Buckling of a structure means failure due to excessive displacements (loss of structural stiffness), and/or
|
|
|
- Candice Waters
- 5 years ago
- Views:
Transcription
1 Buckling Buckling of a rucure mean failure due o exceive diplacemen (lo of rucural iffne), and/or lo of abiliy of an equilibrium configuraion of he rucure The rule of humb i ha buckling i conidered a mode of failure for lender member in compreion, or for hin panel in compreion or hear. Abou 50% of an airplane deign may be limied by he buckling of hin kin. AOE 2104 Inro. o Aero Engineering. Lec. 6: 1 of 19
2 Concep of abiliy of equilibrium Sabiliy of equilibrium mean ha he repone of he rucure due o a mall diurbance from i equilibrium configuraion remain mall; he maller he diurbance he maller he reuling magniude of he diplacemen in he repone.if a mall diurbance caue large diplacemen, perhap even heoreically infinie, hen he equilibrium ae i unable. able equilibrium g unable equilibrium neural equilibrium AOE 2104 Inro. o Aero Engineering. Lec. 6: 2 of 19
3 Sabiliy of equilibrium wih repec o load racical rucure are able a no load. Now conider increaing he load lowly. We are inereed in he value of he load, called he criical load, a which buckling occur. Tha i, we are inereed in when a equence of equilibrium ae a a funcion of he load, one ae for each value of he load, ceae o be able. 0 unloaded configuraion able equilibrium 0 < < ure compreion repone able equilibrium > urely compreive configuraion loe abiliy o a combined bending compreion configuraion AOE 2104 Inro. o Aero Engineering. Lec. 6: 3 of 19
4 Load-horening curve for compreion erfecly raigh, elaic column cr 0 compreive axial force axial diplacemen criical load of perfec rucure diplacemen a he criical load < < cr > > cr 1 0 pure compreion 1 u u fla plae column cylindrical hell able u unable cr Afer buckling he column canno rei much of an increae in load. I pobuckling iffne i near zero. I i aid he column i neural in pobuckling AOE 2104 Inro. o Aero Engineering. Lec. 6: 4 of 19
5 Load-horening curve (coninued) A perfecly fla recangular plae All four edge uppored; elaic buckling 1 pure compreion u fla plae column > unloaded edge 0 1 u cylindrical hell cr able u unable unloaded edge > The plae can rei increaed load afer buckling becaue he unloaded edge are uppored. I iffne i reduced in pobuckling. The plae i aid o have pobuckling rengh. AOE 2104 Inro. o Aero Engineering. Lec. 6: 5 of 19
6 Load-horening curve (coninued) A circular cylindrical hell > cr R 1 0 pure compreion cr able u unable The hell canno rei increaed load afer buckling. The load and diplacemen decreae on he iniial, unable pobuckling equilibrium pah. The hell ha no pobuckling rengh. Deigner have o knockdown he value of obained from he heory of he perfec hell by a ubanial amoun. 1 u u fla plae column cylindrical hell AOE 2104 Inro. o Aero Engineering. Lec. 6: 6 of 19
7 Euler load for a pinned-pinned column π EI b 2 The criical load increae wih increaed bending iffne EI, and decreae wih increaing column lengh b. N.B., Eq. 7.24, p. 263, in he ex i incorrec. b 0 < < cr > > cr For deign of elaic column he criical load, or Euler load, i ued o deermine failure by buckling. Alo ue he minimum I for he cro-ecional area. AOE 2104 Inro. o Aero Engineering. Lec. 6: 7 of 19
8 For column deign ue minimum I h h > I min I max h 12 h h w b f f I min I max b f 6 h 2 b f 2 for mo I-ecion h w 12 r I min I max πr 3 hin-walled ube AOE 2104 Inro. o Aero Engineering. Lec. 6: 8 of 19
