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

Size: px
Start display at page:

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

Transcription

1 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

2

3 1 INTRODUCTION Adhesion srengh is one of he mandaory properies of renders, so ha consrucion works in which hey are applied can mee he requiremens of safey in-use and durabiliy, esablished in he Consrucion Producs Direcive (Council Direcive 89/106/EEC). The European sandard EN (CEN, 2003) liss he requiremens and properies for hardened morar, in which figures adhesion o he subsrae. According o he laer norm, he value of he adhesion srengh of morars can be deermined wih pull-off ess described in he European norm EN (CEN, 1996). There have been several experimenal sudies o exend he knowledge of he adhesion mechanism beween a morar and is subsrae, and deermine which facors can aler he render propery. In hese sudies, researchers ofen perform microscopic analysis of he inerface of he sysem subsrae/morar and measure he srengh of he inerfacial bond wih pull-off ess. Adhesion loss is a frequen defec of exernal renders and canno be negleced as he render deachmens can cause hazardous siuaions o passersby. Therefore, in-siu evaluaion of he renders adhesion srengh, in-service condiions, mus be performed periodically. For insance, he American sandard ASTM E2270 (ASTM, 2005), in a periodic deailed building facade inspecion, recommends performing a leas hree pull-off ess per coaed surface. Performing a pull-off es in a rendered facade causes a cerain degree of damage which mus be repaired afer he es. This is a relevan disadvanage of he echnique and is one of he causes for he reduced number of experimenal campaigns in which in-siu pull-off ess are performed. However, here are a few sudies available in which an evaluaion of he adherence of a morar was performed for in-service condiions. For insance, Flores-Colen e al. (2009) performed pull-off ess in building facades wih render adhesion loss in some areas o evaluae he adhesion capaciy of he remaining render o he wall; he auhors were able o idenify some causes for he adhesion deficiency. Quinela (2006) also performed in-siu evaluaion of morar adhesion o sudy he evoluion of his propery hrough weahering cycles, in a wall buil for he purpose of he sudy. The presen disseraion inends o idenify facors ha migh have an impac in he morar-subsrae adhesion and o build a numerical model of morar coaed wall o sudy he influence of hose facors in he modeled sysem inerface (beween he wall and he render). 2 SUBSTRATE/MORTAR ADHESION 2.1 Bond mechanism of a morar o a subsrae The mechanical bond of a morar o is subsrae is due o he peneraion of morar fluids and fines ino he pores and caviies of he subsrae followed by he crysallizaion of binder hydraion producs; he solid crysals provide he mechanical connecion beween morar and subsrae (Figure 1). The subsrae capillary sucion is responsible for he

4 movemen of he morar fluids and fines in he subsrae/morar inerface and in he pores of he firs. When he morar conacs wih he subsrae, is pores are bigger han he subsrae pores, which are unsauraed, hus he capillary sucion by he laer. The subsrae sucion of morar fluids lowers he morar waer/solids raio, which leads o is plasic shrinkage, and, as a consequence, he morar pores size decreases and evenually become smaller hen he subsrae pores; ha is when he occurring sucion sops. Chemical bonding, namely, covalen and Van der Waals bonding, play also a par in he adhesion of he morar, bu wih a minor share. 2.2 Facors ha influence he rendering morar adhesion o he subsrae Several sudies have been performed by differen auhors wih he aim o idenify facors ha influence he adhesion bond beween a morar and is subsrae, in hese sudies several facors are modified in a subsrae/render model, and pull-off ess are performed o evaluae he normal srengh of he bond beween hem. The facors ha influence a morar adhesion have differen naure; some are relaed wih he morar characerisics (cemen proporion, consisency), ohers are relaed wih he subsrae ype (surface roughness, iniial rae absorpion) and ohers are exernal o he subsrae/render sysem (weaher condiions during he morar applicaion, morar applicaion process). Regarding he facors relaed o morar characerisics, i is known ha he increase of cemen proporion in a morar also increases he srengh of is normal and shear bond o he subsrae, and morars wih higher compressive and ensile srengh have more adherence capaciy; morars less viscous and easy o apply or wih a higher capaciy o reain waer perform beer in erms of adhesion (Gaspar, 2011). Figure 1 Mechanical bond beween a morar and is subsrae (Quinela, 2006). The subsrae naure is also significan in he developmen of he adhesive bond wih he subsrae. A rough surface exure helps he peneraion of morar fluids ino he subsrae pores. The iniial rae absorpion can also influence he subsrae/render bond srengh; here is an opimal range of values for his subsrae propery for which he srengh of he menioned bond is maximum. The presence of dus and oil in he surface of he subsrae prevens he peneraion of morar fluids ino is pores and caviies, and he subsrae/morar bond is unable o develop. Mois-curing and he applicaion of render hrough mechanical projecion are exernal facors ha have proven o improve he morar adherence capaciy (Gaspar, 2011).

