ANALYSIS OF VIBRATIONS OF THREE DEGREE OF FREEDOM DYNAMICAL SYSTEMS WITH SMA SPRING
|
|
|
- Bethanie Garrett
- 8 years ago
- Views:
Transcription
1 NYSIS O VIBRIONS O HREE DEGREE O REEDO DYNIC SYSES WIH S SPRING So Dnut Institute of ine Design unents Wrsw Universit of enoog - Wrsw 8 Nrbutt Str. Pon e-i: s@sir.pw.eu.p bstrt: is work rws ttention to te nsis of nis of tree-egree-of-freeo utopretri sste wit two penuus onnete b S Spe eor o spring in te neigbouroo of inerti n extern resonne. e sste onsists of te bo of ss wi is ung on spring n per n two penuus of te engt n sses n ounte to te bo of ss n onnete b S spring. e bo of ss is subjete to verti exittion wie one of te penuus is exite in te orizont iretion. ponoi oe is ssue to esribe te bevior of te spe eor eeent. e equtions of otion ve been sove nueri n tere ws stuie te infuene of teperture on te energ trnsfer between te oes of vibrtion. Soutions for te sste response re presente for speifi vues of te preters of te sste. It ws sown tt in tis tpe of sste one oe of vibrtion igt exite or p noter oe n tt exept ifferent kins of perioi vibrtion tere so pper oti vibrtion. Kewors: noniner ouping vibrtions spe eor. INRODUCIONS e subjet of tis work is n investigtion of nis of tree-egree-of-freeo sste wit two onnete b S spring penuus. Dni sstes wit eeents of te teti or psi oupe penuus ve iportnt ppitions [ ]. If te penuu is suspene to te fexibe eeent in tis sste our te utopretri exittion s resut of inerti ouping. In te sstes of tis tpe our te intern resonne of pretri tpe [ ]. It is we known tt intern resonne n give rise to ouping between te responses of vrious oes. e oe utopretri sste wit te spring ss per sste oupe to te n penuus ws stuie b Vs n Bjj [ ]. e noniner response of tree egree of freeo utopretri sstes wit penuus were investigte b utor et.: in se wen esti penuu is suspene to te fexibe eeent [7] for sste wit oube penuu [8] n for sste wit two penuus onnete b spring [9]. e onept of nge Young s ouus bse on te biit of ter riven S spring to ter its stiffness in te stress-free stte ws use for te utopretri sste oifition b utor n Pietrzkowski [] n utor n Gjos []. Due to te effet of te stress inue pse trnsition tese preters were rete to te ppie stress. Spe eor o S teris beuse of teir unique eni bevior ike spe eor effet pseuoesti effet n teperture epenent teri properties sow gret vntges s eeents of vne eni strutures. e biit to nge n ten reover rge pprent psti strin is resut of reversibe rtensite pse trnsition ue to te teperture or stress. Experients on S teris ve prove tt te Young ouus s we s intern frition s strong epenene on te rtensite frtion []. e S springs n oposites reinfore wit S fibers n be use in te tive strutur vibrtion ontro [ ] n buking ontro []. e ppition of S fibers for te sei-tive ontro of inte bes n ptes s been presente b Pietrzkowski [ 7]. e utor nse te nges of ntur frequenies of te struture ue to te ter tivtion n ni response of te sste in pure rtensite n ustenite pses of S fibers. In te present pper te pseuoesti effet in te utopretri sste wit S spring is stuie. Pseuoestiit n spe eor re bot ssoite wit teroesti rtensite trnsfortions. e spe eor effet is penoenon were psti efore objet reower teir origin for fter going troug proper et tretent. e pseuoesti bevior is rterize b opete strin reover opnie b rge steresis in oing-unoing e. ere re ot of ppers eite to te onstitutive esription of te bevior of Ss owever tis is not we estbise topi. e ponoi onstitutive oe ws propose b k [8] n b ier n Xu [9]. is oe were use b Svi et [] to esribe te bevior of te spe eor brs or b Piirio et. [ ] to esribe non Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN
2 nsis of vibrtions... So Dnut ie sste wit Ss spring. In tis pper te ponoi onstitutive oe is ssue to esribe te bevior of te utoprrtri sste wit Ss eeent. e S presents two stbe pses: ustenite n rtensiti. e unixi stress σ is fift egree ponoi of te strin []: ε ε ε σ were re onstnts of te teri ε is strin is teperture is te teperture beow wi te rtensiti pse is stbe. eperture bove wi ustenite is stbe is writing b eqution:. SYSE DESCRIPION ND EQUIONS O OION e investigte sste ig. onsists te two oupe penuus onnete b S spring wi verti istne fro te bo of ss is intersetion engt n estiit fore S σ of engts n sses n ngs own fro te bo of ss suspene b n eeent rterize b iner estiit of rigiit Sk n iner ping R. ig. Seti igr of sste It is itte tt ping fores ppie in te inge opposes te otion of te penuus n. e penuu of ss is subjete to roni verti exittion t v t wie one of te penuus is exite in te orizont iretion b fore t t. is sste s tree egrees of freeo. s generize oorintes re ssue te verti ispeent of te bo of ss esure fro te equiibriu position n te nges n of efetions of te penuus esure fro te verti ine. strin of Ss spring is: ε e eqution of otions te stuie sste erive s grnge s equtions re in for: t k t g g introuing iensioness tie n iensioness preters: f f g k b b t v µ µ γ θ γ γ β β τ k t k t Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN
3 nsis of vibrtions... So Dnut we n trnsfor into iensioness for brs were oitte for onveniene: β γ f µ τ bifurtion igrs wit respet to preter θ re presente in ig. for ping preter γ..;.;.;.; ; f ;.; f.; γ :γ. n in ig. for γ..;.;.;.; ; f ;.; f.; γ :γ. β θ γ b b f µ τ β γ b θ b. NUERIC RESUS Eqution of otion in iensioness for were sove nueri. In siutions were use te vues of Ss teri properties for Cu-Zn--Ni o t 7 K use b Svi et. [] n Piirio et. []. ese teri properties re:.9[p/k];.88x 7 [P];.8x 9 [P]; 88[K];.[K]. Cutions ve been one for ifferent vues of te sste preters espei θ. Exepr resuts te energ trnsfer for two vues of preter θ wt orresponing two pses: θ.7 wen rtensiti pse is stbe n vues of preter θ. wen ustenite pse is stbe were presente b utor in previous work []. Ner te intern n extern resonne epening on seetion of psi sste preters te pitues of vibrtions of oupe boies be rete ifferent otions: n penuus re perioi or qusi-perioi vibrtions but soeties te otions re oti. or rterizing n irregur oti response fors trnsition zone between one n noter tpe of regur ste resonnt otion bifurtion igrs n noter esriptors re use to prove te rter of vibrtions [ ]. Infuene of preters of te sste on fore vibrtions of n utopretri sste is ver iportnt. In te present pper te bifurtion igrs wit respet to te teperture preter θ in te se wen te bo of ss is subjete to verti exittion for ifferent ping preters re onstrute : in ig. for γ. n in ig. for γ..;.;.;.;.; f.; ; f ; γ :γ. e resuts re presente for veoities. In te se wen one of te penuus is exite in te orizont iretion ig. Bifurtion igr versus for oorintes: for:.;.;.;.;.; f.; ; f ; γ :γ n γ.. Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN 78-7
![In siutions were use te vues of Ss teri properties for Cu-Zn--Ni o t 7 K use b Svi et. [] n Piirio et. []. ese teri properties re:.9[p/k];.88x 7 [P];.8x 9 [P]; 88[K];](/docs-images/51/14041977/images/page_3.jpg ".[K]. Cutions ve been one for ifferent vues of te sste preters espei θ. Exepr resuts te energ trnsfer for two vues of preter θ wt orresponing two pses: θ.7 wen rtensiti pse is stbe n vues of preter θ.")
4 nsis of vibrtions... So Dnut ig. Bifurtion igr versus for oorintes: for:.;.;.;.;.; f.; ; f ; γ :γ n; γ.. ig. Bifurtion igr versus for oorintes: for:.;.;.;.; ; f ;.;n for: f.; γ :γ ; γ.. Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN 78-7
5 nsis of vibrtions... So Dnut ig. Bifurtion igr versus for oorintes: for:.;.;.;.; ; f ;.;n for: n f.; γ :γ ; γ.. ig. Bifurtion igr versus f for oorintes: for:.;.;.;.; ; f ;.; γ.: γ γ n. Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN 78-7
6 nsis of vibrtions... So Dnut ig.7 Poinre ps for oorintes: for:.;.;.;.;.; γ.; γ :γ ; θ.; f.99 ig.8 xi exponent of punov for oorintes: for:.;.;.;.;.; γ.; γ :γ ; θ.; f.99 Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN 78-7
7 nsis of vibrtions... So Dnut Next re presente bifurtion igrs for oorintes n. wen s bifurtion preter is te pitues of exittion. Exepr resuts for for vue θ. ustenite pse te S spring re given for te oorintes n in ig. were te bifurtion preter is te pitue of exittion f. s n be seen fro tese bifurtion igrs sever penoen n be observe e.g. te existene of regur or oti ttrtors n vrious bifurtions. e bifurtion igrs sow tt te otion of te in bo of ss n te penuus s ifferent rteristis n be perioi qusi-perioi n oti. o verif tese penoen power spetr ensities teir st ourier rnsfor Poinré ps n te rgest punov exponents orresponing to oorintes n re onstrute. Exepr resuts Poinre ps n xi exponent of punov for oorintes: for:.;.;.;.;.; γ.; γ :γ ; θ.; n for te bifurtion preter f.99 re presente in ig.7 n in ig.8. s n be seen fro ig.7 te Poinrè ps tre te strnge ttrtors n on ig.8 te rgest punov exponents orresponing to oorinte n oorintes n re positive. us in te onsiere se te otion is oti. CONCUSIONS e infuene of teperture on te beviour of n utopretri sste wit two penuus onnete b n S spring is ver interesting n iportnt ner te intern n extern resonnes. In utopretri sstes te energ is trnsferre between te oes of vibrtion in e e. e tie of tis e epens on te vues of te preters n nueri utions for tis tpe of sstes sou be rrie out over stisftori ong tie. Depening on te seetion of te psi sste preters te pitues of