RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revision E W( )
|
|
- Margaret Bond
- 6 years ago
- Views:
Transcription
1 RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revisio E B To Ivie Eil: o@viiod.co Apil, 3 Viles A pliude coefficie E k leg id ple siffess fco elsic odulus ple ickess veue ple ss edig oe,, u, v ode ue idices Poisso's io ss pe volue elive displcee, ou-of-ple olied ode spe picipio fco eciio feuec ul feuec odl dpig () W( ) elive displcee, ou-of-ple se ipu cceleio Fouie sfo of se ipu cceleio (,, ) Relive displcee U (,, ) Asolue Acceleio
2 Ioducio Coside e ecgul ple i Figue. Assue i is sipl-suppoed log ec edge. Y X Figue. Nol odes Alsis Noe e ple siffess fco is give E 3 () Te goveig euio of oio is () Assue oic espose. (,,) (, )ep( j) (3)
3 3 ) ep( j ) ep( j () (5) Te oud codiios e (,), (,) fo =, (6) ) (,, ) (, fo =, (7) Assue e folloig displcee fucio ic sisfies e oud codiios, ee c is pliude coefficie d e ieges. si A si (,) (8) Te pil deives e si cos A (9) si si A () si cos A ()
4 si si A () Siill, si si A (3) Also, si si A () si si A si si A (5) (6) (7) (8)
5 5 (9) Noe e ve ues e / k () / k () Nolied ode Spes Te ode spes e olied suc d d (,) () si A si (3) d d si A si () d d si si A (5) d d cos cos A (6)
6 (7) cos si d A (8) cos d A si A (9) A (3) A (3) A A (3) (33) (3) A (35) Noe A is cosideed o e diesioless, loug e uis us e cosise ii e lsis. 6
7 7 Picipio Fcos Te ss desi is cos. Tus (,)d d (36) d d si A si (37) d d si si A (38) d d si si (39) d si cos () d si cos () cos cos () cos cos (3)
8 cos cos () cos cos (5) Effecive odl ss (, )d d eff, (6) )d d (, Te odes spes e olied suc Tus (,)dd (7) eff, )d d (, (8) eff, (9) 8
9 9 Respose o Bse Eciio Te foced espose euio fo ple i se oio is (5) ee is se eciio. Te e o e ig-d-side is e ieil foce pe ui e. Te displcee is T () ) (,,) (, (5) si si (,) (5) (53)
10 T () ) (, T () ) (, T () ) (, T () ) (, (5)
11 T () ) (, T () ) (, T () ) (, T () ) (, (55) si si (,) (56) si si ) (, (57) ) (, ) (, (58) si si ) (, (59)
12 si si ) (, (6) ) (, ) (, (6) si si ) (, (6) si si ) (, (63) ) (, ) (, (6) T () ) (, T () ) (, T () ) (, T () ) (, (65)
13 3 T () ) (, T () ) (, (66) T () ) (, T () ) (, (67) T () ) (, T () ) (, (68)
14 ulipl ec e uv(, ). uv(, ) (, ) T () uv(, ) (, ) T () uv(, ) (69) Iege i espec o sufce e. uv (, ) (, ) T () dd uv (, ) (, ) T () dd uv (, ) dd (7)
15 5 )d d ) (, uv (, T () )d d ) (, uv (, T () ) uv (, (7) Te eigevecos e oogol suc uv (,) (,)d d fo u o v (7) uv (,) (,)dd fo u = d v = (73)
16 T () T () (, )d d (7) T () T () (, )d d (75) d d T () d T () (76) d Add dpig e. d d T () d T () T () (77) d T () T () T () () (78) 6
17 Te folloig soluio is ke fo Refeece 3. Te sfe fucio is (, ) H (,, ) (79) ( ) j H(,, ) (,, ) W (8) Te elive displcee is (, ) (,, ) W (8) ( ) j (,, ) si si W (8) ( ) j Te elive veloci is (, ) (,, ) j W ( (83) ) j si si (,, ) j W ( (8) ) j 7
18 Te solue cceleio is (, ) U (,, ) W (85) ( ) j si si U (,, ) W (86) ( ) j Te edig oes e,,,, (87),,,, (88) Le ẑ e e disce fo e ceelie i e veicl is. Te edig sesses fo Refeece e E ẑ,,,, (89) 8
19 E ẑ W,, (, ) ( ) j (9) E ẑ,, W si si ( ) j (9) E ẑ,,,, (9) E ẑ W,, (, ) ( ) j (93) E ẑ,, W si si ( ) j (9) 9