5 Table 1 Lis of facors ha according o he lieraure can influence he subsrae/morar bond (Gaspar, 2011). Facors relaed o he rendering morar composiion (includes cemen and aggregaes characerisics and proporion) characerisics such as: compressive and ensile srengh, consisency, waer reenion hickness number of rendering sysem layers Facors relaed o he subsrae surface exure iniial rae absorpion porosiy iniial humidiy conen cleaning surface reamens Exernal facors render applicaion process mois-curing weaher condiions during applicaion 2.3 Mehods o evaluae he adhesion of morars The pull-off es is he mos used mehod o measure he adherence capaciy of a morar o he subsrae and is described in he European norm EN (CEN, 2000); his es measures he srengh of he normal bond beween a morar and a subsrae. The RILEM mehods MR14 (RILEM, 1982) and MR 20 (RILEM, 1982) describe wo es mehods o measure he srengh of a subsrae/morar shear bond. 3 MODELING A SUBSTRATE/RENDER SYSTEM IN ANSYS SOFTWARE 3.1 Overview of he ANSYS sofware ANSYS is a general purpose finie elemen modeling package for numerically solving a wide variey of engineering problems. These problems include: saic/dynamic srucural analysis (boh linear and non-linear), hea ransfer and fluid problems, as well as acousic and elecromagneic problems. ANSYS is ofen used by mechanical engineers o deermine in-use sress disribuions of vehicles componens. In he civil engineer area, ANSYS can be a helpful ool in modeling he mos complex srucures if combined wih he CivilFEM package sofware ha runs wihin ANSYS Muliphysics. 3.2 Modeling an inerface wih ANSYS Muliphysics 11.0 ANSYS Muliphysics 11.0 provides, in is finie elemen library, he called inerface elemens o model inerfaces beween srucural elemens. The several inerface elemens available differ in heir node number. The 2D models of a rendered facade (Figure 2) and of he pull-off mechanism ha were buil in ANSYS o sudy he influence of he inerface beween a render and is background wall have a plane geomery; herefore, he finie inerface elemen ype INTER202, which is a plane elemen wih four nodes, was used o model he inerface (Figure 3).

6 Undeformed shape Deformed shape I,J I J Y X Render Inerface Background wall Y X K,L n K n L Capion: I,J,K,L - elemen nodes X,Y - global coordinae sysem n, - elemen coordinae sysem Figure 2 Building facade geomery. Figure 3 Finie elemen INTER202 geomery. In he beginning of he soluion, he inerface elemen doesn have hickness, which means some of is nodes are iniially coinciden; wih he applicaion of forces in he model, he displacemen beween nodes wihin he inerface elemen increase, simulaing an inerfacial displacemen beween he wall and he render surfaces. The inerface elemens behave according o he exponenial cohesive zone model inroduced by Xu and Needleman (1993). The cohesive zone model consiss of a consiuive relaion beween he racion (T) acing on he inerface and he corresponding inerfacial separaion (Δ). The inerface racion and separaion are defined in he normal (n) and angenial () inerface direcion; hese direcions are based on he elemen coordinae sysem which is shown in Figure 4. The exponenial form of he cohesive zone model uses a surface poenial (ϕ) o define he inerface normal and angenial racion, according o Eq. (1) and Eq. (2): T n = ϕ(δ) n (1) T = ϕ(δ) (2) If he work associaed wih he separaion process in he normal and angenial direcion is assumed o be he same, hen he surface poenial is given by Eq. (3): ϕ (δ) = exp (1) σ max δ n Δ n exp ( Δ n ) exp ( Δ 2 δ n δ 2 n δ ) (3) where σ max represens he maximum normal racion a he inerface, δ n is he normal inerfacial separaion where σ max is aained in a paricular case in which here is no angenial separaion (Figure 4, righ) and δ is he shear inerface separaion for which 2 2 δ is he shear separaion corresponding o he maximum shear sress a he inerface (τ max ), when here is no normal inerfacial separaion (Figure 4, lef). The normal and shear

