Considerations on Certain Tribological Aspects of the System Brake Shoe Drum

Size: px
Start display at page:

Download "Considerations on Certain Tribological Aspects of the System Brake Shoe Drum"

Transcription

1 SCIENTIFIC BLLETIN, Serie C, Fascicle: Mechanics, Tribology, Machine Manuacuring Technology ISSN , Volume 2 No. XXVII Consideraions on Cerain Tribological Aspecs o he Sysem Brake Shoe Drum Mioriţa ngureanu, Vasile Nasui 2 Absrac: The paper presens some consideraions abou he ribological sysem brake shoe-drum in he braking process o mining hoising machines. Bellow are presened he componens o he ribosysem, is parameers and he analysis o he uncional parameers or braking process. Key words: ribological sysem, parameers, braking process. INTRODCTION The brake shoe-drum ribosysem An assembly o elemens inerconneced by srucure and uncion deine a sysem. Czihoş [6], presens in a general manner he ribomechanical sysem. According him is an eniy whose echnical uncions are relaed o he ineracions o he suraces in relaive movemen esablishing is rame conen and main characerisics. The speciic problem o each ribological sysem, especially complex, can be approached sysemically in an uniary orm. [2] The mechanical ribosysems are grouped ino ive caegories: Tribosysems o guiding o movemen; Tribosysems o inormaion ranser; Tribosysems o ransmission o load; Tribosysems o maerial ranspor; Tribosysems o abricaion. The sudy and previous research on ricion processes, aging processes and lubricaion and also on heir implicaions have been conduced on each rybosysem. A rybosysem has he ollowing characerisics (Fig.): Fig.. The general srucure o a ribosysem 8

2 SCIENTIFIC BLLETIN, Serie C, Fascicle: Mechanics, Tribology, Machine Manuacuring Technology ISSN , Volume 2 No. XXVII Elemen, 2,,...,n; Relevan properies o Elemen, 2,,...,n; Speciic relaions beween he elemens o he sysem. 2. THE SHOE-DRM BRAKING TRIBOSYSTEM STRCTRE To deermine he srucure o he brake shoedrum ricion ribosysem we sar orm he general relaions o ribosysems and rom he uncional scheme o he braking sysem ( Fig. ), S { E P R } where: E srucure elemens { E E E E } E 2 (2) i..n, curren number o maerial elemens o he sysem P - relevan properies o he elemen P i { P ( E ) P ( E ) P ( E )} j 2 j 2 n () j..n, curren number o he propery R speciic relaions beween elemens nj n Brake shoe Overall dimensions Type o maerial Relaions beween elemens Inercalae Maerial Abrasive dus Air humidiy Rim brake Overall dimensions Roughness Consrucional ype Fig. 2.The shoe-drum braking ribosysem srucure Enrances [X], exis [Y] a) Enrances X are considered he daes o he braking process, ha is he he process parameers. b) Exis Y are represened by he wear parameers o he shoe and drum, he qualiy parameers o he braking process (eg. he braking duraion), energeical parameers o he process (he ransormaion o braking work in hea). The Funcion o Tribosysem T Fig.. Brake execuion mechanism or hoising machine 2Ţ,5x,7A.[5] In order o reach he aim he sop o he drum he uncion o he sysem is he ransormaion o he enrances ino exis wih he help o a ranser uncion (T). The ranser uncion is he one ha shapes he process by an equaion o he ype: T [ X ] [ Y ] (5) 82

3 SCIENTIFIC BLLETIN, Serie C, Fascicle: Mechanics, Tribology, Machine Manuacuring Technology ISSN , Volume 2 No. XXVII The shaping is locaed on maerial level as well as on energeical and inormaional also[7]. In conclusion, he movemens o he ribosysem elemens are aken ino consideraion, movemens appeared as a sequence o he applicaion o a orce, he ransormaions o he elemens during he process, he inluence o disurbing acors on he process as well as he analysis o he losses. On he basis o he above said we can build he general scheme o he ricion ribosysem, scheme ha hus becomes he sar reerence poin or ulerior using. These will consider he ype o hoising machines, he sae o he sysem a he momen o he braking process (he posiion o he cage, he speed o he sysem).. THE ANALYSIS OF THE FNCTIONAL PARAMETERS THAT INFLENCE THE TRIBOLOGICAL SYSTEM FOR A 2Ţ,5X,7A MACHINE As resuled rom he ribosysem scheme ( Fig. ), or he sudy o he coupling under ribological aspec, he ollowing process parameers are o ineres : The conac pressure beween he shoe and he drum ( or sudying he wear and he deormaions ); The braking work ( or sudying he heaing o coupling elemens).. The Conac Pressure beween he shoe and he drum The disribuion o speciic pressures on ricion suraces beween he shoe and he drum deermines he ype o he wear and inluences is durabiliy [2]. As research [],[] prove, or he brakes where he orce developed by he acioning mechanism is a basic parameer, aer he running, he wearing o he shoes on he lengh levels and esablishes as uniorm, in hese condiions he disribuion o he pressures can be considered consan and uniorm on all he conac lengh. The exernal orces ha ac on he drum and deermine he conac pressures are ( Fig. 4): Fig. 4. The calculaion scheme or conac pressure Normal orce ( reacion) N Fricion orce T T µ N (6) µ - he ricion coeicien beween he she and he rim The conac pressure beween he shoe and he drum is deermined: N p (7) S S- he drum conac surace o a shoe S b l (8) where : b- he widh o he shoe, - he lengh o he shoe. The conac pressure is condiioned by he orces developed by he acioning device. The normal orce in his case is deermined by he realion [8]: G d z N a i (9) where : G - he ransverse elasiciy module o he arch maerial d - he diameer o arch maerial, z - number o he arches in he package ( loor) deormaion o arches in braking posiion c he raio beween he medium diameer o he arches D m and he diameer o he round seel: c D m () d 8

