, L. G. Mikheeva, and I. D.
More informationLab 4: Frequency Response of CG and CD Amplifiers.
ESE 34 Electronics aboratory B Departent of Electrical and Coputer Enineerin Fall 2 ab 4: Frequency esponse of CG and CD Aplifiers.. OBJECTIVES Understand the role of input and output ipedance in deterinin
More informationTransient radiation of a thin wire antenna buried in a dielectric half space
Transient radiation of a thin wire antenna buried in a dielectric half space D. Poljak ', B. Jajac * & N.Kovai: ~Departmentof Electronics, 2Department ofelectrical Engineering, University of Split, Croatia
More informationDynamic Response of Cantilever Retaining Walls Considering Soil Non-Linearity
Missouri University of Science and Technoloy Scholars' Mine International Conferences on Recent Advances in Geotechnical Earthquake Enineerin and Soil Dynamics 2 - Fifth International Conference on Recent
More informationIntegration in General Relativity
arxiv:physics/9802027v1 [math-ph] 14 Feb 1998 Interation in General Relativity Andrew DeBenedictis Dec. 03, 1995 Abstract This paper presents a brief but comprehensive introduction to certain mathematical
More informationAcoustic Noise Reduction of Switched Reluctance Motor Drives
Middle-East Journal of Scientific Research 8 (6): 118-16, 11 ISSN 199-933 IDOSI Publications, 11 Acoustic Noise Reduction of Switched Reluctance Motor Drives M. Divandari and M.M. Kabir Department of Enineerin,
More informationEnergizing Math with Engineering Applications
Enerizin Math with Enineerin Applications Understandin the Math behind Launchin a Straw-Rocket throuh the use of Simulations. Activity created by Ira Rosenthal (rosenthi@palmbeachstate.edu) as part of
More informationa/2 a/2 thickness: b TWO DIMENSIONAL ANALYSIS OF AN E-CORE INDUCTOR
TWO DIMENSIONAL ANALYSIS OF AN E-CORE INDUCTOR R. Mertens, K. Hameyer and R. Belmans Katholieke Universiteit Leuven, Dep. EE (ESAT), Div. ELEN, Kardinaal Mercierlaan 94, B-3001 Heverlee, Belium ABSTRACT:
More informationBoundary element modelling of the metalic post protection zone
Boundary element modelling of the metalic post protection zone B. 3ajac1, D. poljak2 &N. ~0vai5' I Department of Electrical Engineering, University of Split, Croatia 2 Department of Electronics, University
More informationHEAT TRANSFER IN EXHAUST SYSTEM OF A COLD START ENGINE AT LOW ENVIRONMENTAL TEMPERATURE
THERMAL SCIENCE: Vol. 14 (2010) Suppl. pp. S219 S232 219 HEAT TRANSFER IN EXHAUST SYSTEM OF A COLD START ENGINE AT LOW ENVIRONMENTAL TEMPERATURE by Snežana D. PETKOVIĆ a Radivoje B. PEŠIĆ b b and Jovanka
More informationANALYZE In all three cases (a) (c), the reading on the scale is. w = mg = (11.0 kg) (9.8 m/s 2 ) = 108 N.
