AN EXPERIMENTAL INVESTIGATION OF PENETRATION FAILURE MODES IN COMPOSITE LAMINATES
|
|
- Melina York
- 5 years ago
- Views:
Transcription
1 16 TH INTRNATIONAL CONFRNC ON COMPOSIT MATRIALS AN XPRIMNTAL INVSTIGATION OF PNTRATION FAILUR MODS IN COMPOSIT LAMINATS Guiping Zho*, Zhengho Wng**, Jinxin Zhng**, Chongdu Cho*** *MO Key Lbortory for Strength nd Vibrtion, School of Aerospce, Xi n Jiotong University, P.R.Chin ** Deprtent of Civil ngineering, Xi n Jiotong University, P.R.Chin *** Deprtent of Mechnicl ngineering, Inh University, S. Kore Keywords: coposite terils, ipct, high velocity, energy bsorption, dge Abstrct The ipct tests were conducted with highvelocity gs cnnon. Three kinds of stcking sequence coposite lintes [(45/-45) 4 ] s, [(0/45/90/-45) ] s nd [(0/45/90/-45) 4 ] s were ipcted by projectile with velocity of /s. A lser velocity surveying pprtus ws eployed to esure the striking nd residul velocities of the projectiles. The process of ipct perfortion ws observed by tking photogrphs with high-speed fring cer to those trgets. And the ipct frcture behvior nd the energy bsorption property were nlyzed. The bllistic chrcteristics were represented by the experientil foruls which gve the reltionship between the striking nd residul velocities of the projectile. The experientil foruls cn estite the bllistic liit penetrtion velocities nd the residul velocities. 1 Introduction Fiber reinforced coposite terils re used extensively in ilitry nd civil pplictions due to their excellent echnicl properties like high specific strength, specific stiffness, resistnce to corrosion, incresed ftigue life ong others. However, they re susceptible to ipct dge due to their low toughness properties. Coposites tht re used in erospce nd lnd bsed structurl coponents re often subjected to high velocity ipct threts like broken engine prts, turbine bldes, frgents fro bobs, shells, ortrs, nd grendes. There re ny issues tht deterine the response of the coposite terils to ipct threts. These include: type nd volue frction of the fibers, linte thickness, boundry conditions, the trix syste, the ly-up sequence, geoetry, size nd the kinetic energy of the ipctor. A study on ipct response of coposite lintes concluded tht ipct perfortion is the ost iportnt dge stge in coposite lintes subjected to ipct loding. The reson is tht ipct chrcteristics nd echnicl properties degrdtion of coposite lintes rech criticl vlues when perfortion tkes plce [1-3]. In order to investigte ipct perfortion behvior of crbon fiber reinforced coposite, the ipct tests were conducted with high-velocity gs cnnon. The perfortion behviors were evluted by bsorbed energies during perfortion, orphologicl in situ observtions using high-speed fring cers nd postorte observtions. The bllistic chrcteristics were represented by given experientil forul, which gve the reltionship between the striking nd residul velocities of the projectile. Speciens nd Projectile T300 crbon fibers were used in king coposite linte speciens. The weight frction of fibers ws kept constnt t 60%. The trix of the speciens ws fro thero-setting epoxy resin. The cure of ll lintes ws done t roo teperture, 3 0 C, nd reltive huidity 50%. Three kinds of stcking sequence, [(45/-45) 4 ] s, [(0/45/90/-45) ] s nd
2 GUIPING ZHAO, Zhengho Wng, Jinxin Zhng, Chongdu Cho [(0/45/90/-45) 4 ] s were used in the test. The configurtion of the speciens is in plne re nd.4 (4.8) in thickness (Fig. 1). A steel bullet of weight 19.99g ws used s projectile in the test. The size of the bullet is shown in Fig.. chnged fro the ipct energy s to the residul energy r fter perforting specien. The energy bsorbed by the specien ws s - r =0.5(v s -v r ), where is the ss of bullet. After the experients, postorte orphologicl observtions were crried out on the speciens to investigte their filure odes. A seril of highspeed photogrphs of thick-0 specien ipcted t the velocity of 161 /s re shown in Fig. 5. Fig. 1. Diensions of specien (T is the thickness) Fig. 3. Schetic digr of ipct testing Fig.. Diensions of projectile 3 xperients The high velocity ipct tests were de by using gs cnnon. The specien ws ounted in clp supported boundry condition long its four edges. Fig. 3 shows schetic digr of the ipct perfortion experientl setup. Vrying the pressure of gs in the firing chber vried the ipct velocity. The ipct tests were designed to investigte