20 E ẑ,,,, (95) (, ) E ẑ W (96) ( ) j,, E ẑ W,, cos cos ( ) j (97) Refeeces. ve Seieg, Viio Alsis fo Elecoic Euipe, Wile-Iesciece, Ne Yok, Au W. Leiss, Viio of Ples, NASA SP-6, Niol Aeouics d Spce Adiisio, Wsigo.C., T. Ivie, Sed-Se Viio Respose of Cileve Be Sujeced o Bse Eciio Revisio A, Viiod, 9.. J.S. Ro, ics of Ples, Nos, Ne eli, 999.
21 APPENIX A Nol Sess-Veloci Reliosip Te iu solue spil sesses fo give ode, e, E ẑ W ( ) j (A-), E ẑ W ( ) j (A-) Te iu spil veloci fo give ode, is W (A-3) ( ) j Tus E ẑ, (A-) E ẑ, (A-5)
Physics 232 Exam I Feb. 14, 2005
Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..
More informationPhysics 232 Exam I Feb. 13, 2006
Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.
More informationEE757 Numerical Techniques in Electromagnetics Lecture 9
EE757 uericl Techiques i Elecroeics Lecure 9 EE757 06 Dr. Mohed Bkr Diereil Equios Vs. Ierl Equios Ierl equios ke severl ors e.. b K d b K d Mos diereil equios c be epressed s ierl equios e.. b F d d /
More informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationPhysics 232 Exam II Mar. 28, 2005
Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ
More informationOH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
More information176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
More informationDuration Notes 1. To motivate this measure, observe that the duration may also be expressed as. a a T a
Duio Noes Mculy defied he duio of sse i 938. 2 Le he sem of pymes cosiuig he sse be,,..., d le /( + ) deoe he discou fco. he Mculy's defiiio of he duio of he sse is 3 2 D + 2 2 +... + 2 + + + + 2... o
More informationBy Tom Irvine December 27,
THE STEADY-STATE VIBRATION RESPONSE OF A BAFFED PATE SIMPY-SUPPORTED ON A SIDES SUBJECTED TO RANDOM PRESSURE PANE WAVE EXCITATION AT OBIQUE INCIDENCE Revisi A By T Irvie Deceber 7, 04 Eil: @vibrid.c The
More informationON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES
M aheaical I equaliies & A pplicaios Volue 19, Nube 1 (216), 287 296 doi:1.7153/ia-19-21 ON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES W. ŁENSKI AND B. SZAL (Couicaed by
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More informationElectromechanical System Dynamics, energy Conversion, and Electromechanical Analogies. Modeling of Dynamic Systems
Elecroecicl Syse Dyics, eergy Coersio, d Elecroecicl Alogies Modelig of Dyic Syses Modelig of dyic syses y e doe i seerl wys: Use e sdrd equio of oio Newo s Lw for ecicl syses Use circuis eores O s lw
More informationOne of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of
Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo
More informationI M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o
I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l
More informationTHIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
More informationTechnical Vibration - text 2 - forced vibration, rotational vibration
Technicl Viion - e - foced viion, oionl viion 4. oced viion, viion unde he consn eenl foce The viion unde he eenl foce. eenl The quesion is if he eenl foce e is consn o vying. If vying, wh is he foce funcion.
