A Study on Nonlinear Forced Vibration of an Axial Moving Viscoelasticity Beam using the Multi-Scale Approach
|
|
- William Little
- 6 years ago
- Views:
Transcription
1 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING A Study on Nonlnar Forcd Vbraton of an Axal Movng Vscolastcty Bam usng th Mult-Scal Approach Bao-Fu Kou *, Xao-L Hu Collg of Mchancal Engnrng, Tayuan unvrsty of scnc and tchnology, Tayuan, 3, Chna *Corrspondng author:koubaofu@63.com Abstract Th mult-scal mthod s usd to analys th stady-stat rspons ampltud of a nonlnar forcd vbraton of axal movng vscolastcty bam, and th Galrkn truncaton mthod s appld to solv ts numrcal dffrntal quaton by dscrtzaton. Th nfluncs on th stady-stat rspons ampltud du to varous factors such as: ) vard vscosty dampng coffcnt, ) xtrnal xctaton, ) nonlnar coffcnts and v) movng vlocty ar analysd. Th rsults agr wth thos n th ltratur,.. th xtrnal motvaton and vscous dampng coffcnt hav grat ffct on th dynamcs bhavour of th vbraton systm. Th rsults ar thn drvd for dffrnt ordr Galrkn truncatons and compard, and th nstablty boundary condtons ar dtrmnd. Th rsults show that th unstabl condton s manly nducd by th xtrnal xctaton and vscosty dampng, whch agrs wll wth th rsults n th ltratur. Our study provds rlabl thortcal bass for th opraton of flxbl dvcs wth scurty and stablty. Kywords: Axal movng bam, mult-scal mthod, Galrkn truncaton, stady-stat rspons. I. INTRODUCTION Axally movng vscolastc bam, as a smplfd physcal modl s wdly usd n a numbr of systms, such as host, powr transmsson blts, band saws, aral ropway ct.. Undr th acton of xtrnal xctatons, ths systms may produc unwantd vbratons and rsonancs, causng consdrabl damag n th normal opraton. Th vbraton s rlatd to th systm s flxbl structur, whch can b approxmatvly rgardd as th bam wth vscolastc proprts. Thrfor, studs on th nonlnar forcd vbraton of axal movng vscolastc bam has caught many scholars ys [-5]. Th govrnng quaton for th longtudnal vbratons of vscolastc movng body s a typcal contnuous systm, contanng mxd partal drvatv trms of both tm and spac [6]. Aftr th rsarch on transvrs vbraton of axally movng lastc bam by Pasn [7], a numbr of scholars dvotd thmslvs to focusng on vbraton problms. Among th studs rvwd, most vbraton problms ar smplfd basd on th Krchhoff thory. Oz [8] dscussd th plan vbraton of an lastomr n vscous mdum and obtand th rlatonshp btwn fr vbraton frquncy and dampng. Lu [9] stablshd th dynamc quaton of vbraton wth rod cntrln as any plan curv and dscussd th plan vbraton problms of lastc rod wth crcular cross scton n vscous mdum. Du to th lmtaton n statcs catgory, th Krchhoff thory s not suffcnt to calculat proprly whn solvng th contnuum movmnt problms. Thn, a srs of mthods such as th dffrntal quadratur, fnt dffrnc wr dvlopd and tstd, whch mak th nonlnar rsponss of axally movng bam undr paramtrc xctatons b acquantd by us. But thr s stll dsagrmnt btwn axal tnson of movng bam and spd pulsaton []. Galrkn truncaton mthod was rcntly usd to study th stablty and dynamcs of axally movng bam wth smpl support. Its basc prncpl s to ovrlap th fnt polynomal functon and gt a srs of algbrac quatons sutabl for crtan boundary condtons. Ghaysh [] dscussd th branch and chaotc charactrstcs of axal movng body undr th longtudnal forcd vbraton and plan nonlnar vbraton whch coupld th radal and transvrs drcton. Dng t. al [] studd th chaotc dynamc bhavor of vscolastc bam wth paramtrc xctaton whch s causd by xtrnal harmonc xctaton and spd pulsaton, and obsrvd th doublng bfurcaton phnomnon of axally movng bam on dsturbanc vlocty ampltud by Poncar mappng. Th mult-scal approach (MSA) s appld to dtrmn th ampltud-frquncy charactrstcs and stady-stat rspons of nonlnar forcd vbraton whn approxmatly solvng th axally movng contnuum ssu n ordr to kp hgh accuracy and low computatonal cost. Th vbraton s a mult-scal coupld phnomnon and th man faturs of th objctv world complxty, namly, cohrnt structur and random fluctuatons appar smultanously or altrnatly and coupld wth ach othr, whch dtrmns that t cannot b xpland from a sngl pont of vw [3]. Currntly, many scholars nvstgatd th vbraton problms of movng body from th angl of mult-scal. Chn [] analyzd th stabl boundary of axal shft vscolastc bam undr clampd condtons through th avrag approach and got th stabl boundars of clampd bam by usng th mult-scal approach. Yao [5] studd th nonlnar dynamc bhavor of axal movng bam wth paramtrc xctaton undr mult-puls xctaton by combnng th multpl tm scals mthod and Galrkn truncaton mthod. Pakdmrl [6] appld th mult-scal approach to th partal dffrntal quatons and studd th stablty of acclratd bam whn th stffnss s small. DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
2 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING In ths papr, th mult-scal approach s appld to solv govrnng quatons and th dffrnt truncaton Galrkn mthod s usd to study th nonlnar forcd vbraton of axal movng vscolastc bam. Th nfluncs of vscous dampng, xtrnal ncntvs, nonlnar coffcnt and movng vlocty on stady-stat rspons ampltud ar studd and abundant ampltud rspons rsult ar obtand, manwhl, th boundary condtons whn nstablty s occurrd ar also analyzd. II. GOVERNING EQUATION Klvn modl has bn wdly usd n th axal movng bam. Aftr Mocknsturm t. al [7] dmd that th physcal tm should b takn nto consdraton to xprss th nrgy dsspaton durng stady movmnt, Chn t. al [8] appld th physcal tm drvatv n vscolastc proprts of axally movng bam. Thr was a smply clampd axally movng bam wth unform dnsty ρ and cross-sctonal ara A. And th lngth btwn supports L, ntal tnson P, axal vlocty v, xctaton ampltud F. Th modl was shown n Fg., n whch cross-sctonal ara momnt of nrtal I, lastc rato s E and vscosty coffcnt s η. Th control quaton can b show as Equaton () whn consdrng th latral vbraton n th plan only, whr th dsplacmnt X and forc F s th functon of axal coordnat X and tm T. 5 U U dvu U U U U ( v v ) P EI I F () T X T dtx X X X T X Boundary condtons of smply supportd bam at both nds: U (, T ), U ; X U ( L, T ), U () X X X L Brng n th dmnsonlss varabls and paramtrs: U u, L X x, L P t T, AL v A, P EI, P L I k, FL f, (3) 3 L AP P o whr s an small dmnsonlss paramtr. Th dmnsonlss form of Equaton () and () can b show as Equaton () and (5). 