7 inerface racion of he inerface are expressed in Eq. (4) and (5), hese expressions are obained from Eq (1), (2) and (3). T n = exp (1) σ max Δ n δ n exp ( Δ n ) exp ( Δ 2 δ 2 n δ ) (4) T = 2 exp (1) σ δ n max 1 + Δ n exp ( Δ n ) exp ( Δ 2 δ δ δ n δ 2 n δ ) (5) T n σ max T τ max δ n Δ n 2 2 δ Δ Figure 4 Righ, graphical represenaion of Eq. 4, for Δ = 0; lef, graphical represenaion of Eq. 5, for Δ n = 0. The value of he parameers σ max, δ n, and δ mus be specified in ANSYS Muliphysics 11.0 so ha he inerface can be modeled; hey represen he inerface elemen inpus. As for he inerface elemen oupus, hey consis in he normal and shear inerface racion and separaion. 3.3 Modeling a subsrae and a render wih ANSYS Muliphysics 11.0 In he modeling of he subsrae and he render of he facade wih he geomery presened in Figure 3, he srucural, plane elemen wih four nodes, PLANE182 was used. The render and he subsrae maerial behave according o a linear consiuive model wih a maximum Von Mises sress (σ 1 ) ha he maerial can resis, and afer his sress is reached, hey can break. σ σ 1 E ε Figure 5 Render and subsrae behavior consiuive model.

8 The inpus of he PLANE182 elemen are maerial properies such as Poisson raion, Young's modulus (E), densiy and maximum Von Mises sress (σ 1 ). The oupus of elemen are mainly sresses and srains. 4 NUMERICAL MODEL OF THE WALL/MORTAR SISTEM 4.1 Parameric analysis None of he hree inerface parameers (σ max, δ n and δ ) are given in experimenal ess; he resul of he pull-off es is assumed o be close o he value of σ max. δ n and δ represen he disance ha he bonding crysals can be pushed from he background pores before he adhesion sars losing srengh. In hese analyses he wall/render models were subjec o a uniform racion applied on he render surface, besides he acion of heir weigh; he value of he hree inerface parameers were alered and he resuling inerface racions and separaions were compared. The firs referred acion inends o simulae he wind sucion ha affecs exernal render in-use condiions, which is an acion ha can be direcly inpued in he models. By increasing he value of δ n, he value of Δ n increase and he inerface deforms more. A very small value of Δ n implies ha he render and he wall ac as one, like in a model wihou inerface. Wih a large value of Δ n, he sress of he render is no ransmied o he wall; in his case, a render fracure is more likely o occur. As he value of σ max increases, he value of Δ n decreases. As he sudied acion acs in he normal direcion, he normal sress is higher han he shear one. The influence of Δ in he shear ension (T ) is idenical o he influence of Δ n in he normal sress (T n ). 4.2 Modeling of facors ha influence subsrae/render adhesion In secion 2.2, a lis of facors ha can influence he render adhesion o is background was presened. There are wo possible ways in which hese facors can be inroduced in he numerical model. Each facor ha causes a geomerical change in he sysem, like render cracks, can be inroduced by a change in he finie elemens. Oher facors, such as he wall roughness, can be inroduced by alering he inerface parameers. For insance, i is known hrough experimenal ess ha he wall roughness increases he adhesive srengh of he render; so by increasing he value of σ max in he numerical inerface, wall roughness is aken ino accoun. The ype of he rendering morar, is consisence, wall and render cracking, he render applicaion process and he presence of differen render layers were he facors inroduced in he numerical model. A bad render consisence can cause macro-defecs in he inerface wih he wall. The macro-defecs are creaed by deleing finie elemens in he inerface. The presence of a higher concenraion of macro-defecs induces more sress in he inerface, which will deform more. (Figure 6).This behavior is wha was expeced: he numerical model is predicing real behavior.

9 10% of macro-defecs 20% of macro-defecs Deails T n (Pa) 10% of macro-defecs 20% of macro-defecs Figure 6 Normal inerface sress (T n ) due o he presence of macro-defecs. Wall and render cracking will also submi he inerface o more sress. As for he render applicaion, he ergonomics of he applier will cause an heerogeneous inerface wih areas wih a beer bond; he exisence of differen bond srenghs hrough he inerface, will generae more sress in i. 5 CONCLUSION There are many facors ha can have an impac in a morar adhesive srengh for insiu condiions; he mehods used o measure adhesive srengh like he pull-off es have many limiaions for in-siu applicaion. Numerical models can be a useful ool o evaluae he influence of any facor in a wall/render adhesion in service condiions. The numerical models predic he expecable behavior and are capable o incorporae any facor. From he numerical model, we can conclude ha he presence of cracks in he render and in he wall, as well macro-defecs in he inerface, have a negaive impac on he render adhesion. The heerogeneiy of he render or of he inerface also decrease he srengh of he inerfacial render-wall bond.