9 Deign buckling load for an elaic plae For purpoe of deign, he compreive buckling load of a recangular, hin plae wih all four edge uppored by hinge i ν 4π 2 cr E 3 b 12( 1 ν 2 ) where i oion raio, a dimenionle maerial propery. ν 0.3 For mo aluminum alloy. all four edge wih hinge uppor a 0 < «a and b b Acually a b i a funcion of he plae apec raio. The formula given above i good lower bound eimae of for a b > 1.0. AOE 2104 Inro. o Aero Engineering. Lec. 6: 9 of 19
10 Buckling load for a circular cylindrical hell Theory give he formula for he criical compreive axial normal re,, a σ cr σ 1 cr E ( ν 2 ) R The correponding compreive axial normal force,, a he buckling i obained from σ cr ( 2πR) hin hell R ---» 1 R L AOE 2104 Inro. o Aero Engineering. Lec. 6: 10 of 19
11 Deign buckling load for he hell The formula for σ cr above i valid for elaic buckling of a hin, circular cylindrical hell if he hell i moderaely long. Moderaely long i characerize by parameer Z > 2.85, where hi parameer (called he Badorf parameer) i defined by Z L ν 2 R If he hell i oo long i will buckle a a column raher han hell, and we ue Euler formula o eimae ha criical load. For deign we ue a knockdown facor, which accoun for he fac ha experimenal value of he buckling load of axially compreed circular cylindrical hell are ubanially le han he heoreical predicion. Tha i, he deign buckling load i relaed o he heoreical value by σ cr deign γ γσ cr heory AOE 2104 Inro. o Aero Engineering. Lec. 6: 11 of 19
12 Deign buckling load for he hell (concluded) The knockdown facor i a funcion of he radiu o hickne R γ R raio,. Facor decreae for hinner hell, i.e., a increae. For example, a deign recommendaion i R/ γ R If i mall, hen he hell will no buckle in he elaic maerial range. AOE 2104 Inro. o Aero Engineering. Lec. 6: 12 of 19
13 Srucural erformance Indice For aeropace applicaion weigh i an exremely imporan meaure of he performance of a rucure. In comparing differen maerial one need o ake ino accoun heir relaive efficiency in erm of rengh o weigh raio and iffne o weigh raio. However, hee raio depend on he ype of loading. We will compare hee performance indice for a panel of lengh a, widh b, and hickne. a b AOE 2104 Inro. o Aero Engineering. Lec. 6: 13 of 19
14 Tenion panel The weigh of he panel i w ( ρg)ab where g ρ ma deniy acceleraion due o graviy Aume he lengh a and widh b are given. For he panel ubjeced o enion, he axial force N i N pecified. Le σ f denoe he failure rengh of he maerial. The value of σ could be he a f enile rengh, or he yield rengh, or an allowable re for he maerial. b N AOE 2104 Inro. o Aero Engineering. Lec. 6: 14 of 19
15 Tenion panel (coninued) The axial normal re in he panel i, and we e hi equal o he failure re σ f of he maerial and olve for he hickne o ge N ( bσ f ). Now eliminae he hickne in he weigh equaion o find N ( b) w N a ( ρg) σ f Here he axial force N i a pecified funcional requiremen, lengh a i pecified geomery, and σ f ( ρg) i a maerial propery. A maerial wih a large value of σ f ( ρg) will reul in a lower weigh panel of pecified dimenion a by b ha ha o carry he pecified enile force N. AOE 2104 Inro. o Aero Engineering. Lec. 6: 15 of 19
16 Tenion panel (coninued) From able 7.3 in he ex, we li value of rengh o pecific weigh raio, ( ρg), for eleced maerial. σ f Maerial, lug/in 3, in 10 3 in 4340 Seel T4 Aluminum T6 Aluminum Tianium Graphie/Epoxy a Spruce wood a a. correced from he value lied in Table 7.3 ρ σ u ( ρg) AOE 2104 Inro. o Aero Engineering. Lec. 6: 16 of 19