vibrtion of tree oes be rete ifferent n two tpes intern resonnes re observe. Cnging te teperture of te S spring ens we n nge te utopretri sste beviour. Referenes [] Den Hrtog J.P. 9 eni Vibrtions Grw-Hi Book Copn In. [] Drzin P. G. 99 Noniner sstes Cbrige Universit Press. [] So D. 997e energ trnsfer in noniner oupe two-egreeof-freeo sstes Pubig House of te Wrsw Universit of enoog enik in pois. [] So D. e Dnis of Coupe ree Degree of reeo eni Sste enis n eni Engineering [] Vs. Bjj.K. Dnis of utopretri vibrtion bsorber ug utipe penuus Journ of Soun n Vibrtion -. [] Vs. Bjj.K. Gob nis of n utopretri sste wit utipe penuus Journ of Coputtion n Noniner Dnis -. [7] So D. e perioi n oti vibrtion of ni sste wit esti penuu Proeeings of ESD 8 t Bienni SE Conferene on Engineering Sstes Design n nsis Ju-7 orino It ESD-9-8. [8] So D. Gjos K. Effet of ping on te perioi n oti vibrtion of sste wit oube penuu Proeeings of ESD 8 t Bienni SE Conferene on Engineering Sstes Design n nsis Ju-7 orino It ESD [9] So. D. 7 Noniner ositions of n utopretri sste wit two oupe penuus Proeeings of te SE 7 Interntion Design Engineering eni Conferenes & Coputers n Infortion I Engineering Conferene IDEC/CIE 7 Sept s Vegs Nev US DEC [] So D. Pietrzkowski. Dnis of ter tivte spe eor o in utopretri sstes wit two penuus Int. J. Non-iner e oi:./j.ijnonine.9.. in print. [] So D. Gjos K.8 e nis of n utopretri sste wit two oupe penuus onnete b S spring Proeeings of te 9 t Bienni SE Conferene on Engineering Sstes Design n nsis ESD 8 Ju 7-9 Hif Isre ESD8-9-. [] Jkson C.. Wgner H.J. Wsiewski R.J. 97 -Nitino-e o wit eor: Its Pisi turg Properties n ppitions NS-SP- Wgton D.C. [] ing C. Rogers C.. 99 One - Diension eroni Constitutive Retions for Spe eor teris J. of Inte. ter. Sts. n Strut. 7-. [] ing C. Rogers C.. 99 One Design of Spe eor os Cois n teir pitions in Vibrtions Contro Reent vvnes in tive Contro of Soun n Vibrtions Rogers C.. e. enoi Pubig nster Bse [] Rogers C.. ing C. Ji J. 989 Bevior of Spe eor o Reinfore Coposite Ptes Prts I n II Proeeings of te t Strutures Strutur Dnis n teri Conferene obie -7 [] Pietrzkowski. 998 Dnis of ter tivte spe eor o reinfore inte bes Journ of eoreti n ppie enis [7] Pietrzkowski. Ntur frequen oifition of ter tivte oposite ptes eni Vo. - [8] k. 98 oe free energ enis n teronis of spe eor os t et [9] uer I. Xu H. 99 On te pseuo-esti steresis t et. ter. 9-7 [] Svi.. Peo P..C.. Brg..B. Cos in spe eor two-br truss Int. Journ of Non-iner enis [] Piirio V. Btzr J.. Pontes Jr. B.R. eiks J..P. 7 On noniner response of non-ie vibrting sste wit spe eor o S 9 t Conferene on Dni Sstes eor n ppitions Proeeings Eit.J.wrejewiz P.Oejnik J.rozowski oz De.7- Pon [] Piirio V. Btzr J.. Pontes Jr. B.R. eiks J..P. 8 On Soerfe Effet in Non-Ie Vibrting Sste wit S Ug n verging eto Euroe 98 Cooquiu Book of bstrts ubin Universit of enoog Pon 7-7. [] So. D. 9e pseuoesti effet in utopretri sste wit S spring t Conferene on Dni Sstes eor n ppitions Proeeings Eit.J.wrejewiz P.Oejnik J.rozowski oz De.7- Pon -. [] Bker G.. Goub J. P. 99 Coti nis: n introution. Cbrige Universit Press. [] Szepisk-Stupnik W. CosBifurtions n rts roun Us Wor Sientifi onon. 7 Proeeings of te 9t Brziin Conferene on Dnis Contro n teir ppitions Serr Negr SP - ISSN 78-7
ASPECTS CONCERNING A DYNAMIC MODEL FOR A SYSTEM WITH TWO DEGREES OF FREEDOM
Buetin of the Trnsivni University of Brşov Series I: Engineering Sciences Vo. 4 (53 No. - ASPECTS CONCERNING A DYNAMIC MODEL FOR A SYSTEM WITH TWO DEGREES OF FREEDOM M. BOTIŞ C. HARBIC Abstrct: In this
J. Q. Mou, Fukun Lai, I. B. L. See, and W. Z. Lin Data Storage Institute, 5 Engineering Drive 1, Singapore 117608
Anlysis of Noteook Computer Cssis Design for rd Disk Drive nd Speker Mounting J. Q. Mou, Fukun Li, I. B. L. See, nd W. Z. Lin Dt Storge Institute, 5 Engineering Drive 1, Singpore 117608 Astrt - Cssis design
Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m
. Slr prout (ot prout): = osθ Vetors Summry Lws of ot prout: (i) = (ii) ( ) = = (iii) = (ngle etween two ientil vetors is egrees) (iv) = n re perpeniulr Applitions: (i) Projetion vetor: B Length of projetion
Derivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
Tensile strength of single fibers: test methods and data analysis. J. Andersons Institute of Polymer Mechanics, University of Latvia
Tensie strength of singe fibers: test ethods nd dt nysis J. Andersons Institute of oyer Mechnics, University of Ltvi Outine otivtion fiber strength s sttistic vribe inconsistency in Weibu distribution
α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
THE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.