10 REFERENCES Xu, X. P.; Needleman, A. (1993) - Numerical simulaion of fas crack growh in brile solids. Journal of he Mechanics and Physics of Solids, vol 42: pp Chandra, N.; Li, H.; She, C.; Ghonem, H. (2000) - Some issues in he applicaion of cohesive zone models for meal-ceramic inerfaces. In: Inernaional Journal of solids and Srucures 39 (2002): pp ANSYS (2007) - Release 11.0 Documenaion for ANSYS. ANSYS (2009) - Fluid Analysis soluions brochure, 12.1 release.

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

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

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

Vehicle Arrival Models : Headway

Vehicle Arrival Models : Headway Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where

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

Failure of the work-hamiltonian connection for free energy calculations. Abstract

Failure of the work-hamiltonian connection for free energy calculations. Abstract Failure of he work-hamilonian connecion for free energy calculaions Jose M. G. Vilar 1 and J. Miguel Rubi 1 Compuaional Biology Program, Memorial Sloan-Keering Cancer Cener, 175 York Avenue, New York,

More information

Numerical Evaluation of an Add-On Vehicle Protection System

Numerical Evaluation of an Add-On Vehicle Protection System Numerical Evaluaion of an Add-On Vehicle Proecion Sysem Geneviève Toussain, Amal Bouamoul, Rober Durocher, Jacob Bélanger*, Benoî S-Jean Defence Research and Developmen Canada Valcarier 2459 Bravoure Road,

More information

ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE

ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE Dr Zhaohui Huang Universiy of Sheffield 6 May 2005 1 VULCAN layered slab elemens: connecion o beam elemens Plae Elemen Slab nodes y x Reference Plane h

More information

Linear Response Theory: The connection between QFT and experiments

Linear Response Theory: The connection between QFT and experiments Phys540.nb 39 3 Linear Response Theory: The connecion beween QFT and experimens 3.1. Basic conceps and ideas Q: How do we measure he conduciviy of a meal? A: we firs inroduce a weak elecric field E, and

More information

Material #1. r θ x Material #2. Material #1

Material #1. r θ x Material #2. Material #1 I T y Maerial Adherend T d c r θ x Maerial Adhesive T Maerial Adherend T I Fig. 1. A crack wihin he adhesive layer in an adhesive bond. The adherend is designaed as maerial 1 and adhesive is designaed

More information

10. State Space Methods

10. State Space Methods . Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he

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

Finite Element Analysis of Structures

Finite Element Analysis of Structures KAIT OE5 Finie Elemen Analysis of rucures Mid-erm Exam, Fall 9 (p) m. As shown in Fig., we model a russ srucure of uniform area (lengh, Area Am ) subjeced o a uniform body force ( f B e x N / m ) using

More information

Chapter 12: Velocity, acceleration, and forces

Chapter 12: Velocity, acceleration, and forces To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable

More information

6.01: Introduction to EECS I Lecture 8 March 29, 2011

6.01: Introduction to EECS I Lecture 8 March 29, 2011 6.01: Inroducion o EES I Lecure 8 March 29, 2011 6.01: Inroducion o EES I Op-Amps Las Time: The ircui Absracion ircuis represen sysems as connecions of elemens hrough which currens (hrough variables) flow

More information

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms

More information

Numerical investigation of Ranque-Hilsch energy separation effect A.S. Noskov 1,a, V.N. Alekhin 1,b, A.V. Khait 1,a

Numerical investigation of Ranque-Hilsch energy separation effect A.S. Noskov 1,a, V.N. Alekhin 1,b, A.V. Khait 1,a Applied Mechanics and Maerials Online: 2013-01-11 ISSN: 1662-7482, Vol. 281, pp 355-358 doi:10.4028/www.scienific.ne/amm.281.355 2013 Trans Tech Publicaions, Swizerland Numerical invesigaion of Ranque-Hilsch

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

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

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

Modeling the Dynamics of an Ice Tank Carriage

Modeling the Dynamics of an Ice Tank Carriage Modeling he Dynamics of an Ice Tank Carriage The challenge: To model he dynamics of an Ice Tank Carriage and idenify a mechanism o alleviae he backlash inheren in he design of he gearbox. Maplesof, a division

More information

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he

More information

Class Meeting # 10: Introduction to the Wave Equation

Class Meeting # 10: Introduction to the Wave Equation MATH 8.5 COURSE NOTES - CLASS MEETING # 0 8.5 Inroducion o PDEs, Fall 0 Professor: Jared Speck Class Meeing # 0: Inroducion o he Wave Equaion. Wha is he wave equaion? The sandard wave equaion for a funcion

More information

Chapter 2. First Order Scalar Equations

Chapter 2. First Order Scalar Equations Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.