More informationIJRET: International Journal of Research in Engineering and Technology eissn: pissn:
IJRE: Iiol Joul o Rh i Eii d holo I: 39-63 I: 3-738 VRIE OF IME O RERUIME FOR ILE RDE MOWER EM WI DIFFERE EO FOR EXI D WO E OF DEIIO VI WO REOLD IVOLVI WO OMOE. Rvihd. iiv i oo i Mhi R Eii oll RM ROU ih
More informationSoftware Process Models there are many process model s in th e li t e ra t u re, s om e a r e prescriptions and some are descriptions you need to mode
Unit 2 : Software Process O b j ec t i ve This unit introduces software systems engineering through a discussion of software processes and their principal characteristics. In order to achieve the desireable
More informationSupplementary Information
Supplemeay Ifomaio No-ivasive, asie deemiaio of he coe empeaue of a hea-geeaig solid body Dea Ahoy, Daipaya Saka, Aku Jai * Mechaical ad Aeospace Egieeig Depame Uivesiy of Texas a Aligo, Aligo, TX, USA.
More informationSpectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
More informationVIBRATIONAL CHARACTERISTICS MODELING OF A PZT5A MEMS RESONATOR DISC METALLIZED WITH ALTERNATING ELECTRICAL SOURCE
Ieiol Joul of echicl d Poducio gieeig esech d evelope IJP ISSP: 49-689; ISS: 49-8 Vol. 8 Issue Ap 8 5-48 TJPC Pv. Ld. VIBATIOAL CHAACTISTICS OLIG OF A PZT5A S SOATO ISC TALLIZ WITH ALTATIG LCTICAL SOUC
More informationOptimal Estimator for a Sample Set with Response Error. Ed Stanek
Optial Estiator for a Saple Set wit Respose Error Ed Staek Itroductio We develop a optial estiator siilar to te FP estiator wit respose error tat was cosidered i c08ed63doc Te first 6 pages of tis docuet
More informationThe Central Limit Theorems for Sums of Powers of Function of Independent Random Variables
ScieceAsia 8 () : 55-6 The Ceal Limi Theoems fo Sums of Poes of Fucio of Idepede Radom Vaiables K Laipapo a ad K Neammaee b a Depame of Mahemaics Walailak Uivesiy Nakho Si Thammaa 86 Thailad b Depame of
More informationApplications of force vibration. Rotating unbalance Base excitation Vibration measurement devices
Applicaios of foce viaio Roaig ualace Base exciaio Viaio easuee devices Roaig ualace 1 Roaig ualace: Viaio caused y iegulaiies i he disiuio of he ass i he oaig copoe. Roaig ualace 0 FBD 1 FBD x x 0 e 0
More informationC5 PRO Ignition Kit. Instruction manual with visual guide for Magneto style distributor kit
C5 PRO Ignition Kit Instruction manual with visual guide for Magneto style distributor kit You kit i ludes: elf o tai ed Ig iio odule a d housi g ith o e i gle o Dual to e oils depe di g o appli aio pa
More informationChapter 6 - Work and Energy
Caper 6 - Work ad Eergy Rosedo Pysics 1-B Eploraory Aciviy Usig your book or e iere aswer e ollowig quesios: How is work doe? Deie work, joule, eergy, poeial ad kieic eergy. How does e work doe o a objec
More informationGeneralized Fibonacci-Type Sequence and its Properties
Geelized Fibocci-Type Sequece d is Popeies Ompsh Sihwl shw Vys Devshi Tuoil Keshv Kuj Mdsu (MP Idi Resech Schol Fculy of Sciece Pcific Acdemy of Highe Educio d Resech Uivesiy Udipu (Rj Absc: The Fibocci
More informationWELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU MATHEMATICS. FORMULA BOOKLET (New Specification)
WELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU Gl Ciic o Eucio Avc Lvl/Avc Susii Tssgi Asg Giol So Uwch/Uwch Gol MATHEMATICS FORMULA BOOKLET Nw Spciicio Issu 004 Msuio Suc o sph 4π A o cuv suc
More informationLIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR
Reseh d ouiios i heis d hei Siees Vo. Issue Pges -46 ISSN 9-699 Puished Oie o Deee 7 Joi Adei Pess h://oideiess.e IPSHITZ ESTIATES FOR UTIINEAR OUTATOR OF ARINKIEWIZ OPERATOR DAZHAO HEN Dee o Siee d Ioio
More informationCHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE
Fameal Joal of Mahemaic a Mahemaical Sciece Vol. 7 Ie 07 Page 5- Thi pape i aailable olie a hp://.fi.com/ Pblihe olie Jaa 0 07 CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE Caolo
More informationYamaha Virago V-twin. Instruction manual with visual guide for Yamaha XV
Yamaha Virago V-twin Instruction manual with visual guide for Yamaha XV700-1100 PHOTO HOWN FOR ILLU TRATION PURPO E ONLY We o use a o e pie e housi g a d s all si gle to e oils fo i p o ed ope aio. If
More informationINVERSE HEAT CONDUCTION PROBLEM IN A THIN CIRCULAR PLATE AND ITS THERMAL DEFLECTION
INVERSE HEA CONDUCION PROBLEM IN A HIN CIRCULAR PLAE AND IS HERMAL DEFLECION G G G G A ik C DsukG ABSRAC A ivs obl of si coducio i i fii cicul l wi giv u disibuio o iio sufc of i cicul l big fucio of bo
More informationElectrostatic/magnetostatic forces
Eecsc/gnesc ces spes ppc: eneg e ec eneg ce (vec) ve (vec) en ( eneg ) ( snce) ne s cn gve e O ce (n pessue) u cn en snge sp cne s pe e ce spe epe: pe pes eecsc: ppe vge gnesc: cuen I Den. Nekk 00, s upe
More informationAgenda Rationale for ETG S eek ing I d eas ETG fram ew ork and res u lts 2
Internal Innovation @ C is c o 2 0 0 6 C i s c o S y s t e m s, I n c. A l l r i g h t s r e s e r v e d. C i s c o C o n f i d e n t i a l 1 Agenda Rationale for ETG S eek ing I d eas ETG fram ew ork
More informationME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
More informationDangote Flour Mills Plc
SUMMARY OF OFFER Opening Date 6 th September 27 Closing Date 27 th September 27 Shares on Offer 1.25bn Ord. Shares of 5k each Offer Price Offer Size Market Cap (Post Offer) Minimum Offer N15. per share
More informationMath 2414 Homework Set 7 Solutions 10 Points
Mah Homework Se 7 Soluios 0 Pois #. ( ps) Firs verify ha we ca use he iegral es. The erms are clearly posiive (he epoeial is always posiive ad + is posiive if >, which i is i his case). For decreasig we
More informationc. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f
Essential Skills Chapter f ( x + h) f ( x ). Simplifying the difference quotient Section. h f ( x + h) f ( x ) Example: For f ( x) = 4x 4 x, find and simplify completely. h Answer: 4 8x 4 h. Finding the
More informationK owi g yourself is the begi i g of all wisdo.
I t odu tio K owi g yourself is the begi i g of all wisdo. A istotle Why You Need Insight Whe is the last ti e ou a e e e taki g ti e to thi k a out ou life, ou alues, ou d ea s o ou pu pose i ei g o this
More informationUse precise language and domain-specific vocabulary to inform about or explain the topic. CCSS.ELA-LITERACY.WHST D
Lesson eight What are characteristics of chemical reactions? Science Constructing Explanations, Engaging in Argument and Obtaining, Evaluating, and Communicating Information ENGLISH LANGUAGE ARTS Reading
More informationDETAIL MEASURE EVALUATE
MEASURE EVALUATE B I M E q u i t y BIM Workflow Guide MEASURE EVALUATE Introduction We o e to ook 2 i t e BIM Workflow Guide i uide wi tr i you i re ti ore det i ed ode d do u e t tio u i r i d riou dd
More informationFBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf
.4 Base Exiaio Ipoa lass of vibaio aalysis Peveig exiaios fo passig fo a vibaig base hough is ou io a suue Vibaio isolaio Vibaios i you a Saellie opeaio Dis dives, e. FBD of SDOF Base Exiaio x() y() Syse
More information... (1) Thus: ... (2) Where f(x + y) is a function to be found, in here we assume symmetry and the moments are a function on x + y only.