17 Tenion panel pecified iffne The panel iffne i pecified, where iffne K i defined a K N and i he elongaion under enile load N. σ From Hooke law, bu and. So, N Eε σ N ( b) ε a N be( a) a b N Noe ha K N and we ee ha K b ---- E a. AOE 2104 Inro. o Aero Engineering. Lec. 6: 17 of 19
18 Tenion panel pecified iffne (con.) Now olve for o ge Ka Eb Eliminae hickne in he weigh equaion and wrie i a w Ka E ( ρg) where K i he funcional requiremen (pecified iffne) a 2 i he pecified geomery and E ( ρg) i a maerial propery AOE 2104 Inro. o Aero Engineering. Lec. 6: 18 of 19
19 Tenion panel pecified iffne (concl.) A maerial wih a large value of pecific modulu reul in a lower weigh panel. The pecific modulu i Young modulu divided by he pecific weigh of he maerial. E ( ρg) Maerial, lug/in 3, ρ in 10 6 in 4340 Seel a 2024-T4 Aluminum T6 Aluminum a Tianium Commen The meal panel all have abou he ame pecific iffne. Graphie/Epoxy impreive Spruce wood a a. Correced from he value lied in Table 7.3 of he ex AOE 2104 Inro. o Aero Engineering. Lec. 6: 19 of 19
Lecture 5 Buckling Buckling of a structure means failure due to excessive displacements (loss of structural stiffness), and/or
AOE 204 Inroducion o Aeropace Engineering Lecure 5 Buckling Buckling of a rucure mean failure due o exceive diplacemen (lo of rucural iffne), and/or lo of abiliy of an equilibrium configuraion of he rucure
u(t) Figure 1. Open loop control system
Open loop conrol v cloed loop feedbac conrol The nex wo figure preen he rucure of open loop and feedbac conrol yem Figure how an open loop conrol yem whoe funcion i o caue he oupu y o follow he reference
( ) - maximum permissible bending. IJSRD - International Journal for Scientific Research & Development Vol. 4, Issue 01, 2016 ISSN (online):
IJSRD - Inernaional Journal for Scienific Reearch & Developmen Vol. 4, Iue 01, 016 ISSN (online): 31-0613 Dr.N.Arunachalam 1 P.Prakah K.Jayakarhik 3 M.Narmadha 4 1 Profeor & Dean,3 PG Scholar 4 Aociae
Introduction to Congestion Games
Algorihmic Game Theory, Summer 2017 Inroducion o Congeion Game Lecure 1 (5 page) Inrucor: Thoma Keelheim In hi lecure, we ge o know congeion game, which will be our running example for many concep in game
6.302 Feedback Systems Recitation : Phase-locked Loops Prof. Joel L. Dawson
6.32 Feedback Syem Phae-locked loop are a foundaional building block for analog circui deign, paricularly for communicaion circui. They provide a good example yem for hi cla becaue hey are an excellen
INTRODUCTION TO INERTIAL CONFINEMENT FUSION
INTODUCTION TO INETIAL CONFINEMENT FUSION. Bei Lecure 7 Soluion of he imple dynamic igniion model ecap from previou lecure: imple dynamic model ecap: 1D model dynamic model ρ P() T enhalpy flux ino ho
Rectilinear Kinematics
Recilinear Kinemaic Coninuou Moion Sir Iaac Newon Leonard Euler Oeriew Kinemaic Coninuou Moion Erraic Moion Michael Schumacher. 7-ime Formula 1 World Champion Kinemaic The objecie of kinemaic i o characerize
Randomized Perfect Bipartite Matching
Inenive Algorihm Lecure 24 Randomized Perfec Biparie Maching Lecurer: Daniel A. Spielman April 9, 208 24. Inroducion We explain a randomized algorihm by Ahih Goel, Michael Kapralov and Sanjeev Khanna for
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
1 exp( c) 1 ( )
Maerial Model LS-DYNA Theory Manual For exponenial relaionhip: 0 ε 0 cε h( ε) exp ε > 0 c 0 exp( c) Lmax ε Lmax ε > 0 c 0 where Lmax SSM ; and c CER. Sre of Damping Elemen i: σ D ε ε (9.56.5) 3 max Toal
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
Problem Set If all directed edges in a network have distinct capacities, then there is a unique maximum flow.