More information

3.3 Internal Stress. Cauchy s Concept of Stress

3.3 Internal Stress. Cauchy s Concept of Stress INTERNL TRE 3.3 Inernal ress The idea of sress considered in 3.1 is no difficul o concepualise since objecs ineracing wih oher objecs are encounered all around us. more difficul concep is he idea of forces

More information

DESIGN OF TENSION MEMBERS

DESIGN OF TENSION MEMBERS CHAPTER Srcral Seel Design LRFD Mehod DESIGN OF TENSION MEMBERS Third Ediion A. J. Clark School of Engineering Deparmen of Civil and Environmenal Engineering Par II Srcral Seel Design and Analysis 4 FALL

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

Chapter 14 Homework Answers

Chapter 14 Homework Answers 4. Suden responses will vary. (a) combusion of gasoline (b) cooking an egg in boiling waer (c) curing of cemen Chaper 4 Homework Answers 4. A collision beween only wo molecules is much more probable han

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion

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

Comparing Means: t-tests for One Sample & Two Related Samples

Comparing Means: t-tests for One Sample & Two Related Samples Comparing Means: -Tess for One Sample & Two Relaed Samples Using he z-tes: Assumpions -Tess for One Sample & Two Relaed Samples The z-es (of a sample mean agains a populaion mean) is based on he assumpion

More information

STATE-SPACE MODELLING. A mass balance across the tank gives:

STATE-SPACE MODELLING. A mass balance across the tank gives: B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing

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

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

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

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

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

CH.7. PLANE LINEAR ELASTICITY. Continuum Mechanics Course (MMC) - ETSECCPB - UPC

CH.7. PLANE LINEAR ELASTICITY. Continuum Mechanics Course (MMC) - ETSECCPB - UPC CH.7. PLANE LINEAR ELASTICITY Coninuum Mechanics Course (MMC) - ETSECCPB - UPC Overview Plane Linear Elasici Theor Plane Sress Simplifing Hpohesis Srain Field Consiuive Equaion Displacemen Field The Linear

More information

Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles

Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance

More information

A Robust Cohesive Zone Model for Cyclic Loading

A Robust Cohesive Zone Model for Cyclic Loading 14 h Inernaional LS-DYNA Users Conference Session: Simulaion A Robus Cohesive Zone Model for Cyclic Loading Ala Tabiei and Wenlong Zhang Deparmen of Mechanical Engineering Universiy of Cincinnai, Cincinnai,

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

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION DOI: 0.038/NCLIMATE893 Temporal resoluion and DICE * Supplemenal Informaion Alex L. Maren and Sephen C. Newbold Naional Cener for Environmenal Economics, US Environmenal Proecion

More information

Inventory Control of Perishable Items in a Two-Echelon Supply Chain

Inventory Control of Perishable Items in a Two-Echelon Supply Chain Journal of Indusrial Engineering, Universiy of ehran, Special Issue,, PP. 69-77 69 Invenory Conrol of Perishable Iems in a wo-echelon Supply Chain Fariborz Jolai *, Elmira Gheisariha and Farnaz Nojavan

More information

Section 7.4 Modeling Changing Amplitude and Midline

Section 7.4 Modeling Changing Amplitude and Midline 488 Chaper 7 Secion 7.4 Modeling Changing Ampliude and Midline While sinusoidal funcions can model a variey of behaviors, i is ofen necessary o combine sinusoidal funcions wih linear and exponenial curves

More information

EE650R: Reliability Physics of Nanoelectronic Devices Lecture 9:

EE650R: Reliability Physics of Nanoelectronic Devices Lecture 9: EE65R: Reliabiliy Physics of anoelecronic Devices Lecure 9: Feaures of Time-Dependen BTI Degradaion Dae: Sep. 9, 6 Classnoe Lufe Siddique Review Animesh Daa 9. Background/Review: BTI is observed when he