THE LONGITUDINAL FIELD IN THE GTEM 175 AND THE NATURE OF THE TERMINATION. Benjmin Guy Loder Ntionl Physil Lbortory, Queens Rod, Teddington, Middlesex, Englnd. TW11 LW Mrtin Alexnder Ntionl Physil Lbortory,
Memory Channel Storage. A Diablo Technologies Whitepaper. April 2015
A Diablo Technologies Whitepaper!! M a x i m i z i n g Y o u r R O I : VDI with Memory Channel Storage April 2015 Rick y Trigalo, Director of Virtualization Solutions Arch it ecture Rodi Campos, Product
THE GEOMETRY OF PYRAMIDS
TE GEOMETRY OF PYRAMIDS One of te more interesting solid structures wic s fscinted individuls for tousnds of yers going ll te wy bck to te ncient Egyptins is te pyrmid. It is structure in wic one tkes
CHAPTER 31 CAPACITOR
. Given tht Numer of eletron HPTER PITOR Net hrge Q.6 9.6 7 The net potentil ifferene L..6 pitne v 7.6 8 F.. r 5 m. m 8.854 5.4 6.95 5 F... Let the rius of the is R re R D mm m 8.85 r r 8.85 4. 5 m.5 m
Section 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations
Difference Equations to Differential Equations Section 3.3 Differentiation of Polynomials an Rational Functions In tis section we begin te task of iscovering rules for ifferentiating various classes of
ASUS TRANSFORMER PAD TF300T MANUALE UTENTE
ASUS TRANSFORMER PAD TF300T MANUALE UTENTE GKEFQ-Q0NMS901 PDF 171.93KB 05 Apr, 2014 TABLE OF CONTENT Introdution Brief Desription Min Topi Tenil Note Appendix Glossry PDF file: sus trnsformer pd tf300t
SAT Math Must-Know Facts & Formulas
SAT Mat Must-Know Facts & Formuas Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationas: fractions, tat is, anyting expressabe as a ratio of integers Reas: integers pus rationas
Models RSR-M, RSR-N and RSR-TN
odels RSR-, RSR- and RSR-T 1.6 troug 2-l 1 2 1 odel RSR3 2-l 1.6 troug 2 1 1 odel RSR3 Outer dimensions dimensions odel o. Heigt idt engt Greasing ole Grease nipple RSR 3 RSR 3 RSR 5 RSR 5 RSR 5T odel
How To Ensure That An Eac Edge Program Is Successful
Introduction Te Economic Diversification and Growt Enterprises Act became effective on 1 January 1995. Te creation of tis Act was to encourage new businesses to start or expand in Newfoundland and Labrador.
Orthopoles and the Pappus Theorem
Forum Geometriorum Volume 4 (2004) 53 59. FORUM GEOM ISSN 1534-1178 Orthopoles n the Pppus Theorem tul Dixit n Drij Grinerg strt. If the verties of tringle re projete onto given line, the perpeniulrs from
Sequential Auctions of Oligopoly Licenses: Bankruptcy and Signaling
Sequential Autions of Oligopoly Lienses: Bankrupty an Signaling Georgios Katsenos Institut für Mikroökonomik, Leibniz Universität Hannover Deember 2010 Abstrat This paper ompares two proeures for alloating
CANKAYA UNIVERSITY FACULTY OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT ME 212 THERMODYNAMICS II HW# 11 SOLUTIONS
CNKY UNIVESIY FCULY OF ENGINEEING MECHNICL ENGINEEING DEMEN ME HEMODYNMICS II HW# SOLUIONS Deterne te ulton reure of wter or t -60 0 C ung dt lle n te te tle. Soluton Ste tle do not ge turton reure for
Turbulence simulation in wavelet domain based on Log- Poisson model: univariate and multivariate wind processes
he Seventh Interntion Cooquium on Buff Body Aerodynmis nd Appitions (BBAA7) Shnghi, Chin; September -6, 0 urbuene simution in wveet domin bsed on Log- Poisson mode: univrite nd mutivrite wind proesses
College Planning Using Cash Value Life Insurance
College Planning Using Cas Value Life Insurance CAUTION: Te advisor is urged to be extremely cautious of anoter college funding veicle wic provides a guaranteed return of premium immediately if funded
Derivatives Math 120 Calculus I D Joyce, Fall 2013
Derivatives Mat 20 Calculus I D Joyce, Fall 203 Since we ave a good understanding of its, we can develop derivatives very quickly. Recall tat we defined te derivative f x of a function f at x to be te
Keywords: Three-degree of freedom, mathematical model, free vibration, axial motion, simulate.