5 u u d u u u u ( ) k f () t x t dt x x x x t u (, t), u,, u ( l, t) u x x x xl (5) Fg. Schmatc of axally movng bams. III. MULTI-SCALE APPROACH Th mult-scal approach can b usd n solvng th nonlnar partal dffrntal quaton problm approxmatly. Undr th smply supportd boundary condtons, th mult-scal approach s mployd to solv th partal dffrntal quatons (), wth th tm scal as T=εt. Th quaton can b wrttn by. u x, t; ) u ( x, T, T ) u ( x, T, ) (6) ( T whr u and u rprsnt th fast scal and slow scal dsplacmnt functon rspctvly. T =t and T =εt ar sparatly th fast tm scal and slow tm scal. Insrtng Equaton () nto Equaton (6) and sparatng th dffrnt ordrs, w gt, (7) t T T Whn Equaton (7) s substtutd n Equaton (), on obtans Equaton (8) and (9) by u and u. 5 u u d u u u u ( ) k f (8) T x T dt x x x x T u T u d u u u u u Th soluton of Equaton (8) s gvn by Wckrt and Mot [9] : u 5 ( ) k ( ) (9) x T dt x x x x T T T T T ( x) A ( T ) ( x) A ( T ) () whr ω and ϕ rprsnt th -th natural frquncy and th corrspondng complx modal functon of lnar homognous systm rspctvly. Th ϕ (x) that mt th condton of both-clampd bam can b xprssd as DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
3 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING ( x) ( ( r x ( r r3 r r )( r3 r r )( r3 r ( r r )( ) r x ( r r n )( r3 r r )( ) ( r r3 )( r r r ) ( r r )( ) r r r3 ) ( r r3 )( ) r r r x r ) r3 ) r3 x () whr r m (m =,, 3, ) s th soluton of th followng algbrac quaton: k r f m ( ) r r, () m Th -th vbraton modl s consstnt wth th nonlnar frquncy wthout consdrng th ntrnal rsonanc. Put Equaton () nto Equaton (9), w gt, u u u u da ( ) ( ) T T x x x dt 3 k A A ( ) T m cc NST T (3) whr cc rprsnts th complx conjugat of all trms abov and NST mans non-constant trm. Equaton (3) may hav th boundd soluton unlss t satsfy th followng condton. da 3 T T ( ) f k AA ( ) dt () () (5) Ak ( w ), whr th nnr product dfnton of complx functons g and h s ntroduc n th rang of [, ]. g, h ghdx, (5) Apply th nnr product dstrbuton rat to quaton () and th soluton of th quaton can b xprssd as, da k A A (6) dt whr k s dfnd by Equaton (7) and Equaton(8) as, 3 k ( A ' dx dx k dx dx) ' A s gvn by (7) (8) of th nonlnar fr vbraton sparatly. And th ral and magnary parts of A can b shown as: a f Im( )sn( ) -R( )cos( ) R( ) a ( an, n) 3 (9) f Im( )cos( ) R( )sn( a Im( k ) a ( an, n) n 3 a T whr σ s th harmonc paramtr. In ordr to analyz th ampltud rspons nar th rsonanc pont, th rlatonshp btwn dsturbanc frquncy ω and natural frquncy ω can b wrttn as Equaton (). And th rlatonshp btwn ampltud rspons and harmonc paramtr s obtand by lmnatng th phas, as shown Equaton (). / 3 ) () 3 3 R( ) a Im( k ) a a Im( k ) a f () In ordr to asly calculat, th Galrkn truncaton mthod s adoptd to convrt th dffrntal quaton of contnuum systm nto th ordnary dffrntal quaton wth fnt dmnson and th dynamc charactrstcs of axally acclratng vscolastc bam s analyzd numrcally, whr th dsplacmnt varabls can b rprsntd as, N u( x, t) q ( t) ( x) () N F( x) f ( x), (3) Th dscrtzaton quatons wll constran quckly wth th ncras of, whr q stands for th gnralzd dsplacmnt functon and f mans th -th forcd vbraton ampltud whch s a constant valu. Insrtng Equaton () and (3) nto Equaton (3), multply by th corrspondng charactrstc functon and convrt nto th dscrt functon [, ], whch can xprss as matrx: Iq Cq Kq Mq N () n whr a and rprsnt th ampltud and phas angl whr I C K M and N rprsnt th mass matrx th dampng matrx th stffnss matrx th xtrnal stffnss DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
4 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING matrx and th xtrnal xctaton matrx sparatly. q q t) q ( t) q ( t), ( x) ( x) ( ) (5) ( x I T dx (6) T () T C dx k dx (7) T () T () K ( ) dx dx k dx (8) 3 T () T T M dx k d k dx (9) A. Modl Valdaton IV. RESULT ANALYSIS Fg. shows th chang of latral vbraton dsplacmnt n th cntr of axally movng vscolastc bam wth tm undr th systm paramtrs st as vscous dampng coffcnt k=.5, xtrnal xctaton f=.8, movng vlocty γ=.5, and nonlnar coffcnt v=. It s obsrvd that th vbraton dsplacmnt s stabl whn loadng prodcally. Howvr, th prodcal changng of dsplacmnt s not th ky to masur th vbraton charactrstcs. In ths papr, th nvstgaton focus s th varaton of ampltud, namly, th rlatv valu btwn th maxmum and mnmum dsplacmnt varaton. u(.5, t) t Fg. Dsplacmnt varaton of th vscolastcty bam cntr wth tm In ordr to vrfy th fasblty of th mult-scal modl, Fg.3 gvs th quanttatv comparsons among th mult-scal calculaton, dffrntal quadratur mthod (DQM) [] and fnt dffrnc mthod (FDM) [] wth paramtrs as k=., f=., γ=, and v=. It s clar that by th abov thr mthods, th curvs that rprsnt th chang of th stady-stat rspons ampltud wth harmonc paramtrs show grat agrmnt. Thus, t s fasbl to mploy th mult-scal mthod to smulat th vbraton of vscolastc bam. Undr th sam paramtrs, th valus of th stady stat rspons ampltud got by mult-scal mthod ar btwn that of DQM and FDM, whch rsults from th dffrnt dsposals at th nonlnar paramtr trms. And th mult-scal mthod can obtan rlatvly accurat rsult by contrast. a.3.. MSA FDM DQM Fg.3 Comparson of forcd vbraton btwn dffrnt numrcal mthods. B. Forcd Vbraton Analyss Th stady stat rspons of vbraton ampltud s affctd by macro prformanc, such as vscous dampng coffcnt k, xtrnal xctaton f, movng vlocty γ and nonlnar coffcnt v. Fg. (a) shows th rlatonshp btwn stady stat rspons ampltud and vscous dampng coffcnt wth f =., γ=, and v=. It can b sn that th stady-stat rspons ampltud dcrass wth th ncras of dampng coffcnt and ths varaton s obvous nar th natural frquncy ω (σ=). In othr words, th vscosty play a rol to absorb vbraton, and that s why flxbl structur s usd n many transportaton systms wth dynamc load. For xampl, th wr rop n hostng systm. Th nconspcuous rlatonshp btwn varaton of stady-stat rspons ampltud and nonlnar coffcnt s dpctd n Fg. (b) wth k=., f =., and γ=. Furthr, th law that th stady-stat rspons dcrass wth th ncras of movng vlocty s obtand n Fg. (c) wth k=., f=., and v=. It s found that hghr vlocty can mprov th dynamc balanc of systm and aggravat th bfurcaton phnomnon, whch agrs wll wth th rsults n ltratur [-]. Th rlatonshp btwn th stady-stat rspons ampltud and xtrnal xctaton s studd wth k=., γ=, and v=. As shown n Fg. (d), th stady stat rspons ampltud wll ncras whn th xtrnal DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