More information

Inequality measures for intersecting Lorenz curves: an alternative weak ordering

Inequality measures for intersecting Lorenz curves: an alternative weak ordering h Inernaional Scienific Conference Financial managemen of Firms and Financial Insiuions Osrava VŠB-TU of Osrava, Faculy of Economics, Deparmen of Finance 7 h 8 h Sepember 25 Absrac Inequaliy measures for

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

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

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

3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon

3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon 3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of

More information

- If one knows that a magnetic field has a symmetry, one may calculate the magnitude of B by use of Ampere s law: The integral of scalar product

- If one knows that a magnetic field has a symmetry, one may calculate the magnitude of B by use of Ampere s law: The integral of scalar product 11.1 APPCATON OF AMPEE S AW N SYMMETC MAGNETC FEDS - f one knows ha a magneic field has a symmery, one may calculae he magniude of by use of Ampere s law: The inegral of scalar produc Closed _ pah * d

More information

4. Electric field lines with respect to equipotential surfaces are

4. Electric field lines with respect to equipotential surfaces are Pre-es Quasi-saic elecromagneism. The field produced by primary charge Q and by an uncharged conducing plane disanced from Q by disance d is equal o he field produced wihou conducing plane by wo following

More information

Influence of High Axial Tension on the Shear Strength of non-shear RC Beams

Influence of High Axial Tension on the Shear Strength of non-shear RC Beams Influence of High Axial Tension on he Shear Srengh of non-shear RC Beams Henrik B. JOERGENSEN PhD candidae Univ. of Souhern Denmark hebj@ii.sdu.dk Joergen MAAGAARD Associae Professor Univ. of Souhern Denmark

More information

APPM 2360 Homework Solutions, Due June 10

APPM 2360 Homework Solutions, Due June 10 2.2.2: Find general soluions for he equaion APPM 2360 Homework Soluions, Due June 10 Soluion: Finding he inegraing facor, dy + 2y = 3e µ) = e 2) = e 2 Muliplying he differenial equaion by he inegraing

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

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check

More information

Cumulative Damage Evaluation based on Energy Balance Equation

Cumulative Damage Evaluation based on Energy Balance Equation Cumulaive Damage Evaluaion based on Energy Balance Equaion K. Minagawa Saiama Insiue of Technology, Saiama S. Fujia Tokyo Denki Universiy, Tokyo! SUMMARY: This paper describes an evaluaion mehod for cumulaive

More information

Basic Circuit Elements Professor J R Lucas November 2001

Basic Circuit Elements Professor J R Lucas November 2001 Basic Circui Elemens - J ucas An elecrical circui is an inerconnecion of circui elemens. These circui elemens can be caegorised ino wo ypes, namely acive and passive elemens. Some Definiions/explanaions

More information

Viscoelastic Catenary

Viscoelastic Catenary Viscoelasic Caenary Anshuman Roy 1 Inroducion This paper seeks o deermine he shape of a hin viscoelasic fluid filamen as i sags under is own weigh. The problem is an exension of he viscous caenary [1]

More information

Families with no matchings of size s

Families with no matchings of size s Families wih no machings of size s Peer Franl Andrey Kupavsii Absrac Le 2, s 2 be posiive inegers. Le be an n-elemen se, n s. Subses of 2 are called families. If F ( ), hen i is called - uniform. Wha is

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

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

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time.

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time. Supplemenary Figure 1 Spike-coun auocorrelaions in ime. Normalized auocorrelaion marices are shown for each area in a daase. The marix shows he mean correlaion of he spike coun in each ime bin wih he spike

More information

The following report makes use of the process from Chapter 2 in Dr. Cumming s thesis.

The following report makes use of the process from Chapter 2 in Dr. Cumming s thesis. Zaleski 1 Joseph Zaleski Mah 451H Final Repor Conformal Mapping Mehods and ZST Hele Shaw Flow Inroducion The Hele Shaw problem has been sudied using linear sabiliy analysis and numerical mehods, bu a novel

More information

Robust estimation based on the first- and third-moment restrictions of the power transformation model

Robust estimation based on the first- and third-moment restrictions of the power transformation model h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,

More information

T L. t=1. Proof of Lemma 1. Using the marginal cost accounting in Equation(4) and standard arguments. t )+Π RB. t )+K 1(Q RB

T L. t=1. Proof of Lemma 1. Using the marginal cost accounting in Equation(4) and standard arguments. t )+Π RB. t )+K 1(Q RB Elecronic Companion EC.1. Proofs of Technical Lemmas and Theorems LEMMA 1. Le C(RB) be he oal cos incurred by he RB policy. Then we have, T L E[C(RB)] 3 E[Z RB ]. (EC.1) Proof of Lemma 1. Using he marginal