CSE 202: Deign and Analyi of Algorihm Winer 2013 Problem Se 3 Inrucor: Kamalika Chaudhuri Due on: Tue. Feb 26, 2013 Inrucion For your proof, you may ue any lower bound, algorihm or daa rucure from he ex
Motion In One Dimension. Graphing Constant Speed
Moion In One Dimenion PLATO AND ARISTOTLE GALILEO GALILEI LEANING TOWER OF PISA Graphing Conan Speed Diance v. Time for Toy Car (0-5 ec.) be-fi line (from TI calculaor) d = 207.7 12.6 Diance (cm) 1000
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
Chapter 7: Inverse-Response Systems
Chaper 7: Invere-Repone Syem Normal Syem Invere-Repone Syem Baic Sar ou in he wrong direcion End up in he original eady-ae gain value Two or more yem wih differen magniude and cale in parallel Main yem
, the. L and the L. x x. max. i n. It is easy to show that these two norms satisfy the following relation: x x n x = (17.3) max
ecure 8 7. Sabiliy Analyi For an n dimenional vecor R n, he and he vecor norm are defined a: = T = i n i (7.) I i eay o how ha hee wo norm aify he following relaion: n (7.) If a vecor i ime-dependen, hen
Discussion Session 2 Constant Acceleration/Relative Motion Week 03
PHYS 100 Dicuion Seion Conan Acceleraion/Relaive Moion Week 03 The Plan Today you will work wih your group explore he idea of reference frame (i.e. relaive moion) and moion wih conan acceleraion. You ll
13.1 Accelerating Objects
13.1 Acceleraing Objec A you learned in Chaper 12, when you are ravelling a a conan peed in a raigh line, you have uniform moion. However, mo objec do no ravel a conan peed in a raigh line o hey do no
6.8 Laplace Transform: General Formulas
48 HAP. 6 Laplace Tranform 6.8 Laplace Tranform: General Formula Formula Name, ommen Sec. F() l{ f ()} e f () d f () l {F()} Definiion of Tranform Invere Tranform 6. l{af () bg()} al{f ()} bl{g()} Lineariy
Let. x y. denote a bivariate time series with zero mean.
Linear Filer Le x y : T denoe a bivariae ime erie wih zero mean. Suppoe ha he ime erie {y : T} i conruced a follow: y a x The ime erie {y : T} i aid o be conruced from {x : T} by mean of a Linear Filer.
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
Notes on cointegration of real interest rates and real exchange rates. ρ (2)
Noe on coinegraion of real inere rae and real exchange rae Charle ngel, Univeriy of Wiconin Le me ar wih he obervaion ha while he lieraure (mo prominenly Meee and Rogoff (988) and dion and Paul (993))
Introduction to SLE Lecture Notes
Inroducion o SLE Lecure Noe May 13, 16 - The goal of hi ecion i o find a ufficien condiion of λ for he hull K o be generaed by a imple cure. I urn ou if λ 1 < 4 hen K i generaed by a imple curve. We will
Network Flows: Introduction & Maximum Flow
CSC 373 - lgorihm Deign, nalyi, and Complexiy Summer 2016 Lalla Mouaadid Nework Flow: Inroducion & Maximum Flow We now urn our aenion o anoher powerful algorihmic echnique: Local Search. In a local earch
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.