5 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING ncntv bcoms ntns, whch agrs wll wth th concluson n tst [3]..3 (a) ordr Galrkn truncaton k=.5.3. (d) f=.5 ordr Galrkn truncaton. f=. k=. a a.. f=.5 k=.3 a (a) Th vscous dampng coffcnt.3 (b) =5 = = ordr Galrkn truncaton (d) th xtrnal xctaton Fg. Influnc of dffrnt paramtrs on th stady-stat rspons ampltud. Th nflunc of xtrnal ncntvs on th stady-stat rspons ampltud s obvous whn th valus ar far away from th natural frquncy ω. Howvr, th xtrnal motvaton s nvtabl n th practcal ngnrng and how to rgulat th systm paramtrs bcoms a ky n systm dsgnng. To conclud that lowr xtrnal motvaton, hghr vscous dampng coffcnt and movng vlocty can ffctvly rstran vbraton, whch s usful for th movng of axal vscolastcty bam. a (c).. (b) Th nonlnar coffcnt =3 =5 ordr Galrkn truncaton = (c) Th opraton vlocty γ C. Vbraton Stablty Fg.5 (a) and (b) show th comparsons of th ral part of stady-stat rspons ampltud whn th ordr of Galrkn truncaton s,, undr th paramtrs as k=.5,f=.,γ=3,υ=5 and k=.3,f=.8, γ=,υ= rspctvly. It s obsrvd that th ordr Galrkn truncaton can produc rlabl prmary rsonanc, but and ordr Galrkn truncatons show clos rsults. That,s to say, th dffrnc among natural frquncs of axal movng bam can b obtand by Galrkn truncaton mthod, whch s rflctd by stady-stat rspons of dffrnt ampltuds n th crtcal rgon []. Thn, th nstablty boundary of man rsonanc s analyzd and Fg.6 (a) and (b) show th rsults of stady-stat rspons ampltud and th nstablty boundars undr th condton of k=.5,f=.5,γ=5,υ= and k=.3, f=.5,γ=5,υ= rspctvly, whr th sold ln rprsnts th stabl rgon, th dottd ln rprsnts th nstablty boundary, and th magnary ln rprsnts th nstablty rgon. By comparson, although th movng vlocty and nonlnar coffcnt s hghr, th rspons ampltud can always kp stabl f th vscous dampng coffcnt ncras and th xtrnal xctaton bcom DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
6 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING wak, whch s consstnt wth th concluson n rfrnc []. Th rsults ndcat that ovr small vscous dampng coffcnt and ovrlarg xtrnal xctaton wll caus nstablty..3 (a) stabl rgon nstablty boundary nstablty rgon.3 (a). ordr Galrkn truncaton ordr Galrkn truncaton ordr Galrkn truncaton a.. a (b) (b) ordr Galrkn truncaton ordr Galrkn truncaton ordr Galrkn truncaton a.. stabl rgon nstablty boundary a Fg.5 Comparson of dffrnt ordrs Galrkn truncaton Ths s bcaus th vscous has th powr to absorb vbraton to kp balanc, and th xtrnal ncntvs nhanc th occurrnc of chaos and bfurcaton [9]. It s known that nstablty wll nflunc th runnng stablty of th flxbl systms and th unwantd phnomna lk skddng may occur wth th ovrlarg movng dsplacmnt of nonlnar movng bam du to th aggravaton of nstablty. Thrfor, th choc of paramtrs n practcal applcatons should b rasonabl to avod th occurrnc of nstablty Fg.6 Stady-stat rspons and th nstablty boundars. V. CONCLUSIONS In ths papr, th nonlnar forcd vbraton of th axally movng vscolastc bams ar rsarchd by usng th mult-scal approach, togthr wth Galrkn truncaton mthod to numrcally solv ts dffrntal quaton, and obtan th rlabl conclusons. Frstly, th accuracy of th modl was vrfd through th quanttatv comparson wth th dffrntal quadratur mthod and fnt dffrnc mthod. Thn, th nfluncs of vscous dampng coffcnt, xtrnal motvaton, nonlnar coffcnt and movng vlocty on th stady-stat rspons ampltud wr analyzd. Th stady-stat rsponss ampltud s nvrsly proportonal to th valu of vscous dampng coffcnt and movng vlocty, and proportonal to xtrnal xctaton. All abov rsults ar consstnt wth th rfrncs. At last, by comparng th dffrnt ordr Galrkn truncaton, th nstablty boundary condtons ar analyzd, and found that th too small vscosty or too larg xtrnal motvatons caus nstablty. Th rsarch that mult-scal approach and Galrkn truncaton mthod ar appld to xplor th nonlnar forcd vbraton of th axally movng vscolastc bam s vry usful. Th DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
7 BAO-FU KOU t al: A STUDY ON NONLINEAR FORCED VIBRATION OF AN AXIAL MOVING conclusons hav grat valu n thory and also can gud us to control nstablty ffctvly through optmzng paramtrs. ACKNOWLEDGMENTS Th work dscrbd n ths papr was supportd by th Foundaton of Scntfc and Tchnologcal Innovaton Rsarch Projcts n Unvrsts of Shanx, Chna (Grant No. 665); and th Scntfc Rsarch Foundaton for th Doctors of Tayuan Unvrsty of Scnc and Tchnology, Chna (Grant No. 55). REFERENCES [] N.H. Zhang, L.Q. Chn, Nonlnar dynamcal analyss of axally movng vscolastc strngs, Chaos, Soltons & Fractals (5) [] J.R. Chang, W.J. Ln, C.J. Huang, S.T. Cho,Vbraton and stablty of an axally movng Raylgh bam, Appld Mathmatcal Modlng 3 () [3] J.A. Wckrt, C.D. MotJr., Currnt rsarch on th vbraton and stablty of axally-movng matrals, Shock and Vbraton Dgst (988) 3 3. [] F. Pllcano, F.Vstron, Complx dynamcs of hgh-spd axally movng systms, Journal of Sound and Vbraton 58 () 3. [5] S. Kazmrad, M.H. Ghaysh, M. Amabl, Thrmal ffcts on nonlnar vbratons of an axally movng bam wth an ntrmdat sprng-mass support, Shock and Vbraton (3) [6] Rdl C H, Tan C A. Coupld forcd rspons of an axally movng strp wth ntrnal rsonanc, Intrnatonal