More information

20. Applications of the Genetic-Drift Model

20. Applications of the Genetic-Drift Model 0. Applicaions of he Geneic-Drif Model 1) Deermining he probabiliy of forming any paricular combinaion of genoypes in he nex generaion: Example: If he parenal allele frequencies are p 0 = 0.35 and q 0

More information

IMPACT OF AN OBLIQUE BREAKING WAVE ON A WALL

IMPACT OF AN OBLIQUE BREAKING WAVE ON A WALL Source: Physics of Fluids Vol 6 No pp 6-64 4 DOI: 6/64445 IMPACT OF AN OIQUE REAKING WAVE ON A WA Jian-Jun SHU School of Mechanical & Aerospace Engineering Nanyang Technological Universiy 5 Nanyang Avenue

More information

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis TRANSPORTATION RESEARCH RECORD 155 35 Curling Sress Equaion for Transverse Join Edge of a Concree Pavemen Slab Based on Finie-Elemen Mehod Analysis TATSUO NISHIZAWA, TADASHI FUKUDA, SABURO MATSUNO, AND

More information

Analysis of Microstrip Coupling Gap to Estimate Polymer Permittivity

Analysis of Microstrip Coupling Gap to Estimate Polymer Permittivity Analysis of Microsrip Couplin Gap o Esimae Polymer Permiiviy Chanchal Yadav Deparmen of Physics & Elecronics Rajdhani Collee, Universiy of Delhi Delhi, India Absrac A ap in he microsrip line can be modeled

More information

CENTRALIZED VERSUS DECENTRALIZED PRODUCTION PLANNING IN SUPPLY CHAINS

CENTRALIZED VERSUS DECENTRALIZED PRODUCTION PLANNING IN SUPPLY CHAINS CENRALIZED VERSUS DECENRALIZED PRODUCION PLANNING IN SUPPLY CHAINS Georges SAHARIDIS* a, Yves DALLERY* a, Fikri KARAESMEN* b * a Ecole Cenrale Paris Deparmen of Indusial Engineering (LGI), +3343388, saharidis,dallery@lgi.ecp.fr

More information

DEPARTMENT OF STATISTICS

DEPARTMENT OF STATISTICS A Tes for Mulivariae ARCH Effecs R. Sco Hacker and Abdulnasser Haemi-J 004: DEPARTMENT OF STATISTICS S-0 07 LUND SWEDEN A Tes for Mulivariae ARCH Effecs R. Sco Hacker Jönköping Inernaional Business School

More information

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

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

Summary of shear rate kinematics (part 1)

Summary of shear rate kinematics (part 1) InroToMaFuncions.pdf 4 CM465 To proceed o beer-designed consiuive equaions, we need o know more abou maerial behavior, i.e. we need more maerial funcions o predic, and we need measuremens of hese maerial

More information

Calculation of the Two High Voltage Transmission Line Conductors Minimum Distance

Calculation of the Two High Voltage Transmission Line Conductors Minimum Distance World Journal of Engineering and Technology, 15, 3, 89-96 Published Online Ocober 15 in SciRes. hp://www.scirp.org/journal/wje hp://dx.doi.org/1.436/wje.15.33c14 Calculaion of he Two High Volage Transmission

More information

Wavepacket and Dispersion

Wavepacket and Dispersion Wavepacke and Dispersion Andreas Wacker 1 Mahemaical Physics, Lund Universiy Sepember 18, 2017 1 Moivaion A wave is a periodic srucure in space and ime wih periods λ and T, respecively. Common examples

More information

) were both constant and we brought them from under the integral.

) were both constant and we brought them from under the integral. YIELD-PER-RECRUIT (coninued The yield-per-recrui model applies o a cohor, bu we saw in he Age Disribuions lecure ha he properies of a cohor do no apply in general o a collecion of cohors, which is wha

More information

Probabilistic Models for Reliability Analysis of a System with Three Consecutive Stages of Deterioration

Probabilistic Models for Reliability Analysis of a System with Three Consecutive Stages of Deterioration Yusuf I., Gaawa R.I. Volume, December 206 Probabilisic Models for Reliabiliy Analysis of a Sysem wih Three Consecuive Sages of Deerioraion Ibrahim Yusuf Deparmen of Mahemaical Sciences, Bayero Universiy,

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

The fundamental mass balance equation is ( 1 ) where: I = inputs P = production O = outputs L = losses A = accumulation