4 SCIENTIFIC BLLETIN, Serie C, Fascicle: Mechanics, Tribology, Machine Manuacuring Technology ISSN , Volume 2 No. XXVII n he number o working coils o he arches; k - coeicien, o end he relaion : k + 2c 2c () For his sysem he ricion orce is : p T 2 G d z µ (2) N p b l G d z i b l a () i 4) Saring orm he equaion (4) we analyse he variaion o he speciic conac pressure o he shoe wih he rim according o he deormaion o he arches ( Fig.5) P i i 47.5 Fig. 5. The conac pressure P i (N/m 2 ) uncion o deormaion o arches i (mm).2 The deerminaion o he braking work In mining here are used dieren ypes o hoising machines, wih dieren ahograms o speed and acceleraion. As a conclusion he deerminaion o an analyical mehod o calculaion o he braking work generally applicable is diicul o realise [4][4]. Expressing he work realised by a shoe over he braking process by he ormula: L M M d ω (5) µ N R (6) The braking momen developed by he wo shoe-brakes applied o he drums is esablished as being he sum o he momens creaed on each shoe, i all our shoes develop he same momen o braking and work simulaneously hen: L M (7) ( ) 4M ( ) where: M - is he momen o ( ) braking developed by a shoe M µ R N (8) ( ) ( ) R- radius drum ( ricion) N ( ) - he resul o normal pressing orces o he shoe onn he drum µ - he ricion coeicien beween he shoe and he drum µ N R ω d µ R N ω (9) As i can be observed by ormula (9) he basic componens on which he braking work depends are: The angular braking speed ω ; The resul o normal pushing orces on he rim N. Bu N - has a variable characer and ω - has a variable characer. As a conclusion, he braking work is a ime uncion and depends on he angular speed o he rim an don he normal orce resuled by pressing he shoe on he drum. 4. CONCLSIONS The paper represens a par o he research on braking sysems on mining hoising machines. On he basis o describing he echnical uncion o he ricion ribosysem shoe-drum we can realise he analysis process or dieren real siuaions (or dieren hoising machines, or dieren ypes o braking, or dieren environmenal condiions). In his paper i has been exempliied he manner o deermining he main uncional parameers ha inluence he ribological sysem or he hoising machine 2Ţ,5x,7A. REFERENCES. Bar L., Banciu M,Marcoş T.,Tudoreanu N.. ş.a., Deerminarea experimenală a orţelor reale de d 84

5 SCIENTIFIC BLLETIN, Serie C, Fascicle: Mechanics, Tribology, Machine Manuacuring Technology ISSN , Volume 2 No. XXVII închidere din sisemul de rânare la maşini de exracţie, CEPROM Sau Mare, Banciu M., Tudoreanu N., Îndrumăor ehnic privind uzura şi oboseala componenelor rânelor maşinilor de exracţie (exemple de calcul) IPROMIN Buzdugan Gh.. - Rezisenţa maerialelor aplicaţii--.. Ediura Academiei Române,Bucureşi Brădeanu, N., Deerminarea domeniului de uilizare a insalaţiilor de exracţie cu unul şi cu mai mule cabluri ; Revisa minelor nr.8/96(pag. 8-22). 5. Coeţiu, R., Pay, G., Coeţiu, A.: Theoreical and experimenal Sudies Abou he Load Variaion Inluence on he Values o Fricion Coeiciens în Rolling Couples Seel Polyamide Maerials. Inernaional Compuer Science Conerence, MicroCAD 2, niversiaea din Miskolc, eb. 2, ISBN , pag Czichos, H., Peersohn, D., Scwarz, W., Oberlächenalas, Technische Oberlachen, Berlin, Czichos, H.,s.a. Hue, Manualul inginerului. Fundamene., Ediura Tehnică, Bucureşi, Maghiari, A., Insalaţii mecanice miniere, Ediura ehnică, Bucureşi, Pavelescu D., Muşa M., Tudor A. Tribologie, Ediura Didacică şi Pedagogică, Bucureşi 977. Popa, A., s. a., Manualul inginerului de mine, vol V, Ediura Tehnică, Bucureşi 989.., ngureanu M., Conribuţii privind sudiul sub aspec ribologic al insalaţiilor de exracţie miniere, Reerade docora2,baia Mare ngureanu N.., Conribuţii privind unele aspece ribologice şi de iabiliae apărue în uncţionarea sculelor miniere de perorare, Teză de docora niversiaea Tehnică Cluj Napoca, 2. * * * Braking or he World s larges mine, World mining equipmen, june * * *Hoiss Advance wih Tehnology, Engineering & Mining Journal, aprilie * * * Maşina podbemnaia şahnaia 2Ţ,5X,7A Tehnicescoe opisanie.. Auhor address: Mioria ngureanu, PhD, eng., Associae Proessor; Faculy o Engineering, Norh niversiy Cener o Baia Mare, Technical niversiy o Cluj Napoca Romania, 48, Baia Mare, Romania, sr. Dr. V. Babes, nr 62/A, m_ungureanu@ubm.ro 2 Vasile Nasui, Proessor; Faculy o Engineering, Norh niversiy Cener o Baia Mare, Technical niversiy o Cluj Napoca Romania, 48, Baia Mare, Romania, sr. Dr. V. Babes, nr 62/A, vasile.nasui@ubm.ro Conac person: Mioria ngureanu, PhD, eng., Associae Proessor; Faculy o Engineering, Norh niversiy Cener o Baia Mare, Technical niversiy o Cluj Napoca Romania, 48, Baia Mare, Romania, sr. Dr. V. Babes, nr 62/A, m_ungureanu@ubm.ro 85