Journal of Non-lnar Mchancs, 37 () -6. [7] Pasn F, Ubr d stabltat dr bgschwngungn von n langsrchtung prodsch hn und hrbwgtn Stabn, 97, Ingnur-Archv, (97) [8] Oz H R. On th vbratons of an axally travlng bam on fxd supports wth varabl vlocty, Journal of Sound and Vbraton, 39 () [9] Y.Z. Lu, On dynamcs of lastc rod basd on xact cossrat modl, Chns Physcs B, 8 (9) 3 [] T.Z. Yang, B. Fang, Y. Chn, Y.X. Zhn, Approxmat solutons of axally movng vscolastc bams subjct to mult-frquncy xctatons, Intrnatonal Journal of Non-lnar Mchancs, (9) 3-38 [] M.H. Ghaysh, H.A. Kafabad, T. Rd, Sub-and supr-crtcal nonlnar dynamcs of a harmoncally xctd axally movng bam, Intrnatonal Journal of Solds and Structurs 9 () 7 3. [] H. Dng, L.Q. Chn, Nonlnar modls for transvrs forcd vbraton of axally movng vscolastc bams, Shock and Vbraton 8 () [3] B. Nayak, S.K.Dwvdy, K.S.R.K.Murthy, Mult-frquncy xctaton of magntorhologcal lastomr-basd sandwch bam wth conductv skns, Intrnatonal Journal of Solds and Structurs 7 () 8-6. [] L.Q. Chn, X.D. Yang, Stablty n paramtrc rsonancs of an axally movng vscolastc bam wth tm-dpndnt vlocty, Journal of Sound and Vbraton, 8(5) [5] M.H. Yao, W. Zhang, J.W. Zu, Mult-puls chaotc dynamcs n non-planar moton of paramtrcally xctd vscolastc movng blt, Journal of Sound and Vbraton. 33 () 6. [6] M. Pakdmrl, H.R. Oz, Infnt mod analyss and truncaton to rsonant mods of axally acclratd bam vbratons, Journal of Sound and Vbraton, 3(8) 5-7. [7] E.M. Mocknsturm, J. Guo, Nonlnar vbraton of paramtrcally xctd, vscolastc, axally movng Strngs, ASME J Appl Mch, 7(5) [8] L.Q. Chn, X.D. Yang, Bfurcaton and chaos of an axally acclratng vscolastc bam,chaos, Soltons and Fractals, 3(5) [9] J.A. Wckrt, C.D. Mot, Classcal vbraton analyss of axally movng contnua, ASME Journal of Appld Mchancs 57 (99) [] G.C. Zhang, H. Dng, L.Q. Chn, S.P. Yang, Galrkn mthod for stady-stat rspons of nonlnar forcd vbraton of axally movng bams at suprcrtcal spds, Journal of Sound and Vbraton 33 () [] M.H. Ghaysh, Nonlnar forcd dynamcs of an axally movng vscolastc bam wth an ntrnal rsonanc, Intrnatonal Journal of Mchancal Scncs 53 () 37. [] B. Wang, Asymptotc Analyss on Wakly Forcd Vbraton of an Axally Movng Vscolastc Bam Consttutd by Standard Lnar Sold Modl, Appld Mathmatcs and Mchancs,33() [3] Y.C. Duan, J.P. Wang, J.Q. Wang, Y.W. Lu, F. Shao, Thortcal and xprmntal study on th transvrs vbraton proprts of an axally movng nstd cantlvr bam, Journal of Sound and Vbraton. 333 () DOI.53/IJSSST.a ISSN: 73-8x onln, prnt
HORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WITH VARIABLE PROPERTIES
13 th World Confrnc on Earthquak Engnrng Vancouvr, B.C., Canada August 1-6, 4 Papr No. 485 ORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WIT VARIABLE PROPERTIES Mngln Lou 1 and Wnan Wang Abstract:
More informationStress-Based Finite Element Methods for Dynamics Analysis of Euler-Bernoulli Beams with Various Boundary Conditions
9 Strss-Basd Fnt Elmnt Mthods for Dynamcs Analyss of Eulr-Brnoull Bams wth Varous Boundary Condtons Abstract In ths rsarch, two strss-basd fnt lmnt mthods ncludng th curvatur-basd fnt lmnt mthod (CFE)
More informationThree-Node Euler-Bernoulli Beam Element Based on Positional FEM
Avalabl onln at www.scncdrct.com Procda Engnrng 9 () 373 377 Intrnatonal Workshop on Informaton and Elctroncs Engnrng (IWIEE) Thr-Nod Eulr-Brnoull Bam Elmnt Basd on Postonal FEM Lu Jan a *,b, Zhou Shnj
More informationA Note on Estimability in Linear Models
Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,
More informationThe Hyperelastic material is examined in this section.
4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):
More informationGrand Canonical Ensemble
Th nsmbl of systms mmrsd n a partcl-hat rsrvor at constant tmpratur T, prssur P, and chmcal potntal. Consdr an nsmbl of M dntcal systms (M =,, 3,...M).. Thy ar mutually sharng th total numbr of partcls
More informationJones vector & matrices
Jons vctor & matrcs PY3 Colást na hollscol Corcagh, Ér Unvrst Collg Cork, Irland Dpartmnt of Phscs Matr tratmnt of polarzaton Consdr a lght ra wth an nstantanous -vctor as shown k, t ˆ k, t ˆ k t, o o
More informationExternal Equivalent. EE 521 Analysis of Power Systems. Chen-Ching Liu, Boeing Distinguished Professor Washington State University
xtrnal quvalnt 5 Analyss of Powr Systms Chn-Chng Lu, ong Dstngushd Profssor Washngton Stat Unvrsty XTRNAL UALNT ach powr systm (ara) s part of an ntrconnctd systm. Montorng dvcs ar nstalld and data ar
More informationJournal of Theoretical and Applied Information Technology 10 th January Vol. 47 No JATIT & LLS. All rights reserved.
Journal o Thortcal and Appld Inormaton Tchnology th January 3. Vol. 47 No. 5-3 JATIT & LLS. All rghts rsrvd. ISSN: 99-8645 www.att.org E-ISSN: 87-395 RESEARCH ON PROPERTIES OF E-PARTIAL DERIVATIVE OF LOGIC
More informationAnalyzing Frequencies
Frquncy (# ndvduals) Frquncy (# ndvduals) /3/16 H o : No dffrnc n obsrvd sz frquncs and that prdctd by growth modl How would you analyz ths data? 15 Obsrvd Numbr 15 Expctd Numbr from growth modl 1 1 5
More informationSeptember 27, Introduction to Ordinary Differential Equations. ME 501A Seminar in Engineering Analysis Page 1. Outline
Introucton to Ornar Dffrntal Equatons Sptmbr 7, 7 Introucton to Ornar Dffrntal Equatons Larr artto Mchancal Engnrng AB Smnar n Engnrng Analss Sptmbr 7, 7 Outln Rvw numrcal solutons Bascs of ffrntal quatons
More informationFrom Structural Analysis to FEM. Dhiman Basu
From Structural Analyss to FEM Dhman Basu Acknowldgmnt Followng txt books wr consultd whl prparng ths lctur nots: Znkwcz, OC O.C. andtaylor Taylor, R.L. (000). Th FntElmnt Mthod, Vol. : Th Bass, Ffth dton,
More informationThe Fourier Transform
/9/ Th ourr Transform Jan Baptst Josph ourr 768-83 Effcnt Data Rprsntaton Data can b rprsntd n many ways. Advantag usng an approprat rprsntaton. Eampls: osy ponts along a ln Color spac rd/grn/blu v.s.