Ec d Numeicl Soluio fo ge eflecio of Elsic No-Pismic Ples B Fid A. Choue P.E. S.E. 7 Fid A. Choue ll ighs eseved Geel Soluio fo smme Cse I: Sig ih Eq. 7 d 8 9 d Eq 8 fom Theo of Ples d Shells Timosheo
More informationThe Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues
Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co
More informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationTable of C on t en t s Global Campus 21 in N umbe r s R e g ional Capac it y D e v e lopme nt in E-L e ar ning Structure a n d C o m p o n en ts R ea
G Blended L ea r ni ng P r o g r a m R eg i o na l C a p a c i t y D ev elo p m ent i n E -L ea r ni ng H R K C r o s s o r d e r u c a t i o n a n d v e l o p m e n t C o p e r a t i o n 3 0 6 0 7 0 5
More informationLinear Time Invariant Systems
1 Liear Time Ivaria Sysems Oulie We will show ha he oupu equals he covoluio bewee he ipu ad he ui impulse respose: sysem for a discree-ime, for a coiuous-ime sysdem, y x h y x h 2 Discree Time LTI Sysems
More information). So the estimators mainly considered here are linear
6 Ioic Ecooică (4/7 Moe Geel Cedibiliy Models Vigii ATANASIU Dee o Mheics Acdey o Ecooic Sudies e-il: vigii_siu@yhooco This couicio gives soe exesios o he oigil Bühl odel The e is devoed o sei-lie cedibiliy
More informationON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID
wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we
More informationCompressive modulus of adhesive bonded rubber block
Songklnkin J. Sci. Tecnol. 0 (, -5, M. - Ap. 008 p://www.sjs.ps.c. Oiginl Aicle Compessive modls of desive bonded bbe block Coeny Decwykl nd Wiiy Tongng * Depmen of Mecnicl Engineeing, Fcly of Engineeing,
More informationUse precise language and domain-specific vocabulary to inform about or explain the topic. CCSS.ELA-LITERACY.WHST D
Lesson seven What is a chemical reaction? Science Constructing Explanations, Engaging in Argument and Obtaining, Evaluating, and Communicating Information ENGLISH LANGUAGE ARTS Reading Informational Text,
More informationSuggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)
per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.