MATHEMATICAL MODELING OF THE TRACTOR-GRADER AGRICULTURAL SYSTEM CINEMATIC DURING LAND IMPROVING WORKS

MATHEMATICAL MODELING OF THE TRACTOR-GRADER AGRICULTURAL SYSTEM CINEMATIC DURING LAND IMPROVING WORKS Bullein of he Transilvania Universiy of Braşov Series II: Foresry Wood Indusry Agriculural Food Engineering Vol. 5 (54) No. 1-2012 MATHEMATICA MODEING OF THE TRACTOR-GRADER AGRICUTURA SYSTEM CINEMATIC

More information

SUFFICIENT CONDITIONS FOR EXISTENCE SOLUTION OF LINEAR TWO-POINT BOUNDARY PROBLEM IN MINIMIZATION OF QUADRATIC FUNCTIONAL

SUFFICIENT CONDITIONS FOR EXISTENCE SOLUTION OF LINEAR TWO-POINT BOUNDARY PROBLEM IN MINIMIZATION OF QUADRATIC FUNCTIONAL HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, Series A, OF HE ROMANIAN ACADEMY Volume, Number 4/200, pp 287 293 SUFFICIEN CONDIIONS FOR EXISENCE SOLUION OF LINEAR WO-POIN BOUNDARY PROBLEM IN

More information

ENGINEERING FOR RURAL DEVELOPMENT Jelgava, MECHANISM MOTION STUDIES WITH COLLISIONS AT SEVERAL POINTS

ENGINEERING FOR RURAL DEVELOPMENT Jelgava, MECHANISM MOTION STUDIES WITH COLLISIONS AT SEVERAL POINTS EGIEERIG FOR RURAL DEVELOPMET Jelgava, 5.-7.5.16. MECHAISM MOTIO STUDIES WITH COLLISIOS AT SEVERAL POITS Edgars Kovals 1, Janis Viba 1, Lauris Sals 1, Svelana Sokolova 1, Vialy Krupenin 1 Riga Technical

More information

I. OBJECTIVE OF THE EXPERIMENT.

I. OBJECTIVE OF THE EXPERIMENT. I. OBJECTIVE OF THE EXPERIMENT. Swissmero raels a high speeds hrough a unnel a low pressure. I will hereore undergo ricion ha can be due o: ) Viscosiy o gas (c. "Viscosiy o gas" eperimen) ) The air in

More information

in Engineering Prof. Dr. Michael Havbro Faber ETH Zurich, Switzerland Swiss Federal Institute of Technology

in Engineering Prof. Dr. Michael Havbro Faber ETH Zurich, Switzerland Swiss Federal Institute of Technology Risk and Saey in Engineering Pro. Dr. Michael Havbro Faber ETH Zurich, Swizerland Conens o Today's Lecure Inroducion o ime varian reliabiliy analysis The Poisson process The ormal process Assessmen o he

More information

Scientific Research of the Institute of Mathematics and Computer Science DIFFERENT VARIANTS OF THE BOUNDARY ELEMENT METHOD FOR PARABOLIC EQUATIONS

Scientific Research of the Institute of Mathematics and Computer Science DIFFERENT VARIANTS OF THE BOUNDARY ELEMENT METHOD FOR PARABOLIC EQUATIONS Scieniic Research o he Insiue o Mahemaics and Compuer Science DIERENT VARIANTS O THE BOUNDARY ELEMENT METHOD OR PARABOLIC EQUATIONS Ewa Majchrzak,, Ewa Ładyga Jerzy Mendakiewicz, Alicja Piasecka Belkhaya

More information

Computer Simulation Technique for the Closed Die Forging Process: A Modular Approach

Computer Simulation Technique for the Closed Die Forging Process: A Modular Approach Proceedings o he 7h WSEAS Inernaional Conerence on SYSTEM SCIENCE and SIMULATION in ENGINEERING (ICOSSSE '8 Compuer Simulaion Technique or he Closed Die Forging Process: A Modular Approach Pro. DIPAKKUMAR

More information

Theory of! Partial Differential Equations!

Theory of! Partial Differential Equations! hp://www.nd.edu/~gryggva/cfd-course/! Ouline! Theory o! Parial Dierenial Equaions! Gréar Tryggvason! Spring 011! Basic Properies o PDE!! Quasi-linear Firs Order Equaions! - Characerisics! - Linear and

More information

Physics Notes - Ch. 2 Motion in One Dimension

Physics Notes - Ch. 2 Motion in One Dimension Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,

More information

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components 7 Esimaion of Kineic Fricion Coefficien for Sliding Rigid Block Nonsrucural Componens Cagdas Kafali Ph.D. Candidae, School of Civil and Environmenal Engineering, Cornell Universiy Research Supervisor:

More information

At the end of this lesson, the students should be able to understand

At the end of this lesson, the students should be able to understand Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress concenraion facor; experimenal and heoreical mehods.

More information

Electrical and current self-induction

Electrical and current self-induction Elecrical and curren self-inducion F. F. Mende hp://fmnauka.narod.ru/works.hml mende_fedor@mail.ru Absrac The aricle considers he self-inducance of reacive elemens. Elecrical self-inducion To he laws of

More information

FRICTION INCREASE OF SPLICED BARS DUE TO FRP WRAPPING

FRICTION INCREASE OF SPLICED BARS DUE TO FRP WRAPPING FRICTION INCREASE OF SPLICED BARS DUE TO FRP WRAPPING Vincenzo GIAMUNDO Ph.D. Suden Deparmen o Srucural Engineering Universiy o Naples Federico II Via Claudio, 21-80125, Naples - Ialy vincenzo.giamundo@unina.i*

More information

Theory of! Partial Differential Equations-I!