ISSN: 9-5967 ISO 900:008 Certiied International Journal o Engineering Science and Innovative Technolog (IJESIT) Volue, Issue 4, Jul 0 A Three-Degree o Freedo Matheatical Model Siulating Free Vibration
Chapter 10: Refrigeration Cycles
Capter 10: efrigeration Cycles Te vapor compression refrigeration cycle is a common metod for transferring eat from a low temperature to a ig temperature. Te above figure sows te objectives of refrigerators
Schedulability Analysis under Graph Routing in WirelessHART Networks
Scedulability Analysis under Grap Routing in WirelessHART Networks Abusayeed Saifulla, Dolvara Gunatilaka, Paras Tiwari, Mo Sa, Cenyang Lu, Bo Li Cengjie Wu, and Yixin Cen Department of Computer Science,
The Concept of the Effective Mass Tensor in GR. The Equation of Motion
The Concept of the Effective Mass Tensor in GR The Equation of Motion Mirosław J. Kubiak Zespół Szkół Technicznych, Gruziąz, Polan Abstract: In the papers [, ] we presente the concept of the effective
Sections 3.1/3.2: Introducing the Derivative/Rules of Differentiation
Sections 3.1/3.2: Introucing te Derivative/Rules of Differentiation 1 Tangent Line Before looking at te erivative, refer back to Section 2.1, looking at average velocity an instantaneous velocity. Here
NBS TECHNICAL NOTE. b 1 b (2 d Revision)
NBS TECHNCAL NOTE b 1 b (2 Revision) NATONAL BUREAU OF STANDARDS The Ntionl Bureu of Stnrs' ws estblishe by n t of Congress Mrh 3, 191. The Bureu's ovel gol is to strengthen n vne the Ntion's siene n tehnology
Verifying Numerical Convergence Rates
1 Order of accuracy Verifying Numerical Convergence Rates We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, suc as te grid size or time step, and
MATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report
University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population
Hydromagnetic Unsteady Mixed Convection Flow Past an Infinite Vertical Porous Plate
pplie Mthemtis. ; (): 39-45 DO:.593/j.m..5 Hyromgneti Unstey Mixe Convetion Flo Pst n nfinite ertil Porous Plte B.. Shrm T. Chn R. C. Chuhry Deprtment of Mthemtis Birl nstitute of Tehnology & Siene Pilni
Math 229 Lecture Notes: Product and Quotient Rules Professor Richard Blecksmith richard@math.niu.edu
Mat 229 Lecture Notes: Prouct an Quotient Rules Professor Ricar Blecksmit ricar@mat.niu.eu 1. Time Out for Notation Upate It is awkwar to say te erivative of x n is nx n 1 Using te prime notation for erivatives,
Visualization of characteristics of the contact network between spheres in 3D assembly
Int. Agrophys., 2013, 27, 275-281 oi: 10.2478/v10247-012-0095-6 INTERNATIONAL Agrophysis www.interntionl-grophysis.org Visuliztion of hrteristis of the ontt network etween spheres in 3D ssemly R. Koy³k*
Recall from last time: Events are recorded by local observers with synchronized clocks. Event 1 (firecracker explodes) occurs at x=x =0 and t=t =0
1/27 Day 5: Questions? Time Dilation engt Contraction PH3 Modern Pysics P11 I sometimes ask myself ow it came about tat I was te one to deelop te teory of relatiity. Te reason, I tink, is tat a normal
Theoretical calculation of the heat capacity
eoretical calculation of te eat capacity Principle of equipartition of energy Heat capacity of ideal and real gases Heat capacity of solids: Dulong-Petit, Einstein, Debye models Heat capacity of metals
State of California Health and Human Services Agency Department of Health Care Services
State of California Healt and Human Servies Ageny Deartment of Healt Care Servies TOBY DOUGLAS DIRECTOR EDMUND G. BROWN JR. GOVERNOR DATE: Deember 19, 2014 ALL PLAN LETTER 14-018 TO: SUBJECT: ALL MEDI-CAL
Instantaneous Rate of Change:
Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over
Parallel-Task Scheduling on Multiple Resources
Parallel-Task Sheuling on Multiple Resoures Mike Holenerski, Reiner J. Bril an Johan J. Lukkien Department of Mathematis an Computer Siene, Tehnishe Universiteit Einhoven Den Doleh 2, 5600 AZ Einhoven,
Overview of Component Search System SPARS-J
Overview of omponent Searc System Tetsuo Yamamoto*,Makoto Matsusita**, Katsuro Inoue** *Japan Science and Tecnology gency **Osaka University ac part nalysis part xperiment onclusion and Future work Motivation
Fluent Merging: A General Technique to Improve Reachability Heuristics and Factored Planning
Fluent Merging: A Generl Tehnique to Improve Rehility Heuristis n Ftore Plnning Menkes vn en Briel Deprtment of Inustril Engineering Arizon Stte University Tempe AZ, 85287-8809 menkes@su.eu Suro Kmhmpti
Area-Specific Recreation Use Estimation Using the National Visitor Use Monitoring Program Data
United States Department of Agriculture Forest Service Pacific Nortwest Researc Station Researc Note PNW-RN-557 July 2007 Area-Specific Recreation Use Estimation Using te National Visitor Use Monitoring
D D. DETAILs FOR x-284561-2. 2 POS. PCB LAYOUT FOR PN.S x-284561-2 PER ALTRI DETTAGLI RIFERIRSI AL FOGLIO 5 (FOR ADDITIONAL DETAILS SEE SHEET 5)
THS RWNG S NPSHE. OPRGHT copyright_date REESE FOR PTON RGHTS RESERE. O ST NS P TR ESRPTON TE WN P Z SE PER ER000 PR0 W JP Z ER00 0M0 F RR RPPRESENTZONE GRF E P/Ns: (GRPH REPRESENTTON OF P/Ns:) RPPRESENTZONE
Referendum-led Immigration Policy in the Welfare State
Referendum-led Immigration Policy in te Welfare State YUJI TAMURA Department of Economics, University of Warwick, UK First version: 12 December 2003 Updated: 16 Marc 2004 Abstract Preferences of eterogeneous
JCM TRAINING OVERVIEW Multi-Download Module 2
Multi-Downlo Moule 2 JCM Trining Overview Mrh, 2012 Mrh, 2012 CLOSING THE MDM2 APPLICATION To lose the MDM2 Applition proee s follows: 1. Mouse-lik on the 'File' pullown Menu (See Figure 35 ) on the MDM2
Journal of Colloid and Interface Science
Journal of Colloid and Interfae Siene 338 (9) 93 Contents lists available at SieneDiret Journal of Colloid and Interfae Siene www.elsevier.om/loate/jis Contat angle of a emisperial bubble: An analytial
1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).
PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a
1 Fractions from an advanced point of view
1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning
Physics 110 Spring 2006 Fluid Mechanics Their Solutions
ic Sprin 00 lui Mecanic Teir Solution reure in a flui arie linearl wit ept Wat i te abolute preure at a ept of 00 in te ocean if te enit of ea i 4 k/? t ti ept wat force ut te frae aroun a circular ubarine
Math 113 HW #5 Solutions
Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten
Formal concept analysis-based class hierarchy design in object-oriented software development
Forml onept nlysis-se lss hierrhy esign in ojet-oriente softwre evelopment Roert Goin 1, Petko Vlthev 2 1 Déprtement informtique, UQAM, C.P. 8888, su. Centre Ville, Montrél (Q), Cn, H3C 3P8 2 DIRO, Université
SUPPLEMENTARY MATERIAL
SUPPLEMENTARY MATERIAL Lyer-speifi exittory iruits differentilly ontrol reurrent network dynmis in the neoortex Rirdo Beltrmo, Giuli D Urso, Mro Dl Mshio, Psqulin Frisello, Seren Bovetti, Yonne Clovis,
The EOQ Inventory Formula
Te EOQ Inventory Formula James M. Cargal Matematics Department Troy University Montgomery Campus A basic problem for businesses and manufacturers is, wen ordering supplies, to determine wat quantity of
15.2. First-Order Linear Differential Equations. First-Order Linear Differential Equations Bernoulli Equations Applications
00 CHAPTER 5 Differential Equations SECTION 5. First-Orer Linear Differential Equations First-Orer Linear Differential Equations Bernoulli Equations Applications First-Orer Linear Differential Equations
CURVES ANDRÉ NEVES. that is, the curve α has finite length. v = p q p q. a i.e., the curve of smallest length connecting p to q is a straight line.
CURVES ANDRÉ NEVES 1. Problems (1) (Ex 1 of 1.3 of Do Crmo) Show tht the tngent line to the curve α(t) (3t, 3t 2, 2t 3 ) mkes constnt ngle with the line z x, y. (2) (Ex 6 of 1.3 of Do Crmo) Let α(t) (e
1: n(k) dk. it is necessarily tied to the. out a possible mis-interpretation
ADDEXDUM TO T 66-15 R A Early August 6, 1968 Several SAC! pysicists ave pointed out a possible is-interpretation of te results of te tick target bresstralung TJI 66-55 progra described in Since te output
Earthquake Loss for Reinforced Concrete Building Structures Before and After Fire damage
Earthquake Loss for Reinfored Conrete Building Strutures Before and After Fire damage Pai-Mei LIU, Yi-Hsuan Tu and Maw-Shyong SHEU 3 ABSTRACT The purpose of this paper is to propose a rational analytial
2. Illustration of the Nikkei 225 option data
1. Introduction 2. Illustration of the Nikkei 225 option data 2.1 A brief outline of the Nikkei 225 options market τ 2.2 Estimation of the theoretical price τ = + ε ε = = + ε + = + + + = + ε + ε + ε =
Pretrial Settlement with Imperfect Private Monitoring
Pretrial Settlement wit Imperfect Private Monitoring Mostafa Beskar Indiana University Jee-Hyeong Park y Seoul National University April, 2016 Extremely Preliminary; Please Do Not Circulate. Abstract We
Torchmark Corporation 2001 Third Avenue South Birmingham, Alabama 35233 Contact: Joyce Lane 972-569-3627 NYSE Symbol: TMK
News Release Torcmark Corporation 2001 Tird Avenue Sout Birmingam, Alabama 35233 Contact: Joyce Lane 972-569-3627 NYSE Symbol: TMK TORCHMARK CORPORATION REPORTS FOURTH QUARTER AND YEAR-END 2004 RESULTS
Can a Lump-Sum Transfer Make Everyone Enjoy the Gains. from Free Trade?