The fundamental mass balance equation is ( 1 ) where: I = inputs P = production O = outputs L = losses A = accumulation Hea (iffusion) Equaion erivaion of iffusion Equaion The fundamenal mass balance equaion is I P O L A ( 1 ) where: I inpus P producion O oupus L losses A accumulaion Assume ha no chemical is produced or

More information

Inventory Analysis and Management. Multi-Period Stochastic Models: Optimality of (s, S) Policy for K-Convex Objective Functions

Inventory Analysis and Management. Multi-Period Stochastic Models: Optimality of (s, S) Policy for K-Convex Objective Functions Muli-Period Sochasic Models: Opimali of (s, S) Polic for -Convex Objecive Funcions Consider a seing similar o he N-sage newsvendor problem excep ha now here is a fixed re-ordering cos (> 0) for each (re-)order.

More information

Forecasting optimally

Forecasting optimally I) ile: Forecas Evaluaion II) Conens: Evaluaing forecass, properies of opimal forecass, esing properies of opimal forecass, saisical comparison of forecas accuracy III) Documenaion: - Diebold, Francis

More information

Turbulent Flows. Computational Modelling of Turbulent Flows. Overview. Turbulent Eddies and Scales

Turbulent Flows. Computational Modelling of Turbulent Flows. Overview. Turbulent Eddies and Scales School of Mechanical Aerospace and Civil Engineering Turbulen Flows As noed above, using he mehods described in earlier lecures, he Navier-Sokes equaions can be discreized and solved numerically on complex

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

di Bernardo, M. (1995). A purely adaptive controller to synchronize and control chaotic systems.

di Bernardo, M. (1995). A purely adaptive controller to synchronize and control chaotic systems. di ernardo, M. (995). A purely adapive conroller o synchronize and conrol chaoic sysems. hps://doi.org/.6/375-96(96)8-x Early version, also known as pre-prin Link o published version (if available):.6/375-96(96)8-x

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

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model Modal idenificaion of srucures from roving inpu daa by means of maximum likelihood esimaion of he sae space model J. Cara, J. Juan, E. Alarcón Absrac The usual way o perform a forced vibraion es is o fix

More information

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran Curren Trends in Technology and Science ISSN : 79-055 8hSASTech 04 Symposium on Advances in Science & Technology-Commission-IV Mashhad, Iran A New for Sofware Reliabiliy Evaluaion Based on NHPP wih Imperfec

More information

8. Basic RL and RC Circuits

8. Basic RL and RC Circuits 8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics

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

Traveling Waves. Chapter Introduction

Traveling Waves. Chapter Introduction Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from

More information

Damped mechanical oscillator: Experiment and detailed energy analysis

Damped mechanical oscillator: Experiment and detailed energy analysis 1 Damped mechanical oscillaor: Experimen and deailed energy analysis Tommaso Corridoni, DFA, Locarno, Swizerland Michele D Anna, Liceo canonale, Locarno, Swizerland Hans Fuchs, Zurich Universiy of Applied

More information

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization Proceedings Inverse Analysis for Esimaing Temperaure and Residual Sress Disribuions in a Pipe from Ouer Surface Temperaure Measuremen and Is Regularizaion Shiro Kubo * and Shoki Taguwa Deparmen of Mechanical

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

Matrix Versions of Some Refinements of the Arithmetic-Geometric Mean Inequality

Matrix Versions of Some Refinements of the Arithmetic-Geometric Mean Inequality Marix Versions of Some Refinemens of he Arihmeic-Geomeric Mean Inequaliy Bao Qi Feng and Andrew Tonge Absrac. We esablish marix versions of refinemens due o Alzer ], Carwrigh and Field 4], and Mercer 5]

More information

HW6: MRI Imaging Pulse Sequences (7 Problems for 100 pts)

HW6: MRI Imaging Pulse Sequences (7 Problems for 100 pts) HW6: MRI Imaging Pulse Sequences (7 Problems for 100 ps) GOAL The overall goal of HW6 is o beer undersand pulse sequences for MRI image reconsrucion. OBJECTIVES 1) Design a spin echo pulse sequence o image

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

The equation to any straight line can be expressed in the form:

The equation to any straight line can be expressed in the form: Sring Graphs Par 1 Answers 1 TI-Nspire Invesigaion Suden min Aims Deermine a series of equaions of sraigh lines o form a paern similar o ha formed by he cables on he Jerusalem Chords Bridge. Deermine he

More information