Theory of! Partial Differential Equations-I! hp://users.wpi.edu/~grear/me61.hml! Ouline! Theory o! Parial Dierenial Equaions-I! Gréar Tryggvason! Spring 010! Basic Properies o PDE!! Quasi-linear Firs Order Equaions! - Characerisics! - Linear and

More information

The motions of the celt on a horizontal plane with viscous friction

The motions of the celt on a horizontal plane with viscous friction The h Join Inernaional Conference on Mulibody Sysem Dynamics June 8, 18, Lisboa, Porugal The moions of he cel on a horizonal plane wih viscous fricion Maria A. Munisyna 1 1 Moscow Insiue of Physics and

More information

Characteristics of Linear System

Characteristics of Linear System Characerisics o Linear Sysem h g h : Impulse response F G : Frequency ranser uncion Represenaion o Sysem in ime an requency. Low-pass iler g h G F he requency ranser uncion is he Fourier ransorm o he impulse

More information

STUDY OF WEAR OF FRICTION LINING OF BRAKE SHOE

STUDY OF WEAR OF FRICTION LINING OF BRAKE SHOE th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE Baia Mare, Romania, May 1-1, 00 ISSN-1- STUDY OF WEAR OF FRICTION LINING OF BRAKE SHOE Miorita UNGUREANU 1, Nicolae UNGUREANU, Dinu STOICOVICI 1 Assoc.Pro.Ing.PhD.,

More information

Computation of the Effect of Space Harmonics on Starting Process of Induction Motors Using TSFEM

Computation of the Effect of Space Harmonics on Starting Process of Induction Motors Using TSFEM Journal of elecrical sysems Special Issue N 01 : November 2009 pp: 48-52 Compuaion of he Effec of Space Harmonics on Saring Process of Inducion Moors Using TSFEM Youcef Ouazir USTHB Laboraoire des sysèmes

More information

CALCULATION OF AERODYNAMICAL EFFICIENCY AND OF THE POWER AT THE LEVEL OF THE BLADES AND THE AXLE OF THE WIND TURBINE

CALCULATION OF AERODYNAMICAL EFFICIENCY AND OF THE POWER AT THE LEVEL OF THE BLADES AND THE AXLE OF THE WIND TURBINE Analele Universiăţii din Oradea, Fascicula roecţia Mediului Vol. XVI, 2011 ALULATION OF AERODYNAMIAL EFFIIENY AND OF THE OWER AT THE LEVEL OF THE BLADES AND THE AXLE OF THE WIND TURBINE Dubău ălin * *Universiy

More information

Involute Gear Tooth Bending Stress Analysis

Involute Gear Tooth Bending Stress Analysis Involue Gear Tooh Bending Sress Analysis Lecure 21 Engineering 473 Machine Design Gear Ineracion Line of Ceners Line Tangen o s Line Normal o Line of Ceners 1 s Close Up of Meshed Teeh Line of Conac W

More information

A car following model for traffic flow simulation

A car following model for traffic flow simulation Inernaional Journal of Applied Mahemaical Sciences ISSN 0973-076 Volume 9, Number (206), pp. -9 Research India Publicaions hp://www.ripublicaion.com A car following model for raffic flow simulaion Doudou

More information

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member Verificaion Example Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro Caegory: Isoropic Linear Elasiciy, Dynamics, Member Verificaion Example: 0104 Canilever Beam wih Periodic Exciaion 0104 Canilever Beam

More information

Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/

More information

UNIVERSITY OF TRENTO MEASUREMENTS OF TRANSIENT PHENOMENA WITH DIGITAL OSCILLOSCOPES. Antonio Moschitta, Fabrizio Stefani, Dario Petri.

UNIVERSITY OF TRENTO MEASUREMENTS OF TRANSIENT PHENOMENA WITH DIGITAL OSCILLOSCOPES. Antonio Moschitta, Fabrizio Stefani, Dario Petri. UNIVERSIY OF RENO DEPARMEN OF INFORMAION AND COMMUNICAION ECHNOLOGY 385 Povo reno Ialy Via Sommarive 4 hp://www.di.unin.i MEASUREMENS OF RANSIEN PHENOMENA WIH DIGIAL OSCILLOSCOPES Anonio Moschia Fabrizio

More information

A NOVEL FRICTION LAW

A NOVEL FRICTION LAW THERMAL SCIENCE, Year 2012, Vol. 16, No. 5, pp. 1529-1533 1529 A NOVEL FRICTION LAW by Hai-Yan KONG and Ji-Huan HE * Naional Engineering Laboraory or Modern Silk, College o Teile and Clohing Engineering,

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

Physics 2107 Moments of Inertia Experiment 1

Physics 2107 Moments of Inertia Experiment 1 Physics 107 Momens o Ineria Experimen 1 Prelab 1 Read he ollowing background/seup and ensure you are amiliar wih he heory required or he experimen. Please also ill in he missing equaions 5, 7 and 9. Background/Seup

More information

Some Basic Information about M-S-D Systems

Some Basic Information about M-S-D Systems Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,

More information

Topic Astable Circuits. Recall that an astable circuit has two unstable states;

Topic Astable Circuits. Recall that an astable circuit has two unstable states; Topic 2.2. Asable Circuis. Learning Objecives: A he end o his opic you will be able o; Recall ha an asable circui has wo unsable saes; Explain he operaion o a circui based on a Schmi inverer, and esimae

More information

Math 221: Mathematical Notation

Math 221: Mathematical Notation Mah 221: Mahemaical Noaion Purpose: One goal in any course is o properly use he language o ha subjec. These noaions summarize some o he major conceps and more diicul opics o he uni. Typing hem helps you

More information

A MATHEMATICAL MODEL FOR KINEMATIC LINKAGES MADE OF DEFORMABLE COMPOSITE BARS BUILT BY USING THE HAMILTON S VARIATION PRINCIPLE

A MATHEMATICAL MODEL FOR KINEMATIC LINKAGES MADE OF DEFORMABLE COMPOSITE BARS BUILT BY USING THE HAMILTON S VARIATION PRINCIPLE Romanian Repors in Physics, Vol. 6, No., P. 5 5, 9 A MATHEMATICAL MODEL FOR KINEMATIC LINKAGE MADE OF DEFORMABLE COMPOITE BAR BUILT BY UING THE HAMILTON VARIATION PRINCIPLE ABIN RIZECU, MARCELA URACHE,

More information

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?