Can a Lump-Sum Transfer Make Everyone Enjoy te Gains from Free Trade? Yasukazu Icino Department of Economics, Konan University June 30, 2010 Abstract I examine lump-sum transfer rules to redistribute te
Shell and Tube Heat Exchanger
Sell and Tube Heat Excanger MECH595 Introduction to Heat Transfer Professor M. Zenouzi Prepared by: Andrew Demedeiros, Ryan Ferguson, Bradford Powers November 19, 2009 1 Abstract 2 Contents Discussion
Chapter 11. Limits and an Introduction to Calculus. Selected Applications
Capter Limits and an Introduction to Calculus. Introduction to Limits. Tecniques for Evaluating Limits. Te Tangent Line Problem. Limits at Infinit and Limits of Sequences.5 Te Area Problem Selected Applications
Section 2.3 Solving Right Triangle Trigonometry
Section.3 Solving Rigt Triangle Trigonometry Eample In te rigt triangle ABC, A = 40 and c = 1 cm. Find a, b, and B. sin 40 a a c 1 a 1sin 40 7.7cm cos 40 b c b 1 b 1cos40 9.cm A 40 1 b C B a B = 90 - A
Chapter 7. (a) The compressor work is give by. = m (h 2 h 1 ) = (0.08 kg/s)(416.2 398.6) kj/kg = 1.408 kw. (b) The refrigeration capacity, in tons, is
apter 7 Exaple 7.- 6 ---------------------------------------------------------------------------------- Refrigerant 4a i te working fluid in an ideal vapor-opreion refrigeration yle tat ouniate terally
How To Find The Re Of Tringle
Heron s Formul for Tringulr Are y Christy Willims, Crystl Holom, nd Kyl Gifford Heron of Alexndri Physiist, mthemtiin, nd engineer Tught t the museum in Alexndri Interests were more prtil (mehnis, engineering,
LAPLACE S EQUATION IN SPHERICAL COORDINATES. With Applications to Electrodynamics
LALACE S EQUATION IN SHERICAL COORDINATES With Appitions to Eetodynmis We hve seen tht Lpe s eqution is one of the most signifint equtions in physis. It is the soution to pobems in wide viety of fieds
Research on Risk Assessment of PFI Projects Based on Grid-fuzzy Borda Number
Researc on Risk Assessent of PFI Projects Based on Grid-fuzzy Borda Nuber LI Hailing 1, SHI Bensan 2 1. Scool of Arcitecture and Civil Engineering, Xiua University, Cina, 610039 2. Scool of Econoics and
OxCORT v4 Quick Guide Revision Class Reports
OxCORT v4 Quik Guie Revision Clss Reports This quik guie is suitble for the following roles: Tutor This quik guie reltes to the following menu options: Crete Revision Clss Reports pg 1 Crete Revision Clss
ACT Math Facts & Formulas
Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationals: fractions, tat is, anyting expressable as a ratio of integers Reals: integers plus rationals plus special numbers suc as
4.4 The Derivative. 51. Disprove the claim: If lim f (x) = L, then either lim f (x) = L or. 52. If lim x a. f (x) = and lim x a. g(x) =, then lim x a
Capter 4 Real Analysis 281 51. Disprove te claim: If lim f () = L, ten eiter lim f () = L or a a lim f () = L. a 52. If lim a f () = an lim a g() =, ten lim a f + g =. 53. If lim f () = an lim g() = L
Vehicle longitudinal motion modeling for nonlinear control
eice ongituin motion moeing for noniner contro Ki E joub ou Giri Hmi Oui Luc Dugr tim Zr Coui To cite tis ersion: Ki E joub ou Giri Hmi Oui Luc Dugr tim Zr Coui. eice ongituin motion moeing for noniner
EC201 Intermediate Macroeconomics. EC201 Intermediate Macroeconomics Problem set 8 Solution
EC201 Intermediate Macroeconomics EC201 Intermediate Macroeconomics Prolem set 8 Solution 1) Suppose tat te stock of mone in a given econom is given te sum of currenc and demand for current accounts tat
w ith In fla m m a to r y B o w e l D ise a se. G a s tro in te s tin a l C lin ic, 2-8 -2, K a s h iw a z a, A g e o C ity, S a ita m a 3 6 2 -
E ffic a c y o f S e le c tiv e M y e lo id L in e a g e L e u c o c y te D e p le tio n in P y o d e r m a G a n g re n o su m a n d P so r ia sis A sso c ia te d w ith In fla m m a to r y B o w e l D
Suggested solutions, FYS 500 Classical Mechanics and Field Theory 2014 fall
UNIVERSITETET I STAVANGER Institutt for matematikk og naturvitenskap Suggested solutions, FYS 500 Classical Mecanics and Field Teory 014 fall Set 11 for 17/18. November 014 Problem 59: Te Lagrangian for
Angles formed by 2 Lines being cut by a Transversal
Chapter 4 Anges fored by 2 Lines being cut by a Transversa Now we are going to nae anges that are fored by two ines being intersected by another ine caed a transversa. 1 2 3 4 t 5 6 7 8 If I asked you
f(x + h) f(x) h as representing the slope of a secant line. As h goes to 0, the slope of the secant line approaches the slope of the tangent line.
Derivative of f(z) Dr. E. Jacobs Te erivative of a function is efine as a limit: f (x) 0 f(x + ) f(x) We can visualize te expression f(x+) f(x) as representing te slope of a secant line. As goes to 0,
Angles and Triangles
nges nd Tringes n nge is formed when two rys hve ommon strting point or vertex. The mesure of n nge is given in degrees, with ompete revoution representing 360 degrees. Some fmiir nges inude nother fmiir
FINANCIAL DISTRESS AND BANKS' COMMUNICATIONPOLICY IN CRISIS TIMES
1. FINANCIAL DISTRESS AND BANKS' COMMUNICATIONPOLICY IN CRISIS TIMES Dmien BESANCENOT Rdu VRÂNCEANU Astrct Tis pper nyzes nks communiction poicies in crisis times nd te roe of imperfect informtion in enncing
VEHICLE PLANAR DYNAMICS BICYCLE MODEL
Auptions -Do, VEHE PANA DYNAMS BYE MODE o tel, (esued o instntneous cente o ottion O) o Yw, (wt Globl Ais) ongitudinl elocit is ued to be constnt. Sll slip ngles, i.e. ties opete in the line egion. No
Adaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates
Int J of Mthemtic Sciences nd Appictions, Vo, No 3, Septembe Copyight Mind Rede Pubictions wwwjounshubcom Adptive Conto of Poduction nd Mintennce System with Unknown Deteiotion nd Obsoescence Rtes Fwzy
Lecture 24: Spinodal Decomposition: Part 3: kinetics of the
Leture 4: Spinodal Deoposition: Part 3: kinetis of the oposition flutuation Today s topis Diffusion kinetis of spinodal deoposition in ters of the onentration (oposition) flutuation as a funtion of tie:
SAT Math Facts & Formulas
Numbers, Sequences, Factors SAT Mat Facts & Formuas Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reas: integers pus fractions, decimas, and irrationas ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences:
What is Advanced Corporate Finance? What is finance? What is Corporate Finance? Deciding how to optimally manage a firm s assets and liabilities.