More informationPhysics of Very High Frequency (VHF) Capacitively Coupled Plasma Discharges
Physcs of Vry Hgh Frquncy (VHF) Capactvly Coupld Plasma Dschargs Shahd Rauf, Kallol Bra, Stv Shannon, and Kn Collns Appld Matrals, Inc., Sunnyval, CA AVS 54 th Intrnatonal Symposum Sattl, WA Octobr 15-19,
More informationPhys 774: Nonlinear Spectroscopy: SHG and Raman Scattering
Last Lcturs: Polaraton of Elctromagntc Wavs Phys 774: Nonlnar Spctroscopy: SHG and Scattrng Gnral consdraton of polaraton Jons Formalsm How Polarrs work Mullr matrcs Stoks paramtrs Poncar sphr Fall 7 Polaraton
More information1- Summary of Kinetic Theory of Gases
Dr. Kasra Etmad Octobr 5, 011 1- Summary of Kntc Thory of Gass - Radaton 3- E4 4- Plasma Proprts f(v f ( v m 4 ( kt 3/ v xp( mv kt V v v m v 1 rms V kt v m ( m 1/ v 8kT m 3kT v rms ( m 1/ E3: Prcntag of
More information8-node quadrilateral element. Numerical integration
Fnt Elmnt Mthod lctur nots _nod quadrlatral lmnt Pag of 0 -nod quadrlatral lmnt. Numrcal ntgraton h tchnqu usd for th formulaton of th lnar trangl can b formall tndd to construct quadrlatral lmnts as wll
More informationEconomics 600: August, 2007 Dynamic Part: Problem Set 5. Problems on Differential Equations and Continuous Time Optimization
THE UNIVERSITY OF MARYLAND COLLEGE PARK, MARYLAND Economcs 600: August, 007 Dynamc Part: Problm St 5 Problms on Dffrntal Equatons and Contnuous Tm Optmzaton Quston Solv th followng two dffrntal quatons.
More informationPhysics 256: Lecture 2. Physics
Physcs 56: Lctur Intro to Quantum Physcs Agnda for Today Complx Numbrs Intrfrnc of lght Intrfrnc Two slt ntrfrnc Dffracton Sngl slt dffracton Physcs 01: Lctur 1, Pg 1 Constructv Intrfrnc Ths wll occur
More informationRadial Cataphoresis in Hg-Ar Fluorescent Lamp Discharges at High Power Density
[NWP.19] Radal Cataphorss n Hg-Ar Fluorscnt Lamp schargs at Hgh Powr nsty Y. Aura, G. A. Bonvallt, J. E. Lawlr Unv. of Wsconsn-Madson, Physcs pt. ABSTRACT Radal cataphorss s a procss n whch th lowr onzaton
More informationACOUSTIC WAVE EQUATION. Contents INTRODUCTION BULK MODULUS AND LAMÉ S PARAMETERS
ACOUSTIC WAE EQUATION Contnts INTRODUCTION BULK MODULUS AND LAMÉ S PARAMETERS INTRODUCTION As w try to vsualz th arth ssmcally w mak crtan physcal smplfcatons that mak t asr to mak and xplan our obsrvatons.
More informationLecture 23 APPLICATIONS OF FINITE ELEMENT METHOD TO SCALAR TRANSPORT PROBLEMS
COMPUTTION FUID DYNMICS: FVM: pplcatons to Scalar Transport Prolms ctur 3 PPICTIONS OF FINITE EEMENT METHOD TO SCR TRNSPORT PROBEMS 3. PPICTION OF FEM TO -D DIFFUSION PROBEM Consdr th stady stat dffuson
More informationOptimal Topology Design for Replaceable of Reticulated Shell Based on Sensitivity Analysis
Optmal Topology Dsgn for Rplacabl of Rtculatd Shll Basd on Snstvty Analyss Yang Yang Dpartmnt of Naval Archtctur, Dalan Unvrsty of Tchnology, Laonng, CN Ma Hu Collg of Rsourc and Cvl Engnrng, Northastrn
More informationCHAPTER 33: PARTICLE PHYSICS
Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that
More informationLecture 3: Phasor notation, Transfer Functions. Context
EECS 5 Fall 4, ctur 3 ctur 3: Phasor notaton, Transfr Functons EECS 5 Fall 3, ctur 3 Contxt In th last lctur, w dscussd: how to convrt a lnar crcut nto a st of dffrntal quatons, How to convrt th st of
More informationEXTENDED MULTISCALE FINITE ELEMENT METHOD FOR GEOMETRICALLY NONLINEAR ANALYSIS OF THIN COMPOSITE PLATES ON BENDING PROBLEMS
21 st Intrnatonal Confrnc on Compost Matrals X an, 20-25 th August 2017 XTNDD MULTISCAL FINIT LMNT MTHOD FOR GOMTRICALLY NONLINAR ANALYSIS OF THIN COMPOSIT PLATS ON BNDING PROBLMS Mngfa Rn 1, J Cong 1
More information??? Dynamic Causal Modelling for M/EEG. Electroencephalography (EEG) Dynamic Causal Modelling. M/EEG analysis at sensor level. time.
Elctroncphalography EEG Dynamc Causal Modllng for M/EEG ampltud μv tm ms tral typ 1 tm channls channls tral typ 2 C. Phllps, Cntr d Rchrchs du Cyclotron, ULg, Blgum Basd on slds from: S. Kbl M/EEG analyss
More informationModeling and Simulation Analysis of Power Frequency Electric Field of UHV AC Transmission Line
(IJACSA) Intrnatonal Journal of Advancd Computr Scnc and Applcatons, Vol., o., Modlng and Smulaton Analyss of Powr Frquncy Elctrc Fld of UHV AC Transmsson Ln Chn Han Collg of Elctronc and Elctrcal Engnrng
More informationDynamic Modeling and Vibration Control for Spacecraft s Solar Array Jian-Ping JIANG 1,a, *, Rui XU 2,b
Intrnatonal Confrnc on Mchancs and Cvl Engnrng (ICMCE 2014) Dynamc Modlng and Vbraton Control for Spaccraft s Solar Array Jan-Png JIANG 1,a, *, Ru XU 2,b 1,2 Collg of Arospac Scnc and Engnrng, Natonal
More informationPREDICTION OF STRESS CONCENTRATION FACTORS IN UNLAPPED SQUARE HOLLOW "K" JOINTS BY THE FINITE ELEMENT METHOD
Ngran Journal of chnology, Vol. 5, No., March 006 Jk 5 PREDICION OF SRESS CONCENRAION FACORS IN UNLAPPED SQUARE HOLLOW "K" JOINS BY HE FINIE ELEMEN MEHOD DR.P.N.JIKI Dpartmnt of Cvl Engnrng, Unvrsty of
More informationA Novel Finite Volume Scheme with Geometric Average Method for Radiative Heat Transfer Problems *
Appld Physcs Frontr Novmbr 013 Volum 1 Issu 4 PP.3-44 A Novl Fnt Volum Schm wth Gomtrc Avrag Mthod for Radatv Hat Transfr Problms * Cunyun N 1 Hayuan Yu 1. Dpartmnt of Mathmatcs and Physcs Hunan Insttuton
More informationCOMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP
ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng
More informationStudy of Dynamic Aperture for PETRA III Ring K. Balewski, W. Brefeld, W. Decking, Y. Li DESY
Stud of Dnamc Aprtur for PETRA III Rng K. Balws, W. Brfld, W. Dcng, Y. L DESY FLS6 Hamburg PETRA III Yong-Jun L t al. Ovrvw Introducton Dnamcs of dampng wgglrs hoc of machn tuns, and optmzaton of stupol
More informationA NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION*
A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION* Dr. G.S. Davd Sam Jayakumar, Assstant Profssor, Jamal Insttut of Managmnt, Jamal Mohamd Collg, Truchraall 620 020, South Inda,
More informationFREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED BEAMS
Journal of Appl Mathatcs an Coputatonal Mchancs, (), 9- FREE VIBRATION ANAYSIS OF FNCTIONAY GRADED BEAMS Stansław Kukla, Jowta Rychlwska Insttut of Mathatcs, Czstochowa nvrsty of Tchnology Czstochowa,
More informationOPTIMAL TOPOLOGY SELECTION OF CONTINUUM STRUCTURES WITH STRESS AND DISPLACEMENT CONSTRAINTS
Th Svnth East Asa-Pacfc Confrnc on Structural Engnrng & Constructon August 27-29, 1999, Koch, Japan OPTIMAL TOPOLOGY SELECTION OF CONTINUUM STRUCTURES WITH STRESS AND DISPLACEMENT CONSTRAINTS Qng Quan