Rocket Theories Continued
38 Rocke Theories ---------------------- Coninued and Nozzle heory fundamenals Various Liquid Proellans and heir yical Characerisics Pro Ox/F Thrus I s P c C F V * raio Vac SL Vac SL Vac (kn) (kn) s s
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
Physics 240: Worksheet 16 Name
Phyic 4: Workhee 16 Nae Non-unifor circular oion Each of hee proble involve non-unifor circular oion wih a conan α. (1) Obain each of he equaion of oion for non-unifor circular oion under a conan acceleraion,
EE Control Systems LECTURE 2
Copyrigh F.L. Lewi 999 All righ reerved EE 434 - Conrol Syem LECTURE REVIEW OF LAPLACE TRANSFORM LAPLACE TRANSFORM The Laplace ranform i very ueful in analyi and deign for yem ha are linear and ime-invarian
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
CHAPTER 2 Signals And Spectra
CHAPER Signals And Specra Properies of Signals and Noise In communicaion sysems he received waveform is usually caegorized ino he desired par conaining he informaion, and he undesired par. he desired par
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
1 Motivation and Basic Definitions
CSCE : Deign and Analyi of Algorihm Noe on Max Flow Fall 20 (Baed on he preenaion in Chaper 26 of Inroducion o Algorihm, 3rd Ed. by Cormen, Leieron, Rive and Sein.) Moivaion and Baic Definiion Conider
CHAPTER 7: SECOND-ORDER CIRCUITS
EEE5: CI RCUI T THEORY CHAPTER 7: SECOND-ORDER CIRCUITS 7. Inroducion Thi chaper conider circui wih wo orage elemen. Known a econd-order circui becaue heir repone are decribed by differenial equaion ha
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?
EE202 Circuit Theory II
EE202 Circui Theory II 2017-2018, Spring Dr. Yılmaz KALKAN I. Inroducion & eview of Fir Order Circui (Chaper 7 of Nilon - 3 Hr. Inroducion, C and L Circui, Naural and Sep epone of Serie and Parallel L/C
A STUDY ON COMPLICATED ROLL MOTION OF A SHIP EQUIPPED WITH AN ANTI-ROLLING TANK
607 A STUDY ON COMPLICATED ROLL MOTION OF A SHIP EQUIPPED WITH AN ANTI-ROLLING TANK Harukuni Taguchi, Hirohi Sawada and Kauji Tanizawa Naional Mariime Reearch Iniue (JAPAN) Abrac Nonlinear roll moion of
To become more mathematically correct, Circuit equations are Algebraic Differential equations. from KVL, KCL from the constitutive relationship
Laplace Tranform (Lin & DeCarlo: Ch 3) ENSC30 Elecric Circui II The Laplace ranform i an inegral ranformaion. I ranform: f ( ) F( ) ime variable complex variable From Euler > Lagrange > Laplace. Hence,
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,
236 CHAPTER 3 Torsion. Strain Energy in Torsion
36 CHAPER 3 orsion Srain Energy in orsion Problem 3.9-1 A solid circular bar of seel (G 11. 1 6 psi) wih lengh 3 in. and diameer d 1.75 in. is subjeced o pure orsion by orques acing a he ends (see figure).
Chapter 6. Laplace Transforms
6- Chaper 6. Laplace Tranform 6.4 Shor Impule. Dirac Dela Funcion. Parial Fracion 6.5 Convoluion. Inegral Equaion 6.6 Differeniaion and Inegraion of Tranform 6.7 Syem of ODE 6.4 Shor Impule. Dirac Dela
Geology 229 Engineering Geology. Lecture 12. Elementary Soil Mechanics (cont. 2) (West, Ch. 7)
Geology 229 Engineering Geology Lecure 12 Elemenary Soil echanic (con. 2) (We, Ch. 7) Ouline of hi Lecure 1. Compacion/Conolidaion Soil denificaion include compacion and conolidaion. Denificaion compacion
d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
Laplace Transform. Inverse Laplace Transform. e st f(t)dt. (2)
Laplace Tranform Maoud Malek The Laplace ranform i an inegral ranform named in honor of mahemaician and aronomer Pierre-Simon Laplace, who ued he ranform in hi work on probabiliy heory. I i a powerful
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.