More information

Sub Module 2.6. Measurement of transient temperature

Sub Module 2.6. Measurement of transient temperature Mechanical Measuremens Prof. S.P.Venkaeshan Sub Module 2.6 Measuremen of ransien emperaure Many processes of engineering relevance involve variaions wih respec o ime. The sysem properies like emperaure,

More information

Suggestion of a Load Sharing Ratio for the Design of Spiral Coiltype Horizontal Ground Heat Exchangers

Suggestion of a Load Sharing Ratio for the Design of Spiral Coiltype Horizontal Ground Heat Exchangers Available online a www.sciencedirec.com ScienceDirec Energy Procedia 141 (2017) 292 298 www.elsevier.com/locae/procedia 4 Inernaional Conerence on Power and Energy Sysems Engineering, CPESE 2017, 25-29

More information

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology

More information

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,

More information

A Note on Fractional Electrodynamics. Abstract

A Note on Fractional Electrodynamics. Abstract Commun Nonlinear Sci Numer Simula 8 (3 589 593 A Noe on Fracional lecrodynamics Hosein Nasrolahpour Absrac We invesigae he ime evoluion o he racional elecromagneic waves by using he ime racional Maxwell's

More information

Dirac Particles Emission from Reissner-Nordstrom-Vaidya Black Hole

Dirac Particles Emission from Reissner-Nordstrom-Vaidya Black Hole Journal o Physics: Conerence Series PAPER OPEN ACCESS Dirac Paricles Emission rom Reissner-Nordsrom-Vaidya Black Hole To cie his aricle: Yuan Tiandho and Triyana 016 J. Phys.: Con. Ser. 739 01146 View

More information

Lecture #6: Continuous-Time Signals

Lecture #6: Continuous-Time Signals EEL5: Discree-Time Signals and Sysems Lecure #6: Coninuous-Time Signals Lecure #6: Coninuous-Time Signals. Inroducion In his lecure, we discussed he ollowing opics:. Mahemaical represenaion and ransormaions

More information

Advanced Organic Chemistry

Advanced Organic Chemistry Lalic, G. Chem 53A Chemisry 53A Advanced Organic Chemisry Lecure noes 1 Kineics: A racical Approach Simple Kineics Scenarios Fiing Experimenal Daa Using Kineics o Deermine he Mechanism Doughery, D. A.,

More information

Overview. COMP14112: Artificial Intelligence Fundamentals. Lecture 0 Very Brief Overview. Structure of this course

Overview. COMP14112: Artificial Intelligence Fundamentals. Lecture 0 Very Brief Overview. Structure of this course OMP: Arificial Inelligence Fundamenals Lecure 0 Very Brief Overview Lecurer: Email: Xiao-Jun Zeng x.zeng@mancheser.ac.uk Overview This course will focus mainly on probabilisic mehods in AI We shall presen

More information

CLASS XI SET A PHYSICS. 1. If and Let. The correct order of % error in. (a) (b) x = y > z (c) x < z < y (d) x > z < y

CLASS XI SET A PHYSICS. 1. If and Let. The correct order of % error in. (a) (b) x = y > z (c) x < z < y (d) x > z < y PHYSICS 1. If and Le. The correc order of % error in (a) (b) x = y > z x < z < y x > z < y. A hollow verical cylinder of radius r and heigh h has a smooh inernal surface. A small paricle is placed in conac

More information

th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3256

th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3256 11111 1 h World Conference on Earhquake Engineering Vancouver, B.C., Canada Augus 1-6, 2004 Paper No. 256 TOUCHING ANALYSIS OF TWO BUILDINGS USING FINITE ELEMENT METHOD Mircea IEREMIA 1, Silviu GINJU 1,

More information

ANALYZE OF CONTACT PRESSURES FOR BRAKING SYSTEM FOR HOISTING MACHINE

ANALYZE OF CONTACT PRESSURES FOR BRAKING SYSTEM FOR HOISTING MACHINE 5 th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE ANALYZE OF CONTACT PRESSURES FOR BRAKING SYSTEM FOR HOISTING MACHINE Mioriţa UNGUREANU*, Nicolae UNGUREANU*, Sorin MIHAILESCU** *North University of Baia

More information

New effective moduli of isotropic viscoelastic composites. Part I. Theoretical justification

New effective moduli of isotropic viscoelastic composites. Part I. Theoretical justification IOP Conference Series: Maerials Science and Engineering PAPE OPEN ACCESS New effecive moduli of isoropic viscoelasic composies. Par I. Theoreical jusificaion To cie his aricle: A A Sveashkov and A A akurov

More information

Simulation of magneto-hydrodynamic (MHD) flows in OpenFOAM

Simulation of magneto-hydrodynamic (MHD) flows in OpenFOAM Simulaion o magneo-hydrodynamic (MHD) los in OpenFOAM Sepember 1-15, 2010 NUMAP-FOAM, Universiy o Zagreb Ouline Problem: magneohydrodynamic (MHD) lo Magneo-hydrodynamic equaions Opimizaion o presen solver

More information

Mathematical Theory and Modeling ISSN (Paper) ISSN (Online) Vol 3, No.3, 2013

Mathematical Theory and Modeling ISSN (Paper) ISSN (Online) Vol 3, No.3, 2013 Mahemaical Theory and Modeling ISSN -580 (Paper) ISSN 5-05 (Online) Vol, No., 0 www.iise.org The ffec of Inverse Transformaion on he Uni Mean and Consan Variance Assumpions of a Muliplicaive rror Model

More information

Plasma Astrophysics Chapter 3: Kinetic Theory. Yosuke Mizuno Institute of Astronomy National Tsing-Hua University

Plasma Astrophysics Chapter 3: Kinetic Theory. Yosuke Mizuno Institute of Astronomy National Tsing-Hua University Plasma Asrophysics Chaper 3: Kineic Theory Yosuke Mizuno Insiue o Asronomy Naional Tsing-Hua Universiy Kineic Theory Single paricle descripion: enuous plasma wih srong exernal ields, imporan or gaining