More informationS, we call the base curve and the director curve. The straight lines
Developable Ruled Sufaces wih Daboux Fame i iowsi -Space Sezai KIZILTUĞ, Ali ÇAKAK ahemaics Depame, Faculy of As ad Sciece, Ezica Uivesiy, Ezica, Tuey ahemaics Depame, Faculy of Sciece, Aau Uivesiy, Ezuum,
More informationLower Bounds for Cover-Free Families
Loe Bouds fo Cove-Fee Families Ali Z. Abdi Covet of Nazaeth High School Gade, Abas 7, Haifa Nade H. Bshouty Dept. of Compute Sciece Techio, Haifa, 3000 Apil, 05 Abstact Let F be a set of blocks of a t-set
More informationExecutive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
More informationAn Example file... log.txt
# ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationDegree of Approximation of Fourier Series
Ieaioal Mahemaical Foum Vol. 9 4 o. 9 49-47 HIARI Ld www.m-hiai.com h://d.doi.og/.988/im.4.49 Degee o Aoimaio o Fouie Seies by N E Meas B. P. Padhy U.. Misa Maheda Misa 3 ad Saosh uma Naya 4 Deame o Mahemaics
More informationTHIS PAGE DECLASSIFIED IAW EO 12958
THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationI N A C O M P L E X W O R L D
IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e
More informationHyperbolic Heat Equation as Mathematical Model for Steel Quenching of L-shape and T-shape Samples, Direct and Inverse Problems
SEAS RANSACIONS o HEA MASS RANSER Bos M Be As Bs Hpeo He Eo s Me Moe o See Qe o L-spe -spe Spes De Iese Poes ABIA BOBINSKA o Pss Mes es o L Ze See 8 L R LAIA e@o MARARIA BIKE ANDRIS BIKIS Ise o Mes Cope
More informationLesson Ten. What role does energy play in chemical reactions? Grade 8. Science. 90 minutes ENGLISH LANGUAGE ARTS
Lesson Ten What role does energy play in chemical reactions? Science Asking Questions, Developing Models, Investigating, Analyzing Data and Obtaining, Evaluating, and Communicating Information ENGLISH
More informationSB4223E00 Nov Schematic. Lift Trucks Electric System D110S-5, D130S-5, D160S-5
E00 Nov.00 chematic ift Trucks Electric ystem D0, D0, D0 ETIEE for Engine tart & harging ystem / IITION WIT / 0 / / / / Warning amp GE / 0 FUE OX / X ED D D D D EP EP EP F N INTEOK EY 0 a / / D X D D IUIT
More informationOutline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem
adial diffsio eqaio Febay 4 9 Diffsio Eqaios i ylidical oodiaes ay aeo Mechaical Egieeig 5B Seia i Egieeig Aalysis Febay 4, 9 Olie eview las class Gadie ad covecio boday codiio Diffsio eqaio i adial coodiaes
More informationAttachment H. Housing Opportunity Zones
umbodt ounty enea an 2014 ousing ement ttachment ousing ppotunity Zones ttachment - 1 o V I U V V - V cata ipot U se uk e U 0.25 0.5 ies V I V I V II V k F I I V V V V V V F VI I Z V I V JI QUI U I ve
More informationLinear System Theory
Naioal Tsig Hua Uiversiy Dearme of Power Mechaical Egieerig Mid-Term Eamiaio 3 November 11.5 Hours Liear Sysem Theory (Secio B o Secio E) [11PME 51] This aer coais eigh quesios You may aswer he quesios
More informationInverse Thermoelastic Problem of Semi-Infinite Circular Beam
iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN 78-54 v holic Pobl o Si-ii Cicul B Shlu D Bi M. S. Wbh d N. W. Khobd 3 D o Mhic Godw Uiviy Gdchioli M.S di D o Mhic Svody Mhvidyly Sidwhi
More informationWhat Is Our Relationship with the Earth?