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signal & Syem Prof. Mark Fowler Noe Se #27 C-T Syem: Laplace Tranform Power Tool for yem analyi Reading Aignmen: Secion 6.1 6.3 of Kamen and Heck 1/18 Coure Flow Diagram The arrow here how concepual
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mark Fowler Noe Se #1 C-T Sysems: Convoluion Represenaion Reading Assignmen: Secion 2.6 of Kamen and Heck 1/11 Course Flow Diagram The arrows here show concepual flow beween
PARAMETRIC STUDY ON MOMENT REDISTRIBUTION IN CONTINUOUS RC BEAMS USING DUCTILITY DEMAND AND DUCTILITY CAPACITY CONCEPT *
Iranian Journal of Science & Technolog, Tranacion B, Engineering, Vol. 31, No. B, 49-471 Prined in The Ilamic Reublic of Iran, 7 Shiraz Univeri PARAMETRIC STUDY ON MOMENT REDISTRIBUTION IN CONTINUOUS RC
Chapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws
Chaper 5: Phenomena Phenomena: The reacion (aq) + B(aq) C(aq) was sudied a wo differen emperaures (98 K and 35 K). For each emperaure he reacion was sared by puing differen concenraions of he 3 species
S. S. Patil, S.B.Javheri, C.G.Konapure. Main structure
ISSN: 77-3754 ISO 900:008 Ceriied Inernaional Journal o Engineering and Innovaive Technology (IJEIT) Volume, Iue 6, June0 Eecivene o Muliple Tuned Ma Damper S. S. Pail, S.B.Javheri, C.G.Konapure Abrac
Matlab and Python programming: how to get started
Malab and Pyhon programming: how o ge sared Equipping readers he skills o wrie programs o explore complex sysems and discover ineresing paerns from big daa is one of he main goals of his book. In his chaper,
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
18.03SC Unit 3 Practice Exam and Solutions
Sudy Guide on Sep, Dela, Convoluion, Laplace You can hink of he ep funcion u() a any nice mooh funcion which i for < a and for > a, where a i a poiive number which i much maller han any ime cale we care
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,
Hamilton- J acobi Equation: Weak S olution We continue the study of the Hamilton-Jacobi equation:
M ah 5 7 Fall 9 L ecure O c. 4, 9 ) Hamilon- J acobi Equaion: Weak S oluion We coninue he sudy of he Hamilon-Jacobi equaion: We have shown ha u + H D u) = R n, ) ; u = g R n { = }. ). In general we canno
Stat13 Homework 7. Suggested Solutions
Sa3 Homework 7 hp://www.a.ucla.edu/~dinov/coure_uden.hml Suggeed Soluion Queion 7.50 Le denoe infeced and denoe noninfeced. H 0 : Malaria doe no affec red cell coun (µ µ ) H A : Malaria reduce red cell
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
INDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
TP B.2 Rolling resistance, spin resistance, and "ball turn"
echnical proof TP B. olling reiance, pin reiance, and "ball urn" upporing: The Illuraed Principle of Pool and Billiard hp://billiard.coloae.edu by Daid G. Alciaore, PhD, PE ("Dr. Dae") echnical proof originally
2. VECTORS. R Vectors are denoted by bold-face characters such as R, V, etc. The magnitude of a vector, such as R, is denoted as R, R, V
ME 352 VETS 2. VETS Vecor algebra form he mahemaical foundaion for kinemaic and dnamic. Geomer of moion i a he hear of boh he kinemaic and dnamic of mechanical em. Vecor anali i he imehonored ool for decribing
Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov)
Algorihm and Daa Srucure 2011/ Week Soluion (Tue 15h - Fri 18h No) 1. Queion: e are gien 11/16 / 15/20 8/13 0/ 1/ / 11/1 / / To queion: (a) Find a pair of ube X, Y V uch ha f(x, Y) = f(v X, Y). (b) Find
The Residual Graph. 12 Augmenting Path Algorithms. Augmenting Path Algorithm. Augmenting Path Algorithm
Augmening Pah Algorihm Greedy-algorihm: ar wih f (e) = everywhere find an - pah wih f (e) < c(e) on every edge augmen flow along he pah repea a long a poible The Reidual Graph From he graph G = (V, E,
Macroeconomic Theory Ph.D. Qualifying Examination Fall 2005 ANSWER EACH PART IN A SEPARATE BLUE BOOK. PART ONE: ANSWER IN BOOK 1 WEIGHT 1/3
Macroeconomic Theory Ph.D. Qualifying Examinaion Fall 2005 Comprehensive Examinaion UCLA Dep. of Economics You have 4 hours o complee he exam. There are hree pars o he exam. Answer all pars. Each par has
Wall. x(t) f(t) x(t = 0) = x 0, t=0. which describes the motion of the mass in absence of any external forcing.