More informationCHAPTER 7d. DIFFERENTIATION AND INTEGRATION
CHAPTER 7d. DIFFERENTIATION AND INTEGRATION A. J. Clark School o Engnrng Dpartmnt o Cvl and Envronmntal Engnrng by Dr. Ibrahm A. Assakka Sprng ENCE - Computaton Mthods n Cvl Engnrng II Dpartmnt o Cvl and
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(7): Research Article
Avalabl onln www.ocpr.com Journal of Chmcal and Pharmacutcal Rsarch, 214, 6(7):1394-14 Rsarch Artcl ISSN : 975-7384 COEN(USA) : JCPRC5 Rsarch on fatgu damag of suckr rod basd on damag mchancs Ru-fn Zhou,
More informationMathematical Model of Arterial Hemodynamics, Description, Computer Implementation, Results Comparison
Appld Physcs Rsarch; Vol. 5, No. 3; 3 ISSN 96-9639 E-ISSN 96-9647 Publshd by Canadan Cntr of Scnc and Educaton Mathmatcal Modl of Artral Hmodynamcs, Dscrpton, Computr Implmntaton, Rsults Comparson Elshn
More informationAPPLICATION OF GALERKIN FINITE ELEMENT METHOD IN THE SOLUTION OF 3D DIFFUSION IN SOLIDS
Cênca/Scnc APPLICATION OF GALERKIN FINITE ELEMENT METHOD IN THE SOLUTION OF D DIFFUSION IN SOLIDS E C Romão a, M D d Campos c, J A Martns b, and L F M d Moura a Unvrsdad Estadual d Campnas Faculdad d Engnhara
More informationCHAPTER 4. The First Law of Thermodynamics for Control Volumes
CHAPTER 4 T Frst Law of Trodynacs for Control olus CONSERATION OF MASS Consrvaton of ass: Mass, lk nrgy, s a consrvd proprty, and t cannot b cratd or dstroyd durng a procss. Closd systs: T ass of t syst
More informationReview - Probabilistic Classification
Mmoral Unvrsty of wfoundland Pattrn Rcognton Lctur 8 May 5, 6 http://www.ngr.mun.ca/~charlsr Offc Hours: Tusdays Thursdays 8:3-9:3 PM E- (untl furthr notc) Gvn lablld sampls { ɛc,,,..., } {. Estmat Rvw
More informationElectrostatic Surface Waves on Semi-Bounded Quantum Electron-Hole Semiconductor Plasmas
Commun. Thor. Phys. 67 07 37 3 Vol. 67 No. 3 March 07 Elctrostatc Surfac Wavs on Sm-Boundd Quantum Elctron-Hol Smconductor Plasmas Afshn Morad Dpartmnt of Engnrng Physcs Krmanshah Unvrsty of Tchnology
More informationNaresuan University Journal: Science and Technology 2018; (26)1
Narsuan Unvrsty Journal: Scnc and Tchnology 018; (6)1 Th Dvlopmnt o a Corrcton Mthod or Ensurng a Contnuty Valu o Th Ch-squar Tst wth a Small Expctd Cll Frquncy Kajta Matchma 1 *, Jumlong Vongprasrt and
More informationPolytropic Process. A polytropic process is a quasiequilibrium process described by
Polytropc Procss A polytropc procss s a quasqulbrum procss dscrbd by pv n = constant (Eq. 3.5 Th xponnt, n, may tak on any valu from to dpndng on th partcular procss. For any gas (or lqud, whn n = 0, th
More informationGroup Codes Define Over Dihedral Groups of Small Order
Malaysan Journal of Mathmatcal Scncs 7(S): 0- (0) Spcal Issu: Th rd Intrnatonal Confrnc on Cryptology & Computr Scurty 0 (CRYPTOLOGY0) MALAYSIA JOURAL OF MATHEMATICAL SCIECES Journal hompag: http://nspm.upm.du.my/ournal
More informationHeisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari
snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationBasic Electrical Engineering for Welding [ ] --- Introduction ---
Basc Elctrcal Engnrng for Wldng [] --- Introducton --- akayosh OHJI Profssor Ertus, Osaka Unrsty Dr. of Engnrng VIUAL WELD CO.,LD t-ohj@alc.co.jp OK 15 Ex. Basc A.C. crcut h fgurs n A-group show thr typcal
More informationFINITE ELEMENT METHOD II Autumn 2015
FEM II - Lctur Pag of 4 FINITE ELEMENT METHOD II Autumn 05 Lcturs (5h):. Accuracy, rror stmaton and adaptv rmshng. Hat flow and thrmal strsss n FEM 3. Introducton to structural dynamcs, fr vbratons 4.
More informationStretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES 2016,VOL.0,NO.0,1 20 http://dx.do.org/10.1080/15376494.2016.1194505 ORIGINAL ARTICLE Strtchng and bndng dformatons du to normal and shar tractons of doubly
More informationDiscrete Shells Simulation
Dscrt Shlls Smulaton Xaofng M hs proct s an mplmntaton of Grnspun s dscrt shlls, th modl of whch s govrnd by nonlnar mmbran and flxural nrgs. hs nrgs masur dffrncs btwns th undformd confguraton and th
More informationHeating of a solid cylinder immersed in an insulated bath. Thermal diffusivity and heat capacity experimental evaluation.
Hatng of a sold cylndr mmrsd n an nsulatd bath. Thrmal dffusvty and hat capacty xprmntal valuaton. Žtný R., CTU FE Dpartmnt of Procss Engnrng, arch. Introducton Th problm as ntatd by th follong E-mal from
More informationFrom Structural Analysis to Finite Element Method
From Structural Analyss to Fnt Elmnt Mthod Dhman Basu II Gandhnagar -------------------------------------------------------------------------------------------------------------------- Acknowldgmnt Followng
More informationLinear Algebra Provides a Basis for Elasticity without Stress or Strain
Soft, 05, 4, 5-4 Publshd Onln Sptmbr 05 n ScRs. http://www.scrp.org/ournal/soft http://dx.do.org/0.46/soft.05.400 Lnar Algbra Provds a Bass for Elastcty wthout Strss or Stran H. H. Hardy Math/Physcs Dpartmnt,
More informationStudy interaction between intensive circularly polarized laser and hydrogen atom using a matrix method
ISBN 978-1-84626-020-9 Procdngs of 3 rd Intrnatonal Workshop on Matrx Analyss angzhou,p.r.chna.july 9-13, 2009, pp. 199-202 ( Wll st y th pulshr ) Study ntracton twn ntnsv crcularly polarzd lasr and hydrogn
More informationNATURAL VIBRATION ANALYSIS OF CONTINUOUS HORIZONTALLY CURVED GIRDER BRIDGES USING DQEM *
Th 4 th World Confrnc on Earthquak Engnrng Octobr -7, 008, Bng, Chna TURL VIBRTIO LYSIS OF COTIUOUS HORIZOTLLY CURVED GIRDER BRIDGES USIG DQEM * LI Hongng, WG Tong and WEI Shuangk 3 Profssor, Collg of
More informationNON-SYMMETRY POWER IN THREE-PHASE SYSTEMS
O-YMMETRY OWER THREE-HAE YTEM Llana Marlna MATCA nvrsty of Orada, nvrstat str., no., 487, Orada; lmatca@uorada.ro Abstract. For thr-phas lctrcal systms, n non-symmtrcal stuaton, an analyz mthod costs on
More informationModelling of new generation plasma optical devices
NUKLEONIKA 216;61(2):27212 do: 1.1515/nuka-216-35 ORIGINAL PAPER Modllng of nw gnraton plasma optcal dvcs Irna V. Ltovko, Aly A. Goncharov, Andrw N. Dobrovolsky, Lly V. Nako, Irna V. Nako Abstract. Th
More informationRelate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added
4.3, 4.4 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt
More informationTHE HOMOGENIZED VISCOELASTIC AND RATE DEPENDENT PLASTIC MODEL FOR PLAIN WEAVE FABRIC REINFORCED POLYMER COMPOSITES
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS THE HOMOENIZED ISCOELASTIC AND RATE DEPENDENT PLASTIC MODEL FOR PLAIN WEAE FABRIC REINFORCED POLYMER COMPOSITES 1 Introducton S. L 1, C. Cho 1 *, N.