What Is Our Relationship with the Earth? THIS CHANGES EVERYTHING Official Book & Film Study Guide 25 Learning Objectives Students will: ite de itio o t e co ce t o e t acti i m a d e e e atio a ed o te
More informationMODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC
More informationX-Ray Notes, Part III
oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel
More informationBeechwood Music Department Staff
Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d
More informationChapter 1 Electromagnetic Field Theory
hpe ecgeic Fie The - ecic Fie ecic Dipe Gu w f : S iegece he ε = 6 fee pce. F q fie pi q q 9 F/ i he. ue e f icee chge: qk k k k ue uce ρ Sufce uce ρ S ie uce ρ qq qq g. Shw h u w F whee. q Pf F q S q
More informationDerivation of the Metal-Semiconductor Junction Current
.4.4. Derivio of e Mel-Seiouor uio Curre.4.4.1.Derivio of e iffuio urre We r fro e epreio for e ol urre e iegre i over e wi of e epleio regio: q( µ + D (.4.11 wi be rewrie b uig -/ uliplig bo ie of e equio
More informationF.Y. Diploma : Sem. II [CE/CR/CS] Applied Mathematics
F.Y. Diplom : Sem. II [CE/CR/CS] Applied Mhemics Prelim Quesio Pper Soluio Q. Aemp y FIVE of he followig : [0] Q. () Defie Eve d odd fucios. [] As.: A fucio f() is sid o e eve fucio if f() f() A fucio
More information_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9
C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n
More informationLEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016
CSSRM CNTCT PRGRMME (cdeic Sessio : 05-06) EDER & CIEVER CURSE PSE : M,M,MC, MD, ME,MF, MG, M, MI, MJ, MZ,MZ & MZC Tes Type : MJR TRGET : PRE-MEDIC 06 Tes Per : IPMT TEST DTE : 07-04 - 06 TEST SYUS : SYUS
More informationM Line Card Redundancy with Y-Cab l es Seamless Line Card Failover Solu t ion f or Line Card H ardw or Sof t w are Failu res are Leverages hardware Y-
Line Card Redundancy with Y-Cab l es Technical Overview 1 M Line Card Redundancy with Y-Cab l es Seamless Line Card Failover Solu t ion f or Line Card H ardw or Sof t w are Failu res are Leverages hardware
More informationGet Started on CreateSpace
{paperback self publishing process} Account Set Up Go to CreateSpace.com Click Sign up Fill out Create Account info fields * Under What type of media you are considering punlishing?, you may want to choose
More informationChapter4 Time Domain Analysis of Control System
Chpr4 im Domi Alyi of Corol Sym Rouh biliy cririo Sdy rror ri rpo of h fir-ordr ym ri rpo of h cod-ordr ym im domi prformc pcificio h rliohip bw h prformc pcificio d ym prmr ri rpo of highr-ordr ym Dfiiio
More informationOn Almost Increasing Sequences For Generalized Absolute Summability
Joul of Applied Mthetic & Bioifotic, ol., o., 0, 43-50 ISSN: 79-660 (pit), 79-6939 (olie) Itetiol Scietific Pe, 0 O Alot Iceig Sequece Fo Geelized Abolute Subility W.. Suli Abtct A geel eult coceig bolute
More informationExtension of Hardy Inequality on Weighted Sequence Spaces
Jourl of Scieces Islic Reublic of Ir 20(2): 59-66 (2009) Uiversiy of ehr ISS 06-04 h://sciecesucir Eesio of Hrdy Iequliy o Weighed Sequece Sces R Lshriour d D Foroui 2 Dere of Mheics Fculy of Mheics Uiversiy
More informationComputer Aided Geometric Design
Copue Aided Geoei Design Geshon Ele, Tehnion sed on ook Cohen, Riesenfeld, & Ele Geshon Ele, Tehnion Definiion 3. The Cile Given poin C in plne nd nue R 0, he ile ih ene C nd dius R is defined s he se
More informationHarmonic excitation (damped)
Harmoic eciaio damped k m cos EOM: m&& c& k cos c && ζ & f cos The respose soluio ca be separaed io par;. Homogeeous soluio h. Paricular soluio p h p & ζ & && ζ & f cos Homogeeous soluio Homogeeous soluio
More informationClicks, concurrency and Khoisan