Wat is? Spring 2008 Note: Slides are on te web Wat is finance? Deciding ow to optimally manage a firm s assets and liabilities. Managing te costs and benefits associated wit te timing of cas in- and outflows
Ross Recovery Empirical Project
Jens Carsten Jackwert Marco Menner University of Konstanz jens.jackwert@ni-konstanz.e ttp://www.wiwi.ni-konstanz.e/jackwert/ 2 Motivation State prices q pricing kernel m pysical probabilities f Normally
50 MATHCOUNTS LECTURES (10) RATIOS, RATES, AND PROPORTIONS
0 MATHCOUNTS LECTURES (0) RATIOS, RATES, AND PROPORTIONS BASIC KNOWLEDGE () RATIOS: Rtios re use to ompre two or more numers For n two numers n ( 0), the rtio is written s : = / Emple : If 4 stuents in
2.23 Gambling Rehabilitation Services. Introduction
2.23 Gambling Reabilitation Services Introduction Figure 1 Since 1995 provincial revenues from gambling activities ave increased over 56% from $69.2 million in 1995 to $108 million in 2004. Te majority
On Equivalence Between Network Topologies
On Equivlene Between Network Topologies Tre Ho Deprtment of Eletril Engineering Cliforni Institute of Tehnolog tho@lteh.eu; Mihelle Effros Deprtments of Eletril Engineering Cliforni Institute of Tehnolog
Word Wisdom Correlations to the Common Core State Standards, Grade 6
Reing Stnrs for Informtionl Text Key Ies n Detils 1 Cite textul eviene to support nlysis of wht the text sys expliitly s well s inferenes rwn from the text. 6, 7, 12, 13, 18, 19, 28, 29, 34, 35, 40, 41,
Disability Discrimination (Services and Premises) Regulations 2016 Index DISABILITY DISCRIMINATION (SERVICES AND PREMISES) REGULATIONS 2016
Disability Disrimination (Servies and Premises) Regulations 2016 Index DISABILITY DISCRIMINATION (SERVICES AND PREMISES) REGULATIONS 2016 Index Regulation Page 1 Title... 3 2 Commenement... 3 3 Interpretation...
1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution
1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis
Enterprise Data Center A c h itec tu re Consorzio Operativo Gruppo MPS Case S t u d y : P r o g et t o D i sast er R ec o v er y Milano, 7 Febbraio 2006 1 Il G r u p p o M P S L a B a n c a M o n t e d
DiaGen: A Generator for Diagram Editors Based on a Hypergraph Model
DiGen: A Genertor for Digrm Eitors Bse on Hypergrph Moel G. Viehstet M. Mins Lehrstuhl für Progrmmiersprhen Universität Erlngen-Nürnerg Mrtensstr. 3, 91058 Erlngen, Germny Emil: fviehste,minsg@informtik.uni-erlngen.e
Large-scale Virtual Acoustics Simulation at Audio Rates Using Three Dimensional Finite Difference Time Domain and Multiple GPUs
Large-scale Virtual Acoustics Simulation at Audio Rates Using Tree Dimensional Finite Difference Time Domain and Multiple GPUs Craig J. Webb 1,2 and Alan Gray 2 1 Acoustics Group, University of Edinburg
Maximum area of polygon
Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is
Adaptive Amplitude Demodulation (AAD) as an order tracking method
Adptive Amplitude Demodultion (AAD) s n order trcking metod Piet Vn Vlierberge, Krl Jnssens, Hermn Vn der Auwerer LMS Interntionl, Interleuvenln 68, B-31 Leuven, Belgium, pieter.vnvlierberge@lmsintl.com
The invention of line integrals is motivated by solving problems in fluid flow, forces, electricity and magnetism.
Instrutor: Longfei Li Mth 43 Leture Notes 16. Line Integrls The invention of line integrls is motivted by solving problems in fluid flow, fores, eletriity nd mgnetism. Line Integrls of Funtion We n integrte
iglidur PRT Slewing Ring Bearing
igliur igliur Slewing Ring Bearing Stanar range Completely maintenance-free Easy installation, intercangeable sliing pas ig wear resistance For ig loa capacity, ig stiffness Available as stainless steel
OPTIMAL FLEET SELECTION FOR EARTHMOVING OPERATIONS
New Developments in Structural Engineering and Construction Yazdani, S. and Sing, A. (eds.) ISEC-7, Honolulu, June 18-23, 2013 OPTIMAL FLEET SELECTION FOR EARTHMOVING OPERATIONS JIALI FU 1, ERIK JENELIUS
An inquiry into the multiplier process in IS-LM model
An inquiry into te multiplier process in IS-LM model Autor: Li ziran Address: Li ziran, Room 409, Building 38#, Peing University, Beijing 00.87,PRC. Pone: (86) 00-62763074 Internet Address: jefferson@water.pu.edu.cn
Lecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function
Lecture 10: Wat is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises wen one quantity depends on anoter. Many everyday relationsips between