the dge evolution t the bllistic liit. The bullet ccelerted fro 10 to 300 /s by light gs cnnon, ws ejected fro its luncher tube. It pssed velocity esureent device nd verticlly ipcted the center of the front surfce of the specien. A lser velocity surveying pprtus ws eployed to esure the striking velocity v s nd residul velocities v r of the projectile. A typicl signl output fro velocity esureent is shown in Fig. 4. A high-speed fring cer ws used for the in situ observtion of the ipct perfortion behvior. The kinetic energy of projectile ws Fig. 4. Typicl signl output fro velocity esureent Fig. 5. High-speed photogrphs of thick-0 ipcted t the velocity of 161 /s
3 An experientl investigtion of penetrtion filure odes in coposite lintes 4 Results nd Discussion 4.1 Filure Mode Figs show typicl iges for the front nd rer surfces of the speciens ipcted. For specien nottions, the first word, i.e. thin (thick), represented the thickness of.4 (4.8) speciens. The second nuber 0 stood for stcking sequence [(0/45/90/-45) ] s ([(0/45/90/-45) 4 ] s ) nd 45 for [(45/-45) 4 ] s while the lst nuber ws seril nuber of the speciens. The bllistic liit velocity denoted by v 50 is the threshold velocity t which 50% of the projectiles penetrte, nd 50% re rrested within the bounds of the speciens. We hve considered v 50 s the velocity t which the projectile hs lost eerged fro the rer surfce of the specien. Under this condition, the projectile reins ebedded within the specien, yet visible when viewed fro the rer surfce. Figs.6-8 re rebound cses for three kinds of stcking sequence speciens ipcted. This ens the bullet did not penetrte the speciens nd return to the front of the speciens fter ipct due to the ipct velocity is less thn bllistic liit speed. Figs.9-11 re insert or prtil penetrtion cses. The bullet velocity is t criticl velocity of penetrtions. And Figs 1-14 re coplete penetrtion. In this cse, residul velocity of the bullet cn be esured by the lser velocity surveying pprtus. In spite of siilr ipct energies, those frctured in significntly different filure odes. In both lintes Thin (Fig. 1) nd Thin-0-14 (Fig. 13), cler squre nd circulr hole were observed on the front surfce, respectively. For both lintes, however, delintion ll occurred on the rer surfce in fiber directions, i.e., in horizontl direction for Thin-0-14 nd in 45 0 direction for Thin Fig. 7. Postorte observtions on Thin-0-3 Fig. 8. Postorte observtions on Thick-0-1 Fig.9. Postorte observtions on Thin-45-4 Fig. 10. Postorte observtions on Thin-0-6 Fig. 6. Postorte observtions on Thin-45-3 Fig. 11. Postorte observtions on Thick-0-3 3
4 GUIPING ZHAO, Zhengho Wng, Jinxin Zhng, Chongdu Cho energy ong speciens. The thickness (Fig.16) nd stcking sequence (Fig.16b) of linted coposites re of iportnt roles tht ffected ipct perfortion behvior of the crbon fiber reinforced coposites. Fig. 1. Postorte observtions on Thin () [(0/45/90/-45) ] s nd [(0/45/90/-45) 4 ] s Fig. 13. Postorte observtions on Thin-0-14 Fig. 14. Postorte observtions on Thick Absorbed nergy Once coposite linte ws perforted, ny excess ipct energy would be retined s kinetic energy in the ipctor except tht n insignificnt ount would be converted into dditionl dge. The energy bsorption nd projected dge were xiized t this condition. Hence, perfortion threshold ws n iportnt preter in chrcterizing the ipct response of coposite lintes. The incident velocity, v s, ws esured using chronoscope. This ethod ws not cceptble for esuring the exit velocity, v r, s the projectiles exited the lintes t different ngles nd did not lwys pss through the nrrow perture of the chronoscope. A high speed cer ws lso used to esure the dynic delintion res nd to investigte the pth of the issile through the linte. Fig. 15 shows striking velocities nd bsorbed kinetic energies histogr. In Fig. 15, V s is striking velocity nd K is kinetic energy bsorbed. We could recognize cler differences in the bsorbed (b) [(0/45/90/-45) ] s nd [(45/-45) 4 ] s Fig. 15. Striking velocities nd bsorbed kinetic energies Fig.16. Kinetic energy bsorbed by the coposites A coprison of the effect of ipct velocity on the kinetic energy bsorbed by Thin-45, Thin-0 nd Thick-0 coposites is presented in Fig. 16. It is cler fro the experientl results tht Thick-0 coposites exhibit better projectile energy bsorption cpbility thn the Thin-45 nd Thin-0 coposites.