More informationOutlier-tolerant parameter estimation
Outlr-tolrant paramtr stmaton Baysan thods n physcs statstcs machn larnng and sgnal procssng (SS 003 Frdrch Fraundorfr fraunfr@cg.tu-graz.ac.at Computr Graphcs and Vson Graz Unvrsty of Tchnology Outln
More information:2;$-$(01*%<*=,-./-*=0;"%/;"-*
!"#$%'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%"'()'*+,-."/0.%+1'23"45'46'7.89:89'/' ;8-,"$4351415,8:+#9' Dr. Ptr T. Gallaghr Astrphyscs Rsarch Grup Trnty Cllg Dubln :2;$-$(01*%
More information14. MODELING OF THIN-WALLED SHELLS AND PLATES. INTRODUCTION TO THE THEORY OF SHELL FINITE ELEMENT MODELS
4. ODELING OF IN-WALLED SELLS AND PLAES. INRODUCION O E EORY OF SELL FINIE ELEEN ODELS Srő: Dr. András Skréns Dr. András Skréns BE odlng of thn-walld shlls and plats. Introducton to th thor of shll fnt
More informationOptimal Ordering Policy in a Two-Level Supply Chain with Budget Constraint
Optmal Ordrng Polcy n a Two-Lvl Supply Chan wth Budgt Constrant Rasoul aj Alrza aj Babak aj ABSTRACT Ths papr consdrs a two- lvl supply chan whch consst of a vndor and svral rtalrs. Unsatsfd dmands n rtalrs
More informationDecision-making with Distance-based Operators in Fuzzy Logic Control
Dcson-makng wth Dstanc-basd Oprators n Fuzzy Logc Control Márta Takács Polytchncal Engnrng Collg, Subotca 24000 Subotca, Marka Orškovća 16., Yugoslava marta@vts.su.ac.yu Abstract: Th norms and conorms
More informationST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous
ST 54 NCSU - Fall 008 On way Analyss of varanc Varancs not homognous On way Analyss of varanc Exampl (Yandll, 997) A plant scntst masurd th concntraton of a partcular vrus n plant sap usng ELISA (nzym-lnkd
More informationStatic/Dynamic Deformation with Finite Element Method. Graphics & Media Lab Seoul National University
Statc/Dynamc Dormaton wth Fnt Elmnt Mthod Graphcs & Mda Lab Sol Natonal Unvrsty Statc/Dynamc Dormaton Statc dormaton Dynamc dormaton ndormd shap ntrnal + = nrta = trnal dormd shap statc qlbrm dynamc qlbrm
More information10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D
Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav
More informationSpectral stochastic finite element analysis of structures with random field parameters under bounded-but-uncertain forces
Southrn Cross Unvrsty Publcatons@SCU 23rd Australasan Confrnc on th Mchancs of Structurs and Matrals 24 Spctral stochastc fnt lmnt analyss of structurs wth random fld paramtrs undr boundd-but-uncrtan forcs
More informationINTERFACE CORNERS IN ANISOTROPIC/PIEZOELECTRIC/ VISCOELASTIC MATERIALS
INERFAE ORNERS IN ANISOROPI/PIEZOELERI/ VISOELASI MAERIALS hyanbn Hwu a-lang uo Insttut of Aronautcs and Astronautcs Natonal hng ung Unvrsty anan AIWAN R.O.. Ansotropc matrals bhav dffrntly n dffrnt drctons.
More informationConstitutive Modeling of Progressive Damage in Composite Laminates
Consttutv Modlng of Progrssv amag n Compost Lamnats Chatanya A. nadayalu *, Adt Chattopadhyay and Xu Zhou Arzona Stat Unvrsty, Tmp, AZ 8587-606 A procdur has bn dvlopd for smulatng progrssv damag n compost
More informationte Finance (4th Edition), July 2017.
Appndx Chaptr. Tchncal Background Gnral Mathmatcal and Statstcal Background Fndng a bas: 3 2 = 9 3 = 9 1 /2 x a = b x = b 1/a A powr of 1 / 2 s also quvalnt to th squar root opraton. Fndng an xponnt: 3
More informationCLASSICAL STATISTICS OF PARAMAGNETISM
Prof. Dr. I. assr Phys 530 8-Dc_0 CLASSICAL STATISTICS OF PARAMAGETISM Th most famous typs of Magntc matrals ar: () Paramagntc: A proprty xhbt by substancs whch, whn placd n a magntc fld, ar magntd paralll
More informationEcon107 Applied Econometrics Topic 10: Dummy Dependent Variable (Studenmund, Chapter 13)
Pag- Econ7 Appld Economtrcs Topc : Dummy Dpndnt Varabl (Studnmund, Chaptr 3) I. Th Lnar Probablty Modl Suppos w hav a cross scton of 8-24 yar-olds. W spcfy a smpl 2-varabl rgrsson modl. Th probablty of
More informationEDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In the absence of or in between ELMs)
I. EDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In th absnc of or n btwn ELMs) Abstract W. M. Stacy (Gorga Tch) and R. J. Grobnr (Gnral Atomcs) A constrant on th on prssur gradnt s mposd by momntum
More information2. Grundlegende Verfahren zur Übertragung digitaler Signale (Zusammenfassung) Informationstechnik Universität Ulm
. Grundlgnd Vrfahrn zur Übrtragung dgtalr Sgnal (Zusammnfassung) wt Dc. 5 Transmsson of Dgtal Sourc Sgnals Sourc COD SC COD MOD MOD CC dg RF s rado transmsson mdum Snk DC SC DC CC DM dg DM RF g physcal
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationSoft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D
Comp 35 Machn Larnng Computr Scnc Tufts Unvrsty Fall 207 Ron Khardon Th EM Algorthm Mxtur Modls Sm-Suprvsd Larnng Soft k-mans Clustrng ck k clustr cntrs : Assocat xampls wth cntrs p,j ~~ smlarty b/w cntr
More informationGuo, James C.Y. (1998). "Overland Flow on a Pervious Surface," IWRA International J. of Water, Vol 23, No 2, June.
Guo, Jams C.Y. (006). Knmatc Wav Unt Hyrograph for Storm Watr Prctons, Vol 3, No. 4, ASCE J. of Irrgaton an Dranag Engnrng, July/August. Guo, Jams C.Y. (998). "Ovrlan Flow on a Prvous Surfac," IWRA Intrnatonal
More informationON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS
MATEMATICA MONTISNIRI Vol XL (2017) MATEMATICS ON TE COMPLEXITY OF K-STEP AN K-OP OMINATIN SETS IN RAPS M FARAI JALALVAN AN N JAFARI RA partmnt of Mathmatcs Shahrood Unrsty of Tchnology Shahrood Iran Emals:
More informationMECH321 Dynamics of Engineering System Week 4 (Chapter 6)
MH3 Dynamc of ngnrng Sytm Wk 4 (haptr 6). Bac lctrc crcut thor. Mathmatcal Modlng of Pav rcut 3. ompl mpdanc Approach 4. Mchancal lctrcal analogy 5. Modllng of Actv rcut: Opratonal Amplfr rcut Bac lctrc
More informationGPC From PeakSimple Data Acquisition
GPC From PakSmpl Data Acquston Introducton Th follong s an outln of ho PakSmpl data acquston softar/hardar can b usd to acqur and analyz (n conjuncton th an approprat spradsht) gl prmaton chromatography
More informationFakultät III Univ.-Prof. Dr. Jan Franke-Viebach
Unv.Prof. r. J. FrankVbach WS 067: Intrnatonal Economcs ( st xam prod) Unvrstät Sgn Fakultät III Unv.Prof. r. Jan FrankVbach Exam Intrnatonal Economcs Wntr Smstr 067 ( st Exam Prod) Avalabl tm: 60 mnuts
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article
Avalabl onln www.jocpr.com Journal of Chmcal and Pharmacutcal sarch, 4, 6(5):66-73 sarch Artcl SSN : 975-7384 CDN(SA) : JCPC5 Gap lmnt mthod and ts applcaton on forc analyss of tubng strngs Lu ka #, Song
More informationFEFF and Related Codes
FEFF and Rlatd Cods Anatoly Frnl Profssor Physcs Dpartmnt, Yshva Unvrsty, w Yor, USA Synchrotron Catalyss Consortum, Broohavn atonal Laboratory, USA www.yu.du/faculty/afrnl Anatoly.Frnl@yu.du FEFF: John
More informationChapter 6 Student Lecture Notes 6-1
Chaptr 6 Studnt Lctur Nots 6-1 Chaptr Goals QM353: Busnss Statstcs Chaptr 6 Goodnss-of-Ft Tsts and Contngncy Analyss Aftr compltng ths chaptr, you should b abl to: Us th ch-squar goodnss-of-ft tst to dtrmn
More informationON THE INTEGRAL INVARIANTS OF KINEMATICALLY GENERATED RULED SURFACES *
Iranan Journal of Scnc & Tchnology Transacton A ol 9 No A Prntd n Th Islamc Rpublc of Iran 5 Shraz Unvrsty ON TH INTGRAL INARIANTS OF KINMATICALLY GNRATD RULD SURFACS H B KARADAG AND S KLS Dpartmnt of
More informationA RELIABLE MATRIX CONVERTER FED INDUCTION MOTOR DRIVE SYSTEM BASED ON PARAMETER PLANE SYNTHESIS METHOD
Journal of Rlablty and Statstcal Studs; ISSN (Prnt): 0974-8024, (Onln): 2229-5666 ol. 9, Issu (206): 0-0 A RELIABLE MATRIX CONERTER FED INDUCTION MOTOR DRIE SYSTEM BASED ON PARAMETER PLANE SYNTHESIS METHOD
More informationLecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation
Lctur Rlc nutrnos mpratur at nutrno dcoupln and today Effctv dnracy factor Nutrno mass lmts Saha quaton Physcal Cosmoloy Lnt 005 Rlc Nutrnos Nutrnos ar wakly ntractn partcls (lptons),,,,,,, typcal ractons
More informationFolding of Regular CW-Complexes
Ald Mathmatcal Scncs, Vol. 6,, no. 83, 437-446 Foldng of Rgular CW-Comlxs E. M. El-Kholy and S N. Daoud,3. Dartmnt of Mathmatcs, Faculty of Scnc Tanta Unvrsty,Tanta,Egyt. Dartmnt of Mathmatcs, Faculty
More informationDevelopment and Application of the Finite Difference Time Domain (FDTD) Method
Dvlopmnt and Applcaton of th Fnt Dffrnc Tm Doman (FDTD) Mthod by W Fan Submttd n partal fulflmnt of th rqurmnts for th dgr of Doctor of Phlosophy at Dalhous Unvrsty Halfax, Nova Scota Novmbr, 017 Copyrght
More informationThree-dimensional multiple-relaxation-time lattice Boltzmann model. for convection heat transfer in porous media at the REV scale
Thr-dmnsonal multpl-rlaxaton-tm lattc Boltzmann modl for convcton hat transfr n porous mda at th REV scal Q. Lu Y.-L. H Ky Laboratory of Thrmo-Flud Scnc and Engnrng of Mnstry of Educaton School of Enrgy
More informationΕρωτήσεις και ασκησεις Κεφ. 10 (για μόρια) ΠΑΡΑΔΟΣΗ 29/11/2016. (d)
Ερωτήσεις και ασκησεις Κεφ 0 (για μόρια ΠΑΡΑΔΟΣΗ 9//06 Th coffcnt A of th van r Waals ntracton s: (a A r r / ( r r ( (c a a a a A r r / ( r r ( a a a a A r r / ( r r a a a a A r r / ( r r 4 a a a a 0 Th
More information6 Finite element methods for the Euler Bernoulli beam problem
6 Fnt lmnt mtods for t Eulr Brnoull bam problm Rak-54.3 Numrcal Mtods n Structural Engnrng Contnts. Modllng prncpls and boundary valu problms n ngnrng scncs. Enrgy mtods and basc D fnt lmnt mtods - bars/rods
More informationShape sensing of aerospace structures by coupling of isogeometric analysis and inverse finite element method
Shap snsng of arospac structurs by couplng of sogomtrc analyss and nvrs fnt lmnt mthod dnan Kfal and Erkan Otrkus Unvrsty of Strathclyd, 00 Montros Strt, Glasgow G4 0LZ, UK Ths papr prsnts a novl sogomtrc
More informationLaboratory associate professor Radu Damian Wednesday 12-14, II.12 odd weeks L 25% final grade P 25% final grade
ctur 8/9 C/, MDC Attndanc at mnmum 7 sssons (cours + laboratory) cturs- assocat profssor adu Daman Frday 9-,? III.34, II.3 E 5% fnal grad problms + (p attn. lct.) + (3 tsts) + (bonus actvty) 3p=+.5p all
More informationFakultät III Wirtschaftswissenschaften Univ.-Prof. Dr. Jan Franke-Viebach
Unvrstät Sgn Fakultät III Wrtschaftswssnschaftn Unv.-rof. Dr. Jan Frank-Vbach Exam Intrnatonal Fnancal Markts Summr Smstr 206 (2 nd Exam rod) Avalabl tm: 45 mnuts Soluton For your attnton:. las do not
More informationExercises for lectures 7 Steady state, tracking and disturbance rejection
Exrc for lctur 7 Stady tat, tracng and dturbanc rjcton Martn Hromčí Automatc control 06-3-7 Frquncy rpon drvaton Automatcé řízní - Kybrnta a robota W lad a nuodal nput gnal to th nput of th ytm, gvn by
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More information