Poooy 31 (2014). Sueey ei Cic, cocuecy Koi Jui Bie Uiveiy o Eiu Sueey ei Aeix: Tciio Ti Aeix y ou e coex ei ioy o oio ue o e ou o!xóõ i e iy ouce. 1 Iii o-cic Te o-cic iii e oy ii o oe ue, o ee i ie couio
More informationControl Systems. System response. L. Lanari
Control Systems m i l e r p r a in r e v y n is o System response L. Lanari Outline What we are going to see: how to compute in the s-domain the forced response (zero-state response) using the transfer
More informationAvailable online at J. Math. Comput. Sci. 2 (2012), No. 4, ISSN:
Available olie a h://scik.og J. Mah. Comu. Sci. 2 (22), No. 4, 83-835 ISSN: 927-537 UNBIASED ESTIMATION IN BURR DISTRIBUTION YASHBIR SINGH * Deame of Saisics, School of Mahemaics, Saisics ad Comuaioal
More informationDepartment of Mathematical and Statistical Sciences University of Alberta
MATH 4 (R) Wier 008 Iermediae Calculus I Soluios o Problem Se # Due: Friday Jauary 8, 008 Deparme of Mahemaical ad Saisical Scieces Uiversiy of Albera Quesio. [Sec.., #] Fid a formula for he geeral erm
More informationMaximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002
Mmm lkelhood eme of phylogey BIO 9S/ S 90B/ MH 90B/ S 90B Iodco o Bofomc pl 00 Ovevew of he pobblc ppoch o phylogey o k ee ccodg o he lkelhood d ee whee d e e of eqece d ee by ee wh leve fo he eqece. he
More informationPHY2053 Summer C 2013 Exam 1 Solutions
PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The
More informationCalculus BC 2015 Scoring Guidelines
AP Calculus BC 5 Scorig Guidelies 5 The College Board. College Board, Advaced Placeme Program, AP, AP Ceral, ad he acor logo are regisered rademarks of he College Board. AP Ceral is he official olie home
More informationMv3" L7-- Art L 31. am rt. ao - M rr. a cn. art O' N. t00. to o( C7 c O. Ort. n ' C ( a ( W 0. z D0) Ln rni 90 O H N rt 0. to0) O mx rt N. W n.
S = TG _. -. t s e- ' F F J l T L L " m - F+ m G T. G m ( ( F+ v ( _ = ). i i vi vi t g d d --( ( ( t t ( - : m ET 7 ' m : ( 7 c t+ ) c - 7 7de 7( ( d;:', ` m G - L Lm ) 7 ` 7 [ t d `< ( ) ( m ( ) c. (
More informationSection P.1 Notes Page 1 Section P.1 Precalculus and Trigonometry Review
Secion P Noe Pge Secion P Preclculu nd Trigonomer Review ALGEBRA AND PRECALCULUS Eponen Lw: Emple: 8 Emple: Emple: Emple: b b Emple: 9 EXAMPLE: Simplif: nd wrie wi poiive eponen Fir I will flip e frcion
More informationH STO RY OF TH E SA NT
O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922
More informationIMPACT OF CLIMATE CHANGE ON AGRICULTURAL PRODUCTIVITY AND FOOD SECURITY Khalid Abdul Rahim. A World Leader in New Tropical Agriculture
IMPACT OF CLIMATE CHANGE ON AGRICULTURAL PRODUCTIVITY AND FOOD SECURITY Khalid Abdul Rahim A World Leader in New Tropical Agriculture IMPACT OF CLIMATE CHANGE ON AGRICULTURAL PRODUCTIVITY AND FOOD SECURITY
More informationELECTROPHORESIS IN STRUCTURED COLLOIDS
ELECTROPHORESIS IN STRUCTURE COLLOIS José M. Médez A. Civesv jedez@fis.ivesv.x p://www.fis.ivesv.x V µ E; µ 6πη ε ζ ; i i ζ i i 3 ε ζ ζ 4 THE GENERATION OF ONE PARTICLE EFFECTIVE YNAMICS 5 6 Lgevi euio
More informationProcessamento Digital de Sinal
Deparaeo de Elecróica e Telecouicações da Uiversidade de Aveiro Processaeo Digial de ial Processos Esocásicos uar ado Processes aioar ad ergodic Correlaio auo ad cross Fucio Covariace Fucio Esiaes of he
More information() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration
Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you
More informationChapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10
Chper 0 Siple Hronic Moion nd Elsiciy Gols or Chper 0 o ollow periodic oion o sudy o siple hronic oion. o sole equions o siple hronic oion. o use he pendulu s prooypicl syse undergoing siple hronic oion.
More information