5 An experientl investigtion of penetrtion filure odes in coposite lintes The bsorbed kinetic energy,, the ipct nd the residul kinetic energies re linked by the eqution, 1 1 = vs v r (1) For the trget, when the shpe nd teril of the projectile re unchnged the bllistic liit velocity is constnt. In other words, when bullet ipcts trget t the bllistic liit velocity v 50, the kinetic energy of the bullet is bsorbed entirely by the trget. 1 1 = v50 () Beyond the bllistic liit, the bsorbed kinetic energy increses with incresing ipct velocity. The difference between nd 1 is ssued to be function of striking velocities of the bullet s following. 1 = f ( vs) (3) Bsed on the experientl results, the expression of f(v s ) cn be obtined experientilly s = f v = v +c (4) ( ) 1 s s where nd c re constnts. Different trgets hve different nd c. The forultion described the reltion of 和 v s cn be expressed by sttisticl dt fro experients. = + (5) 0.041vs = vs = vs (5b) (5c) qs.(5), (5b) nd (5c) re foruls of energy bsorption for coposite lintes Thin-45, Thin-0 nd Thick-0, respectively. Inserting qs. (5), (5b) nd (5c) into q. (1), n experientil forul predicting residul velocity cn be expressed s q.(6) for the linted coposites Thin-45, Thin-0 nd Thick-0, respectively vr = vs (6) v v r r = vs (6b) = vs (6c) 5 Sury Filure echniss nd odes of the crbon/epoxy coposite lintes were observed experientlly during high velocity ipct. The thickness nd stcking sequence of linted coposites re of iportnt roles tht ffected ipct perfortion behvior of the crbon fiber reinforced coposites. In spite of siilr ipct energies, coposite lintes frctured in significntly different filure odes. In stcking sequence [(0/45/90/-45) ] s ([(0/45/90/-45) 4 ] s ) nd [(45/-45) 4 ] s, cler circulr nd squre hole were observed on the front surfce, respectively. The velocity of bllistic liits for the crbon/epoxy lintes ipcted by the projectiles ws predicted using current experientil forul (6) by setting v r equl to zero. Acknowledgeents The uthors wish to thnk the Ntionl Bsic Reserch Progr of Chin through Grnt No. 006CB6010, the Ntionl Science Foundtion of Chin (Grnt No ) nd the Ntionl Science Foundtion (eronuticl joint fund) of Chin (Grnt No ) for finncil support of this work. References [1] Morye S., Hine P. nd et l. Modeling of the energy bsorption by polyer coposites upon bllistic ipct. Coposites Science nd Technology, Vol. 60, pp , 000. [] Liu D., Rju B. nd Dng X. Ipct Perfortion Resistnce of Linted nd Assebled Coposite Pltes. Int. J. Ipct ngineering, Vol. 4, pp , 000. [3] Mines R., Roch A. nd Jones N. High Velocity Perfortion Behvior of Polyer Coposite Lintes. Int. J. Ipct ngineering, Vol., pp ,
NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE MATERIALS
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE MATERIALS T. Prk 1, M. Ki 1, B. Jng 1, J. Lee 2, J. Prk 3 * 1 Grdute School,
More informationContact Analysis on Large Negative Clearance Four-point Contact Ball Bearing
Avilble online t www.sciencedirect.co rocedi ngineering 7 0 74 78 The Second SR Conference on ngineering Modelling nd Siultion CMS 0 Contct Anlysis on Lrge Negtive Clernce Four-point Contct Bll Bering
More informationInfluence of Mean Stress
Influence of Men tress Discussion hs been liited to copletely reversible stress thus fr. Mening = 0 However, there re ny instnces of dynic loding when en stress is nonzero. Men tresses Incresing en stress
More informationUNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY
UNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY YIFEI PAN, MEI WANG, AND YU YAN ABSTRACT We estblish soe uniqueness results ner 0 for ordinry differentil equtions of the
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationEFFECTIVE BUCKLING LENGTH OF COLUMNS IN SWAY FRAMEWORKS: COMPARISONS
IV EFFETIVE BUING ENGTH OF OUMN IN WAY FRAMEWOR: OMARION Ojectives In the present context, two different pproches re eployed to deterine the vlue the effective uckling length eff n c of colun n c out the
More informationApplications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More informationINVESTIGATION OF THERMAL PROPERTIES OF SOIL BY IMPULSE METHOD Juraj Veselský
THERMOPHYSICS 6 October 6 5 INVESTIGATION OF THERMAL PROPERTIES OF SOIL BY IMPULSE METHOD Jurj Veselský Fculty of Civil Engineering STU Brtislv, Rdlinského, 8 68 Brtislv Abstrct The therl properties of
More informationThe Atwood Machine OBJECTIVE INTRODUCTION APPARATUS THEORY
The Atwood Mchine OBJECTIVE To derive the ening of Newton's second lw of otion s it pplies to the Atwood chine. To explin how ss iblnce cn led to the ccelertion of the syste. To deterine the ccelertion
More informationDiscussion Question 1A P212, Week 1 P211 Review: 2-D Motion with Uniform Force
Discussion Question 1A P1, Week 1 P11 Review: -D otion with Unifor Force The thetics nd phsics of the proble below re siilr to probles ou will encounter in P1, where the force is due to the ction of n
More informationModeling of the impact on cylindrical composite shell as continuous patch loading
Interntionl Journl of Mechnicl & Mechtronics Engineering IJMME-IJENS Vol: No: 0 8 Modeling of the ipct on cylindricl coposite shell s continuous ptch loding * Frzin Firouzbdi, rn yob, M.R.rjndi, Soheil
More informationDiscussion Introduction P212, Week 1 The Scientist s Sixth Sense. Knowing what the answer will look like before you start.
Discussion Introduction P1, Week 1 The Scientist s Sith Sense As scientist or engineer, uch of your job will be perforing clcultions, nd using clcultions perfored by others. You ll be doing plenty of tht
More informationPHYS 601 HW3 Solution
3.1 Norl force using Lgrnge ultiplier Using the center of the hoop s origin, we will describe the position of the prticle with conventionl polr coordintes. The Lgrngin is therefore L = 1 2 ṙ2 + 1 2 r2
More informationProject A: Active Vibration Suppression of Lumped-Parameters Systems using Piezoelectric Inertial Actuators *
Project A: Active Vibrtion Suppression of Luped-Preters Systes using Piezoelectric Inertil Actutors * A dynic vibrtion bsorber referred to s ctive resontor bsorber (ARA) is considered here, while exploring
More informationECONOMETRIC THEORY. MODULE IV Lecture - 16 Predictions in Linear Regression Model
ECONOMETRIC THEORY MODULE IV Lecture - 16 Predictions in Liner Regression Model Dr. Shlbh Deprtent of Mthetics nd Sttistics Indin Institute of Technology Knpur Prediction of vlues of study vrible An iportnt
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More informationSEA based underwater noise radiation prediction method for ship s conception design
INTER-NOISE 016 SEA bsed underwter noise rdition prediction ethod for ship s conception design Xueren WANG 1 ; Chung WU ; Xuhong IAO 3 ; Kifu YE 4 1 Nvl Acdey of Arent, Chin Hrbin Engineering University,
More informationSOLUTIONS TO CONCEPTS CHAPTER 6
SOLUIONS O CONCEPS CHAPE 6 1. Let ss of the block ro the freebody digr, 0...(1) velocity Agin 0 (fro (1)) g 4 g 4/g 4/10 0.4 he co-efficient of kinetic friction between the block nd the plne is 0.4. Due
More informationMeasurement of Aerosol Parameters with Altitude by Using Two Wavelength Rotational Raman Signals
Journl of the Opticl Society of Kore Vol. 4 No. 3 Septeber 00 pp. -7 DOI: 0.3807/JOSK.00.4.3. Mesureent of Aerosol Preters with Altitude by Using Two Wvelength ottionl n Signls Ikng Song nd Yonggi Ki Deprtent
More informationREGULARITY OF NONLOCAL MINIMAL CONES IN DIMENSION 2
EGULAITY OF NONLOCAL MINIMAL CONES IN DIMENSION 2 OVIDIU SAVIN AND ENICO VALDINOCI Abstrct. We show tht the only nonlocl s-miniml cones in 2 re the trivil ones for ll s 0, 1). As consequence we obtin tht
More informationUNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY
UNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY YIFEI PAN, MEI WANG, AND YU YAN ABSTRACT We study ordinry differentil equtions of the type u n t = fut with initil conditions
More informationRel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited
More informationinteratomic distance
Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule
More informationPhys101 Lecture 4,5 Dynamics: Newton s Laws of Motion
Phys101 Lecture 4,5 Dynics: ewton s Lws of Motion Key points: ewton s second lw is vector eqution ction nd rection re cting on different objects ree-ody Digrs riction Inclines Ref: 4-1,2,3,4,5,6,7,8,9.
More informationFormulae For. Standard Formulae Of Integrals: x dx k, n 1. log. a dx a k. cosec x.cot xdx cosec. e dx e k. sec. ax dx ax k. 1 1 a x.
Forule For Stndrd Forule Of Integrls: u Integrl Clculus By OP Gupt [Indir Awrd Winner, +9-965 35 48] A B C D n n k, n n log k k log e e k k E sin cos k F cos sin G tn log sec k OR log cos k H cot log sin
More informationAN ORIGINAL METHOD FOR URBAN TRAFFIC NOISE PREDICTION
AN ORIGINA METHOD FOR URBAN TRAFFIC NOISE REDICTION Federico Rossi 1, Uberto Di Mtteo, Sofi Sioni 3 1 University of erugi Industril Engineering Deprtent oc. enti Bss 1, 05100, Terni, Itly frossi@unipg.it
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More informationProgressive failure analysis of compression-loaded composite flat panel with cutout
Interntionl Journl on Theoreticl nd Applied Reserch in Mechnicl Engineering (IJTARME) Progressive filure nlysis of compression-loded composite flt pnel with cutout 1 Guspir S. Mkndr, 2 N.K. Chhpkhne, 3
More informationSome History. Over the Next Several Days. Three Stages of Fatigue Failure. Identifying Fatigue Fractures. Three Approaches. Low vs.
Over the Next everl Dys Wht is Ftigue? Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis oe History Ril The cr xles ll-iportnt icrocrck Role of stress concentns ¾oet irplnes ¾ Unixil Fully
More informationThe Spring. Consider a spring, which we apply a force F A to either stretch it or compress it
The Spring Consider spring, which we pply force F A to either stretch it or copress it F A - unstretched -F A 0 F A k k is the spring constnt, units of N/, different for different terils, nuber of coils
More informationDYNAMIC EARTH PRESSURE SIMULATION BY SINGLE DEGREE OF FREEDOM SYSTEM
13 th World Conference on Erthque Engineering Vncouver, B.C., Cnd August 1-6, 2004 per No. 2663 DYNAMIC EARTH RESSURE SIMULATION BY SINGLE DEGREE OF FREEDOM SYSTEM Arsln GHAHRAMANI 1, Seyyed Ahmd ANVAR
More informationESTIMATION OF THE MODULUS OF ELASTICITY FOR DAM CONCRETE
ESTIMATION OF THE MODULUS OF ELASTICITY FOR DAM CONCRETE J. Vilrdell, A. Agudo, L. Agulló nd R. Gettu Universitt Politècnic de Ctluny, Deprtent of Construction Engineering, ETSECCPB-UPC, Edificio C-1,
More informationDETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE
Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING
More informationCHAPTER 5 Newton s Laws of Motion
CHAPTER 5 Newton s Lws of Motion We ve been lerning kinetics; describing otion without understnding wht the cuse of the otion ws. Now we re going to lern dynics!! Nno otor 103 PHYS - 1 Isc Newton (1642-1727)
More informationLab Based Analysis of Speed Control of DC Motor by Using Different Semiconductor Power Converters
Open Access Librry Journl Lb Bsed Anlysis of Speed Control of DC Motor by Using Different Seiconductor Power Converters Abdul Khlique Junejo, Ghull Mustf Bhutto, Munwr Ayz Meon, hsn Ali Buriro Deprtent
More informationMAC-solutions of the nonexistent solutions of mathematical physics
Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences - Finite Elements - Finite Volumes - Boundry Elements MAC-solutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE
More informationME 354 Tutorial, Week#11 Non-Reacting Mixtures Psychrometrics Applied to a Cooling Tower
ME 5 Tutoril, Week# Non-Recting Mixtures Psychroetrics Applied to Cooling Toer Wter exiting the condenser of poer plnt t 5 C enters cooling toer ith ss flo rte of 5000 kg/s. A stre of cooled ter is returned
More informationEffects of Micro-polar Fluids and the Tsann Roughness Model on Performance Characteristics of Two-lobe Bearings
Vol- Issue- 6 IJARIIE-ISSN(O)-95-96 Effects of Micro-polr Fluids nd the Tsnn Roughness Model on Perfornce Chrcteristics of Two-lobe Berings Rohollh Shfei, Mohd Hdi Shfei Mr., Engineering Deprtent, Yd University,
More informationPART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.
PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic
More informationA REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007
A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus
More informationChapter 14. Gas-Vapor Mixtures and Air-Conditioning. Study Guide in PowerPoint
Chpter 14 Gs-Vpor Mixtures nd Air-Conditioning Study Guide in PowerPoint to ccopny Therodynics: An Engineering Approch, 5th edition by Yunus A. Çengel nd Michel A. Boles We will be concerned with the ixture
More informationAn Introduction to Trigonometry
n Introduction to Trigonoetry First of ll, let s check out the right ngled tringle below. The LETTERS, B & C indicte the ngles nd the letters, b & c indicte the sides. c b It is iportnt to note tht side
More informationAMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE
AMPERE 2000 th 30 CONGRESS AMPERE on Mgnetic Resonnce nd Relted Phenomen Lison, Portugl, 23-2 July 2000 Under the uspices of The GROUPEMENT AMPERE Edited y: A.F. MARTINS, A.G. FEIO nd J.G. MOURA Sponsoring
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More informationKinetics of oriented crystallization of polymers in the linear stress-orientation range in the series expansion approach
express Polyer Letters Vol.1, No.4 (18) 48 Avilble online t www.expresspolylett.co https://doi.org/1.144/expresspolylett.18.9 Kinetics of oriented crystlliztion of polyers in the liner stress-orienttion
More informationA. Limits - L Hopital s Rule ( ) How to find it: Try and find limits by traditional methods (plugging in). If you get 0 0 or!!, apply C.! 1 6 C.
A. Limits - L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( x) lim where lim f x x! c g x ( ) = or lim f ( x) = limg( x) = ". ( ) x! c limg( x) = 0 x! c x! c
More informationOXFORD H i g h e r E d u c a t i o n Oxford University Press, All rights reserved.
Renshw: Mths for Econoics nswers to dditionl exercises Exercise.. Given: nd B 5 Find: () + B + B 7 8 (b) (c) (d) (e) B B B + B T B (where 8 B 6 B 6 8 B + B T denotes the trnspose of ) T 8 B 5 (f) (g) B
More informationSecond degree generalized gauss-seidel iteration method for solving linear system of equations. ABSTRACT
Ethiop. J. Sci. & Technol. 7( 5-, 0 5 Second degree generlized guss-seidel itertion ethod for solving liner syste of equtions Tesfye Keede Bhir Dr University, College of Science, Deprtent of Mthetics tk_ke@yhoo.co
More informationAPPLICATIONS OF THE DEFINITE INTEGRAL
APPLICATIONS OF THE DEFINITE INTEGRAL. Volume: Slicing, disks nd wshers.. Volumes by Slicing. Suppose solid object hs boundries extending from x =, to x = b, nd tht its cross-section in plne pssing through
More informationUCSD Phys 4A Intro Mechanics Winter 2016 Ch 4 Solutions
USD Phys 4 Intro Mechnics Winter 06 h 4 Solutions 0. () he 0.0 k box restin on the tble hs the free-body dir shown. Its weiht 0.0 k 9.80 s 96 N. Since the box is t rest, the net force on is the box ust
More informationFBR Neutronics: Breeding potential, Breeding Ratio, Breeding Gain and Doubling time
FBR eutronics: Breeding potentil, Breeding Rtio, Breeding Gin nd Doubling time K.S. Rjn Proessor, School o Chemicl & Biotechnology SASTRA University Joint Inititive o IITs nd IISc Funded by MHRD Pge 1
More information1 Bending of a beam with a rectangular section
1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure
More informationINVESTIGATION ON THE MODEL OF VORTEX-INDUCED
The Seventh Asi-Pcific Conference on Wind Engineering, November 8-1, 9, Tipei, Tiwn ABSTRACT INVESTIGATION ON THE MODEL OF VORTEX-INDUCED VIBRATIONS OF RECTANGULAR SUPER HIGH-RISE BUILDINGS Hi-Yng Wu 1
More informationAN EXACT SOLUTION OF MECHANICAL BUCKLING FOR FUNCTIONALLY GRADED MATERIAL BIMORPH CIRCULAR PLATES
Assocition of Metllurgicl Engineers of Serbi AMES Scientific pper UDC: 6.:66.7/.8 AN EXACT SOLUTION OF MECHANICAL BUCKLING FOR FUNCTIONALLY GRADED MATERIAL BIMORPH CIRCULAR PLATES Jfr Eskndri Jm, Mhmood
More informationStrength of materials II- Fatigue failure
Ftigue filure is one of the so clled cuultive liit sttes. In opposite to instntneous liit sttes, the cuultive ones re hereditry, they depend not only on the instntneous loding (stress-strin) stte of the
More informationApproximate Large Deflection Analysis of Thin Rectangular Plates under Distributed Lateral Line Load
Second Interntionl Conference on Advnces in Engineering nd Technolog Approite Lrge eflection Anlsis of Thin Rectngulr Pltes under istriuted Lterl Line Lod Alln Okodi, Y N. Zir, Jckson A. Mkli Grdute Student,
More informationEffects of peripheral drilling moment on delamination using special drill bits
journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment
More informationSteady Sate Analysis of Self-Excited Induction Generator using Phasor-Diagram Based Iterative Model
WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Stedy Ste nlysis of Self-xcited Induction Genertor using Phsor-Digr Bsed Itertive Model KNWJIT SINGH SNDHU & DHJ JOSHI Deprtent of lectricl
More informationBefore we can begin Ch. 3 on Radicals, we need to be familiar with perfect squares, cubes, etc. Try and do as many as you can without a calculator!!!
Nme: Algebr II Honors Pre-Chpter Homework Before we cn begin Ch on Rdicls, we need to be fmilir with perfect squres, cubes, etc Try nd do s mny s you cn without clcultor!!! n The nth root of n n Be ble
More informationThe heat budget of the atmosphere and the greenhouse effect
The het budget of the tmosphere nd the greenhouse effect 1. Solr rdition 1.1 Solr constnt The rdition coming from the sun is clled solr rdition (shortwve rdition). Most of the solr rdition is visible light
More information7-1: Zero and Negative Exponents
7-: Zero nd Negtive Exponents Objective: To siplify expressions involving zero nd negtive exponents Wr Up:.. ( ).. 7.. Investigting Zero nd Negtive Exponents: Coplete the tble. Write non-integers s frctions
More informationLABYRINTH SEALS DYNAMIC COEFFICIENTS AND CRITICAL SPEED RESEARCH BASED ON CHILDS MODEL
Abstrct LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL M Wensheng, Hung Hi, Feng Guoqun AVIC Shenyng Aeroengine eserch Institute, Shenyng, Chin Keywords:lbyrinth sels, dynmics
More informationThe Moving Center of Mass of a Leaking Bob
The Moving Center of Mss of Leking Bob rxiv:1002.956v1 [physics.pop-ph] 21 Feb 2010 P. Arun Deprtment of Electronics, S.G.T.B. Khls College University of Delhi, Delhi 110 007, Indi. Februry 2, 2010 Abstrct
More informationFATIGUE MECHANISM OF BOLTED JOINTS UNDER MULTI-AXIAL VIBRATION
Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure, Porto/Portugl 24-28 July 2016 Editors J.F. Silv Gomes nd S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6299 FATIGUE MECHANISM
More informationJob No. Sheet 1 of 8 Rev B. Made by IR Date Aug Checked by FH/NB Date Oct Revised by MEB Date April 2006
Job o. Sheet 1 of 8 Rev B 10, Route de Limours -78471 St Rémy Lès Chevreuse Cedex rnce Tel : 33 (0)1 30 85 5 00 x : 33 (0)1 30 5 75 38 CLCULTO SHEET Stinless Steel Vloristion Project Design Exmple 5 Welded
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More information1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt
More informationApplication of Exp-Function Method to. a Huxley Equation with Variable Coefficient *
Interntionl Mthemticl Forum, 4, 9, no., 7-3 Appliction of Exp-Function Method to Huxley Eqution with Vrible Coefficient * Li Yo, Lin Wng nd Xin-Wei Zhou. Deprtment of Mthemtics, Kunming College Kunming,Yunnn,
More informationEmission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract
Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More informationExam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B
PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere
More informationThe graphs of Rational Functions
Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior
More informationESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability
ESCI 343 Atmospheric Dynmics II Lesson 14 Inertil/slntwise Instbility Reference: An Introduction to Dynmic Meteorology (3 rd edition), J.R. Holton Atmosphere-Ocen Dynmics, A.E. Gill Mesoscle Meteorology
More information4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
More informationRecitation 3: More Applications of the Derivative
Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationragsdale (zdr82) HW2 ditmire (58335) 1
rgsdle (zdr82) HW2 ditmire (58335) This print-out should hve 22 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 00 0.0 points A chrge of 8. µc
More informationMotion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons
n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationON THE THEORETICAL FRACTURE STATISTICS OF THE HERTZ INDENTATION TEST
ON THE THEORETICA FRACTURE STATISTICS OF THE HERTZ INDENTATION TEST Gerrdo Díz R. () nd Pblo Kittl D. () () Deprtento de Cienci de los Mteriles, Fcultd de Ciencis Físics y Mteátics, Universidd de Chile,
More informationhttp:dx.doi.org1.21611qirt.1994.17 Infrred polriztion thermometry using n imging rdiometer by BALFOUR l. S. * *EORD, Technion Reserch & Development Foundtion Ltd, Hif 32, Isrel. Abstrct This pper describes
More informationDynamics of an Inertially Driven Robot
Vibrtions in Physicl Systems 018, 9, 01803 (1 of 9) Dynmics of n Inertilly Driven Robot Pweł FRITZKOWSKI Institute of Applied Mechnics, Poznn University of Technology, ul. Jn Pwł II 4, 60-965 Poznn, pwel.itzkowski@put.poznn.pl
More informationVorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen
Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:
More informationSet up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass
Applied Physics Reserch; Vol. 5, No. 1; 013 ISSN 1916-9639 E-ISSN 1916-9647 Published by Cndin Center of Science nd Eduction Set up Invrible Axiom of orce Equilibrium nd Solve Problems bout Trnsformtion
More informationSpace Curves. Recall the parametric equations of a curve in xy-plane and compare them with parametric equations of a curve in space.
Clculus 3 Li Vs Spce Curves Recll the prmetric equtions of curve in xy-plne nd compre them with prmetric equtions of curve in spce. Prmetric curve in plne x = x(t) y = y(t) Prmetric curve in spce x = x(t)
More informationChapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd
Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction
More informationModal Density of Honeycomb Sandwich Composite Cylindrical Shells Considering Transverse Shear Deformation
Modl Density of Honeycob Sndwich Coposite Cylindricl Shells Considering Trnsverse Sher Defortion S. Josephine Kelvin Florence nd K. Renji ISRO Stellite Center, ISRO Vinpur Post, Bnglore, Indi 567. K. Subrnin
More informationPressure Wave Analysis of a Cylindrical Drum
Pressure Wve Anlysis of Cylindricl Drum Chris Clrk, Brin Anderson, Brin Thoms, nd Josh Symonds Deprtment of Mthemtics The University of Rochester, Rochester, NY 4627 (Dted: December, 24 In this pper, hypotheticl
More informationHomework: 5, 9, 19, 25, 31, 34, 39 (p )
Hoework: 5, 9, 19, 5, 31, 34, 39 (p 130-134) 5. A 3.0 kg block is initilly t rest on horizontl surfce. A force of gnitude 6.0 nd erticl force P re then pplied to the block. The coefficients of friction
More informationVISION BASED SURFACE ROUGHNESS EVALUATION OF GROUND COMPONENTS USING WAVELET TRANSFORM AND NEURAL NETWORK
XVIII IMEKO WORLD CONGRESS Metrology for Sustinble Developent Septeber, 7 22, 26, Rio de Jneiro, Brzil VISION BASED SURFACE ROUGHNESS EVALUATION OF GROUND COMPONENTS USING WAVELET TRANSFORM AND NEURAL
More informationIn-Class Problems 2 and 3: Projectile Motion Solutions. In-Class Problem 2: Throwing a Stone Down a Hill
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 In-Clss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the
More informationPhysics Dynamics: Atwood Machine
plce of ind F A C U L Y O F E D U C A I O N Deprtent of Curriculu nd Pedoy Physics Dynics: Atwood Mchine Science nd Mthetics Eduction Reserch Group Supported by UBC echin nd Lernin Enhnceent Fund 0-04
More informationP 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)
1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this
More informationDetermination of the activation energy of silicone rubbers using different kinetic analysis methods
Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN Jen-Clude FETO-ST Institute / Applied echnics Deprtment, 2 rue
More informationStuff You Need to Know From Calculus
Stuff You Need to Know From Clculus For the first time in the semester, the stuff we re doing is finlly going to look like clculus (with vector slnt, of course). This mens tht in order to succeed, you
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
More informationPHYS 705: Classical Mechanics. Small Oscillations: Example A Linear Triatomic Molecule
PHYS 75: Clssicl echnics Sll Oscilltions: Exple A Liner Tritoic olecule A Liner Tritoic olecule x b b x x3 x Experientlly, one ight be interested in the rdition resulted fro the intrinsic oscilltion odes
More information4. Calculus of Variations
4. Clculus of Vritions Introduction - Typicl Problems The clculus of vritions generlises the theory of mxim nd minim. Exmple (): Shortest distnce between two points. On given surfce (e.g. plne), nd the
More informationConducting Ellipsoid and Circular Disk
1 Problem Conducting Ellipsoid nd Circulr Disk Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 (September 1, 00) Show tht the surfce chrge density σ on conducting ellipsoid,
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More information