MECHANICS APPLICATIONS OF SECOND-ORDER ODES 7 Mechanics applicaions of second-order ODEs Second-order linear ODEs wih consan coefficiens arise in many physical applicaions. One physical sysems whose behaviour
Macroeconomics 1. Ali Shourideh. Final Exam
4780 - Macroeconomic 1 Ali Shourideh Final Exam Problem 1. A Model of On-he-Job Search Conider he following verion of he McCall earch model ha allow for on-he-job-earch. In paricular, uppoe ha ime i coninuou
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,
Shells with membrane behavior
Chaper 3 Shells wih membrane behavior In he presen Chaper he sress saic response of membrane shells will be addressed. In Secion 3.1 an inroducory example emphasizing he difference beween bending and membrane
Mathematische Annalen
Mah. Ann. 39, 33 339 (997) Mahemaiche Annalen c Springer-Verlag 997 Inegraion by par in loop pace Elon P. Hu Deparmen of Mahemaic, Norhweern Univeriy, Evanon, IL 628, USA (e-mail: elon@@mah.nwu.edu) Received:
Additional Methods for Solving DSGE Models
Addiional Mehod for Solving DSGE Model Karel Meren, Cornell Univeriy Reference King, R. G., Ploer, C. I. & Rebelo, S. T. (1988), Producion, growh and buine cycle: I. he baic neoclaical model, Journal of
EE 435. Lecture 31. Absolute and Relative Accuracy DAC Design. The String DAC
EE 435 Lecure 3 Absolue and Relaive Accuracy DAC Design The Sring DAC . Review from las lecure. DFT Simulaion from Malab Quanizaion Noise DACs and ADCs generally quanize boh ampliude and ime If convering
Adhesives. We use adhesives to hold things together. For optical applications, we can define several classes of adhesives:
We use adhesives o hold hings ogeher. dhesives For opical applicaions, we can define several classes of adhesives: Opical adhesives Transparen. Opical qualiies are imporan. Srucural adhesives Srengh is
MOMENTUM CONSERVATION LAW
1 AAST/AEDT AP PHYSICS B: Impulse and Momenum Le us run an experimen: The ball is moving wih a velociy of V o and a force of F is applied on i for he ime inerval of. As he resul he ball s velociy changes
MATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES
MAHEMAICAL DESCIPION OF HEOEICAL MEHODS OF ESEVE ECONOMY OF CONSIGNMEN SOES Péer elek, József Cselényi, György Demeer Universiy of Miskolc, Deparmen of Maerials Handling and Logisics Absrac: Opimizaion
A Dynamic Model of Economic Fluctuations
CHAPTER 15 A Dynamic Model of Economic Flucuaions Modified for ECON 2204 by Bob Murphy 2016 Worh Publishers, all righs reserved IN THIS CHAPTER, OU WILL LEARN: how o incorporae dynamics ino he AD-AS model
Control Systems. Lecture 9 Frequency Response. Frequency Response
Conrol Syem Lecure 9 Frequency eone Frequency eone We now know how o analyze and deign yem via -domain mehod which yield dynamical informaion The reone are decribed by he exonenial mode The mode are deermined
Admin MAX FLOW APPLICATIONS. Flow graph/networks. Flow constraints 4/30/13. CS lunch today Grading. in-flow = out-flow for every vertex (except s, t)
/0/ dmin lunch oday rading MX LOW PPLIION 0, pring avid Kauchak low graph/nework low nework direced, weighed graph (V, ) poiive edge weigh indicaing he capaciy (generally, aume ineger) conain a ingle ource
Selfish Routing. Tim Roughgarden Cornell University. Includes joint work with Éva Tardos
Selfih Rouing Tim Roughgarden Cornell Univeriy Include join work wih Éva Tardo 1 Which roue would you chooe? Example: one uni of raffic (e.g., car) wan o go from o delay = 1 hour (no congeion effec) long
LAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
From Complex Fourier Series to Fourier Transforms