Chapter 5 1. We are only concerned with horizontal forces in this problem (ravity plays no direct role). We take East as the +x direction and North as +y. This calculation is efficiently implemented on
More information4/3 Problem for the Gravitational Field
4/3 Problem for the ravitational Field Sere. Fedosin PO bo 6488 Sviaeva str. -79 Perm Russia E-mail: intelli@list.ru Abstract The ravitational field potentials outside and inside a uniform massive ball
More informationProblem Set 2 Solutions
UNIVERSITY OF ALABAMA Department of Physics and Astronomy PH 125 / LeClair Sprin 2009 Problem Set 2 Solutions The followin three problems are due 20 January 2009 at the beinnin of class. 1. (H,R,&W 4.39)
More informationTIME DOMAIN ANALYTICAL MODELING OF A STRAIGHT THIN WIRE BURIED IN A LOSSY MEDIUM. Otto-von-Guericke University Magdeburg, Magdeburg D-39106, Germany
Progress In Electromagnetics Research, Vol., 485 54, TIME DOMAIN ANALYTICAL MODELING OF A STRAIGHT THIN WIRE BURIED IN A LOSSY MEDIUM S. Sesnić, *, D. Poljak, and S. Tkachenko Faculty of Electrical Engineering,
More informationAdjustment of Sampling Locations in Rail-Geometry Datasets: Using Dynamic Programming and Nonlinear Filtering
Systems and Computers in Japan, Vol. 37, No. 1, 2006 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J87-D-II, No. 6, June 2004, pp. 1199 1207 Adjustment of Samplin Locations in Rail-Geometry
More informationFREQUENCY DOMAIN DETERMINISTIC-STOCHASTIC ANALYSIS
FREQUENCY DOMAIN DETERMINISTIC-STOCHASTIC ANALYSIS OF THE TRANSIENT CURRENT INDUCED ALONG A GROUND PENETRATING RADAR DIPOLE ANTENNA OVER A LOSSY HALF-SPACE ANNA ŠUŠNJARA 1 (CORRESPONDING AUTHOR), DRAGAN
More informationarxiv: v1 [quant-ph] 30 Jan 2015
Thomas Fermi approximation and lare-n quantum mechanics Sukla Pal a,, Jayanta K. Bhattacharjee b a Department of Theoretical Physics, S.N.Bose National Centre For Basic Sciences, JD-Block, Sector-III,
More informationSTUDY OF LOSS EFFECT OF TRANSMISSION LINES AND VALIDITY OF A SPICE MODEL IN ELECTROMAG- NETIC TOPOLOGY
Progress In Electromagnetics Research, PIER 90, 89 103, 2009 STUDY OF LOSS EFFECT OF TRANSMISSION LINES AND VALIDITY OF A SPICE MODEL IN ELECTROMAG- NETIC TOPOLOGY H. Xie, J. Wang, R. Fan, andy. Liu Department
More informationREVIEW: Going from ONE to TWO Dimensions with Kinematics. Review of one dimension, constant acceleration kinematics. v x (t) = v x0 + a x t
Lecture 5: Projectile motion, uniform circular motion 1 REVIEW: Goin from ONE to TWO Dimensions with Kinematics In Lecture 2, we studied the motion of a particle in just one dimension. The concepts of
More information1 Introduction. Korea Atomic Energy Research Institute, South Korea.
Tenth International Conference on Computational Fluid Dynamics (ICCFD10), Barcelona, Spain, July 9-13, 2018 ICCFD10-0206 Multi-physics approach for nuclear reactor analysis usin thermal-hydraulics and
More informationFinite Element Method (FEM)
Finite Element Method (FEM) The finite element method (FEM) is the oldest numerical technique applied to engineering problems. FEM itself is not rigorous, but when combined with integral equation techniques
More informationNANO 703-Notes. Chapter 12-Reciprocal space
1 Chapter 1-Reciprocal space Conical dark-field imain We primarily use DF imain to control imae contrast, thouh STEM-DF can also ive very hih resolution, in some cases. If we have sinle crystal, a -DF
More informationEquivalent rocking systems: Fundamental rocking parameters
Equivalent rockin systems: Fundamental rockin parameters M.J. DeJon University of Cambride, United Kindom E.G. Dimitrakopoulos The Hon Kon University of Science and Technoloy SUMMARY Early analytical investiations
More informationPHY 133 Lab 1 - The Pendulum
3/20/2017 PHY 133 Lab 1 The Pendulum [Stony Brook Physics Laboratory Manuals] Stony Brook Physics Laboratory Manuals PHY 133 Lab 1 - The Pendulum The purpose of this lab is to measure the period of a simple
More informationMULTIDIMENSIONAL COUPLED PHOTON-ELECTRON TRANSPORT SIMULATIONS USING NEUTRAL PARTICLE S N CODES
Computational Medical Physics Workin Group Workshop II ep 30 Oct 3 007 University of Florida (UF) Gainesville Florida UA on CD-ROM American Nuclear ociety LaGrane Park IL (007) MULTIDIMNIONAL COUPLD PHOTON-LCTRON
More informationMechanics Cycle 3 Chapter 12++ Chapter 12++ Revisit Circular Motion
Chapter 12++ Revisit Circular Motion Revisit: Anular variables Second laws for radial and tanential acceleration Circular motion CM 2 nd aw with F net To-Do: Vertical circular motion in ravity Complete
More informationANALYSIS OF THE INTERFACIAL AREA TRANSPORT MODEL FOR INDUSTRIAL 2-PHASE BOILING FLOW APPLICATIONS
ANALYSIS OF THE INTERFACIAL AREA TRANSPORT MODEL FOR INDUSTRIAL 2-PHASE BOILING FLOW APPLICATIONS K. Goodheart, N. Alleborn, A. Chatelain and T. Keheley AREVA - AREVA GmbH, Postbox 1109, 91001 Erlanen
More informationNumerical and Experimental Investigations of Lateral Cantilever Shaft Vibration of Passive-Pitch Vertical-Axis Ocean Current
R. Hantoro, et al. / International Enery Journal 1 (011) 191-00 191 Numerical and Experimental Investiations of Lateral Cantilever Shaft Vibration of Passive-Pitch Vertical-Axis Ocean Current R. Hantoro
More informationINFLUENCE OF TUBE BUNDLE GEOMETRY ON HEAT TRANSFER TO FOAM FLOW
HEFAT7 5 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Sun City, South Africa Paper number: GJ1 INFLUENCE OF TUBE BUNDLE GEOMETRY ON HEAT TRANSFER TO FOAM FLOW Gylys
More informationNumerical Simulation for Coal Carbonization Analysis of a Coke Oven Charge Using PHOENICS Huiqing Tang1 Zhancheng Guo1 Xinming Guo2 ABSTRACT
Numerical Simulation for Coal Carbonization Analysis of a Coke Oven Chare Usin PHOENICS Huiqin Tan 1 Zhanchen Guo 1 Xinmin Guo 2 1. Institute of Process Enineerin, Chinese Academy of Sciences, Beijin,
More informationExperiment 1: Simple Pendulum
COMSATS Institute of Information Technoloy, Islamabad Campus PHY-108 : Physics Lab 1 (Mechanics of Particles) Experiment 1: Simple Pendulum A simple pendulum consists of a small object (known as the bob)
More informationA Multigrid-like Technique for Power Grid Analysis
A Multirid-like Technique for Power Grid Analysis Joseph N. Kozhaya, Sani R. Nassif, and Farid N. Najm 1 Abstract Modern sub-micron VLSI desins include hue power rids that are required to distribute lare
More informationthe equations for the motion of the particle are written as
Dynamics 4600:203 Homework 02 Due: ebruary 01, 2008 Name: Please denote your answers clearly, ie, box in, star, etc, and write neatly There are no points for small, messy, unreadable work please use lots
More informationRenormalization Group Theory
Chapter 16 Renormalization Group Theory In the previous chapter a procedure was developed where hiher order 2 n cycles were related to lower order cycles throuh a functional composition and rescalin procedure.
More informationTransient analysis of the behaviour of grounding systems consisted by driven rods
Transient analysis of the behaviour of grounding systems consisted by driven rods I.F. GONOS M.K. ANTONIOU I.A. STATHOPULOS F.V. TOPALIS Department of Electrical and Computer Engineering, High Voltage
More informationIN this paper we investigate a propagative impact model. A propagative model of simultaneous impact: existence, uniqueness, and design consequences
1 A propaative model of simultaneous impact: existence, uniqueness, and desin consequences Vlad Sehete, Student Member, IEEE, Todd D. Murphey, Member, IEEE Abstract This paper presents existence and uniqueness
More informationAorangi (Mt. Cook) we typically view the state of the troposphere on "isobaric surfaces" (surfaces of constant pressure) rather
Ch3 (ctd.) EAS270_Ch3_BehaviourAtmos_B.odp JDW, EAS UAlberta, last mod. 19 Sept. 2016 Atmospheric "behaviour" Aorani (Mt. Cook) "ride" we typically view the state of the troposphere on "isobaric surfaces"
More information(A) (B) (C) (D) None of these
Exercise OBJECTIVE PROBLEMS. Action and reaction (A) act on two different objects (C) have opposite directions. Which fiure represents the correct F.B.D. of rod of mass m as shown in fiure : (B) have equal
More informationNumerical Analysis of Electromagnetic Fields in Multiscale Model
Commun. Theor. Phys. 63 (205) 505 509 Vol. 63, No. 4, April, 205 Numerical Analysis of Electromagnetic Fields in Multiscale Model MA Ji ( ), FANG Guang-You (ྠ), and JI Yi-Cai (Π) Key Laboratory of Electromagnetic
More informationImpact of sidewall spacer on gate leakage behavior of nano-scale MOSFETs
PACS 85.0.Tv Impact of sidewall spacer on ate leakae behavior of nano-scale MOSFETs Ashwani K. Rana 1, Narottam Chand, Vinod Kapoor 1 1 Department of Electronics and Communication, National Institute of
More information