More information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still. Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in

More information

MECHANICS OF MATERIALS Poisson s Ratio

MECHANICS OF MATERIALS Poisson s Ratio Poisson s Raio For a slender bar subjeced o axial loading: ε x x y 0 The elongaion in he x-direcion i is accompanied by a conracion in he oher direcions. Assuming ha he maerial is isoropic (no direcional

More information

THE EFFECT OF SUCTION AND INJECTION ON UNSTEADY COUETTE FLOW WITH VARIABLE PROPERTIES

THE EFFECT OF SUCTION AND INJECTION ON UNSTEADY COUETTE FLOW WITH VARIABLE PROPERTIES Kragujevac J. Sci. 3 () 7-4. UDC 53.5:536. 4 THE EFFECT OF SUCTION AND INJECTION ON UNSTEADY COUETTE FLOW WITH VARIABLE PROPERTIES Hazem A. Aia Dep. of Mahemaics, College of Science,King Saud Universiy

More information

Comparative study between two models of a linear oscillating tubular motor

Comparative study between two models of a linear oscillating tubular motor IOSR Journal of Elecrical and Elecronics Engineering (IOSR-JEEE) e-issn: 78-676,p-ISSN: 3-333, Volume 9, Issue Ver. IV (Feb. 4), PP 77-83 Comparaive sudy beween wo models of a linear oscillaing ubular

More information

CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD

CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD M. AHMETOGLU (AFRAILOV) 1, G. GULYAMOV 2, S. H. SHAMIRZAEV 2, A. G. GULYAMOV 2, M. G. DADAMIRZAEV 2, N. APRAILOV 2, F. KOÇAK

More information

Page 1 o 13 1. The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 ligh-years away. Express his disance in meers. ( ligh-year is he disance coered by ligh in one year. Ligh

More information

Symmetry and Numerical Solutions for Systems of Non-linear Reaction Diffusion Equations

Symmetry and Numerical Solutions for Systems of Non-linear Reaction Diffusion Equations Symmery and Numerical Soluions for Sysems of Non-linear Reacion Diffusion Equaions Sanjeev Kumar* and Ravendra Singh Deparmen of Mahemaics, (Dr. B. R. Ambedkar niversiy, Agra), I. B. S. Khandari, Agra-8

More information

OPTIMAL DESIGN OF WATER SUPPLY NETWORKS IN BUILDINGS

OPTIMAL DESIGN OF WATER SUPPLY NETWORKS IN BUILDINGS OPTIMAL ESIGN OF WATER SUPPLY NETWORKS IN BUILINGS SÂRBU, Ioan eparmen of Building Services, Poliehnica Universiy of Timisoara, Romania. INTROUCTION The inernal cold and warm waer supply neworks do have

More information

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture Scienific Herald of he Voronezh Sae Universiy of Archiecure and Civil Engineering. Consrucion and Archiecure UDC 625.863.6:551.328 Voronezh Sae Universiy of Archiecure and Civil Engineering Ph. D. applican

More information

Lecture #7. EECS490: Digital Image Processing. Image Processing Example Fuzzy logic. Fourier Transform. Basics Image processing examples

Lecture #7. EECS490: Digital Image Processing. Image Processing Example Fuzzy logic. Fourier Transform. Basics Image processing examples Lecure #7 Image Processing Example Fuzzy logic Basics Image processing examples Fourier Transorm Inner produc, basis uncions Fourier series Image Processing Example original image Laplacian o image (c)

More information

Modular and Multi-view Representation of Complex Hybrid Systems

Modular and Multi-view Representation of Complex Hybrid Systems Modular and Muli-view Represenaion of Complex Hybrid Sysems Luc THEVENON, Jean-Marie FLAUS Laboraoire d Auomaique de Grenoble UMR 5528 CNRS-INPG-UJF ENSIEG, BP 46, F-38402, Sain Marin d Hères Cedex FRANCE

More information

The electromagnetic interference in case of onboard navy ships computers - a new approach

The electromagnetic interference in case of onboard navy ships computers - a new approach The elecromagneic inerference in case of onboard navy ships compuers - a new approach Prof. dr. ing. Alexandru SOTIR Naval Academy Mircea cel Bărân, Fulgerului Sree, Consanţa, soiralexandru@yahoo.com Absrac.

More information

Stability and Bifurcation in a Neural Network Model with Two Delays

Stability and Bifurcation in a Neural Network Model with Two Delays Inernaional Mahemaical Forum, Vol. 6, 11, no. 35, 175-1731 Sabiliy and Bifurcaion in a Neural Nework Model wih Two Delays GuangPing Hu and XiaoLing Li School of Mahemaics and Physics, Nanjing Universiy

More information

An Approximate Analytical Method for Stress. Analysis in a Viscoelastic Body with a Circular. Inclusion Considering the Geometric and

An Approximate Analytical Method for Stress. Analysis in a Viscoelastic Body with a Circular. Inclusion Considering the Geometric and onemporary ngineering Sciences, Vol. 9, 16, no. 16, 781-79 HKAR Ld, www.m-hikari.com hp://dx.doi.org/1.1988/ces.16.6565 An Approximae Analyical ehod or Sress Analysis in a Viscoelasic ody wih a ircular

More information

From Particles to Rigid Bodies

From Particles to Rigid Bodies Rigid Body Dynamics From Paricles o Rigid Bodies Paricles No roaions Linear velociy v only Rigid bodies Body roaions Linear velociy v Angular velociy ω Rigid Bodies Rigid bodies have boh a posiion and

More information

CONSIDERATIONS REGARDING THE OPTIMUM DESIGN OF PRESTRESSED ELEMENTS

CONSIDERATIONS REGARDING THE OPTIMUM DESIGN OF PRESTRESSED ELEMENTS Bullein of e Transilvania Universiy of Braşov CIBv 5 Vol. 8 (57) Special Issue No. - 5 CONSIDERTIONS REGRDING THE OPTIU DESIGN OF PRESTRESSED ELEENTS D. PRECUPNU C. PRECUPNU bsrac: Engineering educaion

More information

1. Introduction. Rawid Banchuin

1. Introduction. Rawid Banchuin 011 Inernaional Conerence on Inormaion and Elecronics Engineering IPCSIT vol.6 (011 (011 IACSIT Press, Singapore Process Induced Random Variaion Models o Nanoscale MOS Perormance: Eicien ool or he nanoscale

More information

Non-uniform circular motion *

Non-uniform circular motion * OpenSax-CNX module: m14020 1 Non-uniform circular moion * Sunil Kumar Singh This work is produced by OpenSax-CNX and licensed under he Creaive Commons Aribuion License 2.0 Wha do we mean by non-uniform

More information

arxiv: v1 [physics.data-an] 14 Dec 2015

arxiv: v1 [physics.data-an] 14 Dec 2015 1/ noise rom he nonlinear ransormaions o he variables Bronislovas Kaulakys, Miglius Alaburda, and Julius Ruseckas Insiue o Theoreical Physics and Asronomy, Vilnius Universiy, A. Gošauo 1, 118 Vilnius,

More information

Stochastic Model for Cancer Cell Growth through Single Forward Mutation

Stochastic Model for Cancer Cell Growth through Single Forward Mutation Journal of Modern Applied Saisical Mehods Volume 16 Issue 1 Aricle 31 5-1-2017 Sochasic Model for Cancer Cell Growh hrough Single Forward Muaion Jayabharahiraj Jayabalan Pondicherry Universiy, jayabharahi8@gmail.com

More information

VIRTUAL MACHINE FOR PROCESSING OF CUTTING TOOLS

VIRTUAL MACHINE FOR PROCESSING OF CUTTING TOOLS 7 h INTERNATIONAL MULTIDISCIPLINARY CONFERENCE Baia Mare, Romania, May 7-8, 2007 ISSN-224-3264 VIRTUAL MACHINE FOR PROCESSING OF CUTTING TOOLS Sandu Consanin, assoc. rofessor, Universiy POLITEHNICA of

More information

2002 November 14 Exam III Physics 191

2002 November 14 Exam III Physics 191 November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m

More information

where the coordinate X (t) describes the system motion. X has its origin at the system static equilibrium position (SEP).

where the coordinate X (t) describes the system motion. X has its origin at the system static equilibrium position (SEP). Appendix A: Conservaion of Mechanical Energy = Conservaion of Linear Momenum Consider he moion of a nd order mechanical sysem comprised of he fundamenal mechanical elemens: ineria or mass (M), siffness

More information

NEWTON S SECOND LAW OF MOTION

NEWTON S SECOND LAW OF MOTION Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during

More information

Combined Bending with Induced or Applied Torsion of FRP I-Section Beams

Combined Bending with Induced or Applied Torsion of FRP I-Section Beams Combined Bending wih Induced or Applied Torsion of FRP I-Secion Beams MOJTABA B. SIRJANI School of Science and Technology Norfolk Sae Universiy Norfolk, Virginia 34504 USA sirjani@nsu.edu STEA B. BONDI

More information

L1, L2, N1 N2. + Vout. C out. Figure 2.1.1: Flyback converter

L1, L2, N1 N2. + Vout. C out. Figure 2.1.1: Flyback converter page 11 Flyback converer The Flyback converer belongs o he primary swiched converer family, which means here is isolaion beween in and oupu. Flyback converers are used in nearly all mains supplied elecronic

More information

Kinematics and kinematic functions

Kinematics and kinematic functions Kinemaics and kinemaic funcions Kinemaics deals wih he sudy of four funcions (called kinemaic funcions or KFs) ha mahemaically ransform join variables ino caresian variables and vice versa Direc Posiion

More information

Position, Velocity, and Acceleration

Position, Velocity, and Acceleration rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose

More information

ψ(t) = V x (0)V x (t)

ψ(t) = V x (0)V x (t) .93 Home Work Se No. (Professor Sow-Hsin Chen Spring Term 5. Due March 7, 5. This problem concerns calculaions of analyical expressions for he self-inermediae scaering funcion (ISF of he es paricle in

More information

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi Creep in Viscoelasic Subsances Numerical mehods o calculae he coefficiens of he Prony equaion using creep es daa and Herediary Inegrals Mehod Navnee Saini, Mayank Goyal, Vishal Bansal (23); Term Projec

More information

Lab #2: Kinematics in 1-Dimension

Lab #2: Kinematics in 1-Dimension Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion

More information

Optimal Control of Dc Motor Using Performance Index of Energy

Optimal Control of Dc Motor Using Performance Index of Energy American Journal of Engineering esearch AJE 06 American Journal of Engineering esearch AJE e-issn: 30-0847 p-issn : 30-0936 Volume-5, Issue-, pp-57-6 www.ajer.org esearch Paper Open Access Opimal Conrol

More information

KINEMATICS IN ONE DIMENSION

KINEMATICS IN ONE DIMENSION KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec

More information

CERTAIN CLASSES OF SOLUTIONS OF LAGERSTROM EQUATIONS

CERTAIN CLASSES OF SOLUTIONS OF LAGERSTROM EQUATIONS SARAJEVO JOURNAL OF MATHEMATICS Vol.10 (22 (2014, 67 76 DOI: 10.5644/SJM.10.1.09 CERTAIN CLASSES OF SOLUTIONS OF LAGERSTROM EQUATIONS ALMA OMERSPAHIĆ AND VAHIDIN HADŽIABDIĆ Absrac. This paper presens sufficien

More information

PREDICTION OF BLAST LOADINGS ON BUILDINGS

PREDICTION OF BLAST LOADINGS ON BUILDINGS PREDICTION OF BLAST LOADINGS ON BUILDINGS Assoc. Prof. PhD, Marin LUPOAE Miliary Technical Academy, George Cosbuc 9-49, Buchares, Romania mlupoae@ma.ro Absrac: To deermine he effecs of a vehicle bomb explosion

More information

Material Resistance and Friction in Cold Rolling

Material Resistance and Friction in Cold Rolling h World Congresses of Srucural and Mulidiscilinary Oimizaion Rio de Janeiro, 30 May - 03 June 200, Brazil Maerial Resisance and Fricion in Cold Rolling A.K. Tieu, C. You, H.T. Zhu, C. Lu, Z.Y. Jiang and

More information

SPH3U: Projectiles. Recorder: Manager: Speaker:

SPH3U: Projectiles. Recorder: Manager: Speaker: SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0

More information

ANALYSES OF THE INTERFACE BETWEEN WALL ELEMENTS AND RENDERING LAYERS. Extended Abstract

ANALYSES OF THE INTERFACE BETWEEN WALL ELEMENTS AND RENDERING LAYERS. Extended Abstract INSTITUTO SUPERIOR TÉCNICO Universidade Técnica de Lisboa ANALYSES OF THE INTERFACE BETWEEN WALL ELEMENTS AND RENDERING LAYERS Exended Absrac Sara Maria Garcia Gaspar Ocober, 2011 1 INTRODUCTION Adhesion

More information

Flow-Induced Vibration Analysis of Supported Pipes with a Crack

Flow-Induced Vibration Analysis of Supported Pipes with a Crack Flow-Induced Vibraion Analsis of Suppored Pipes wih a Crack Jin-Huk Lee, Samer Masoud Al-Said Deparmen of Mechanical Engineering American Universi of Sharjah, UAE Ouline Inroducion and Moivaion Aeroacousicall

More information

Simulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010

Simulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Simulaion-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Week Descripion Reading Maerial 2 Compuer Simulaion of Dynamic Models Finie Difference, coninuous saes, discree ime Simple Mehods Euler Trapezoid

More information

Final Spring 2007

Final Spring 2007 .615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o

More information

15. Vector Valued Functions

15. Vector Valued Functions 1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,

More information

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an

More information

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel,

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel, Mechanical Faigue and Load-Induced Aging of Loudspeaker Suspension Wolfgang Klippel, Insiue of Acousics and Speech Communicaion Dresden Universiy of Technology presened a he ALMA Symposium 2012, Las Vegas

More information

Cash Flow Valuation Mode Lin Discrete Time

Cash Flow Valuation Mode Lin Discrete Time IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728,p-ISSN: 2319-765X, 6, Issue 6 (May. - Jun. 2013), PP 35-41 Cash Flow Valuaion Mode Lin Discree Time Olayiwola. M. A. and Oni, N. O. Deparmen of Mahemaics

More information

23.2. Representing Periodic Functions by Fourier Series. Introduction. Prerequisites. Learning Outcomes

23.2. Representing Periodic Functions by Fourier Series. Introduction. Prerequisites. Learning Outcomes Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals

More information

SOME PROPERTIES OF GENERALIZED STRONGLY HARMONIC CONVEX FUNCTIONS MUHAMMAD ASLAM NOOR, KHALIDA INAYAT NOOR, SABAH IFTIKHAR AND FARHAT SAFDAR

SOME PROPERTIES OF GENERALIZED STRONGLY HARMONIC CONVEX FUNCTIONS MUHAMMAD ASLAM NOOR, KHALIDA INAYAT NOOR, SABAH IFTIKHAR AND FARHAT SAFDAR Inernaional Journal o Analysis and Applicaions Volume 16, Number 3 2018, 427-436 URL: hps://doi.org/10.28924/2291-8639 DOI: 10.28924/2291-8639-16-2018-427 SOME PROPERTIES OF GENERALIZED STRONGLY HARMONIC

More information

V AK (t) I T (t) I TRM. V AK( full area) (t) t t 1 Axial turn-on. Switching losses for Phase Control and Bi- Directionally Controlled Thyristors

V AK (t) I T (t) I TRM. V AK( full area) (t) t t 1 Axial turn-on. Switching losses for Phase Control and Bi- Directionally Controlled Thyristors Applicaion Noe Swiching losses for Phase Conrol and Bi- Direcionally Conrolled Thyrisors V AK () I T () Causing W on I TRM V AK( full area) () 1 Axial urn-on Plasma spread 2 Swiching losses for Phase Conrol

More information

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction Developmen of a new merological model for measuring of he waer surface evaporaion Tovmach L. Tovmach Yr. Sae Hydrological Insiue 23 Second Line, 199053 S. Peersburg, Russian Federaion Telephone (812) 323

More information

Dirac s hole theory and the Pauli principle: clearing up the confusion.

Dirac s hole theory and the Pauli principle: clearing up the confusion. Dirac s hole heory and he Pauli rincile: clearing u he conusion. Dan Solomon Rauland-Borg Cororaion 8 W. Cenral Road Moun Prosec IL 656 USA Email: dan.solomon@rauland.com Absrac. In Dirac s hole heory

More information

Multi-Frequency Sheath Dynamics

Multi-Frequency Sheath Dynamics Muli-Frequency Sheah Dynamics Seven Shannon, Alex Paerson, Theodoros Panagopoulos, Daniel Hoffman, John Holland, Dennis Grimard (Universiy of Michigan) Purpose of research RF plasmas wih muliple frequency

More information

Speed Control of Brushless DC Motor Using Proportional Integral Controller

Speed Control of Brushless DC Motor Using Proportional Integral Controller www.ijrase.com Volume 3 Issue XII, December 2015 Inernaional Journal for Research in Applied Science & Engineering Speed Conrol of Brushless DC Moor Using Proporional Inegral Conroller Vikramarajan Jambulingam

More information