Topic From Complex Fourier Series o Fourier Transforms. Inroducion In he previous lecure you saw ha complex Fourier Series and is coeciens were dened by as f ( = n= C ne in! where C n = T T = T = f (e
Effects of Coordinate Curvature on Integration
Effecs of Coordinae Curvaure on Inegraion Chrisopher A. Lafore clafore@gmail.com Absrac In his paper, he inegraion of a funcion over a curved manifold is examined in he case where he curvaure of he manifold
Stability in Distribution for Backward Uncertain Differential Equation
Sabiliy in Diribuion for Backward Uncerain Differenial Equaion Yuhong Sheng 1, Dan A. Ralecu 2 1. College of Mahemaical and Syem Science, Xinjiang Univeriy, Urumqi 8346, China heng-yh12@mail.inghua.edu.cn
13.1 Circuit Elements in the s Domain Circuit Analysis in the s Domain The Transfer Function and Natural Response 13.
Chaper 3 The Laplace Tranform in Circui Analyi 3. Circui Elemen in he Domain 3.-3 Circui Analyi in he Domain 3.4-5 The Tranfer Funcion and Naural Repone 3.6 The Tranfer Funcion and he Convoluion Inegral
Solutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
Module 2: Analysis of Stress
Module/Leon Module : Anali of Sre.. INTRODUCTION A bod under he acion of eernal force, undergoe diorion and he effec due o hi em of force i ranmied hroughou he bod developing inernal force in i. To eamine
STATIC BEHAVIOR OF AXIALLY COMPRESSED CIRCULAR CONCRETE FILLED CFRP-STEEL TUBULAR (C-CF-CFRP-ST) COLUMNS WITH MODERATE SLENDERNESS RATIO
Advanced Seel Conrucion Vol. 12, No. 3, pp. 263-295 (216) 263 STATIC BEHAVIOR OF AXIALLY COMPRESSED CIRCULAR CONCRETE FILLED CFRP-STEEL TUBULAR (C-CF-CFRP-ST) COLUMNS WITH MODERATE SLENDERNESS RATIO Q.L.
Sample Final Exam (finals03) Covering Chapters 1-9 of Fundamentals of Signals & Systems
Sample Final Exam Covering Chaper 9 (final04) Sample Final Exam (final03) Covering Chaper 9 of Fundamenal of Signal & Syem Problem (0 mar) Conider he caual opamp circui iniially a re depiced below. I LI
Let us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
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
Two Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
Explicit form of global solution to stochastic logistic differential equation and related topics
SAISICS, OPIMIZAION AND INFOMAION COMPUING Sa., Opim. Inf. Compu., Vol. 5, March 17, pp 58 64. Publihed online in Inernaional Academic Pre (www.iapre.org) Explici form of global oluion o ochaic logiic
NEUTRON DIFFUSION THEORY
NEUTRON DIFFUSION THEORY M. Ragheb 4//7. INTRODUCTION The diffuion heory model of neuron ranpor play a crucial role in reacor heory ince i i imple enough o allow cienific inigh, and i i ufficienly realiic
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
The Residual Graph. 11 Augmenting Path Algorithms. Augmenting Path Algorithm. Augmenting Path Algorithm
Augmening Pah Algorihm Greedy-algorihm: ar wih f (e) = everywhere find an - pah wih f (e) < c(e) on every edge augmen flow along he pah repea a long a poible The Reidual Graph From he graph G = (V, E,
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Signals & Sysems Prof. Mark Fowler Noe Se #2 Wha are Coninuous-Time Signals??? Reading Assignmen: Secion. of Kamen and Heck /22 Course Flow Diagram The arrows here show concepual flow beween ideas.
Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims
Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,
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.
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
Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k
Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,
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
d = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time
BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions