A Glossary Of Complex Envelope Vectoization And Its Working Principle


 Martina Waters
 8 months ago
 Views:
Transcription
1 Complex Envelope Vectoization fo the solution of midhigh fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza
2 Pesentation layout  Low fequency mapping of HF vibation CEDA  CEV appoach and govening equations  Undesampling  Limits of CEV and emaks  Application of CEV to benchmaks  Test cases and esults  Application of CEV to Bounday Element Fomulation  Test cases and esults  A efeence model fo futue developments WKB  Conclusions
3 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEDA* Assuming a focing tem of adiant fequency ω, the equation of motion fo a onedimensional undamped stuctue is: 2 L[ u] m u f The complex envelope displacement is defined as follows: jk0x u E[ u] u ju e ~ u is the Hilbet Tansfom of u, i.e. ~ u and u + j u is the analytical displacement. E: envelope opeato x u x d *Cacatea and Sestiei: Complex envelope displacement analysis: a quasistatic appoach to vibations. JSV, vol. 2012, 1997.
4 LOW FREQUENCY MAPPING OF HF VIBRATIONS cont d By applying the envelope opeato to the motion equation and expessing the physical displacement in tems of the complex envelope one obtains: L[ 2 jk0x u ] m u f f j f e being L = E L E 1 u admits an invese which is given by: 0 u 2 Re{ u e j k x } CEDA equation So, once the CEDA equation is solved, one can econstuct the physical displacement
5 CEDA LAYOUT IN THE WAVENUMBER DOMAIN Physical signal spectum Analytic signal spectum Shifted signal spectum complex envelope
6 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEDA* When computing the complex envelope displacement we can ecove the physical displacement by the invese tansfomation
7 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEDA Example Fo the exact solution 100 points used against 16 points in CEDA
8 CEV: VECTORIZATION PROCESS CEV: VECTORIZATION PROCESS Because of the difficulties to extend CEDA to multidimensional and viboacoustic This slide systems shows schematically anothe appoach the vectoization was poposed: pocedue: CEV each ow  Complex o column Envelope of the Vectoization. discete suface solution is tansfeed to a stip, so that, at the end, we have a new discete signal that we can manipulate conveniently as a onedimensional system Spectum of the esponse fo a twodimensional system k y k x
9 CEV VECTORIZATION PROCEDURE Note: in the above vectoization pocedue the spectum of the esponse signal is not anymoe concentated aound a single wavenumbe k 0 but athe speads into the whole wavenumbe domain Vectoized signal Fouie Tansfom
10 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEV* FEM Stiffness matix K and mass matix M M u K u p If the excitation is hamonic with fequency ω, one has  ω 2 M + K u = p Au p * Giannini, Cacatea, Sestiei. High fequency vibation analysis by CEV. JASA, 1216, 2007
11 CEV cont d In CEV a set of complex envelope signals u and is poduced fom u p Fom Au p? A u p CEV equation
12 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEV* 2 M K u p DMA Univesità di Roma La Sapienza Au p u and p can be viewed as sampled values of continuous signals us and ps. Because of the vectoized spead in the wavenumbe domain, in CEV two sets of complex envelope signals u s p s ae poduced fom us ps, each one chaacteized by a naow wavenumbe spectum. u s u s 1,2,..., This is obtained by filteing the spectum Uk of us by a set of naow spectal windows W k and shifted by the quantity k towads the wave numbe oigin to poduce U. P
13 The Envelop opeato fo high dimensional poblems Space High Feq. Signal Fouie Tansfom Definition of Bands Fo each band Window Set of low fequency signals obtained by IFT Wavenumbe shift Wavenumbe shift
14 LOW FREQUENCY MAPPING OF HF VIBRATIONS CEV cont d The th complex signal u is obtained by invese Fouie Tansfom and. } { } { 1 1 k k W k k U F k U F s u
15 Set of low wavenumbe signals High Feq. Space Signal The opeation is evesible povided that the whole set of windowed signals ae consideed } 2Re{ 1 s k j P e s u s u } { } { 1 1 k k W k k U F k U F s u 1,2,..., P s u s u DMA Univesità di Roma La Sapienza
16 NUMERICAL RESULTS 34x34 DMA Univesità di Roma La Sapienza
17 How to build A M, K fom the physical matix A M, K The explicit fom of the motion equation is: It can be tuned into continuous fom by using ps and us to obtain: p u A s p d u s a I, 1 s k j I p d u e s a F k k W k k P k k U k k W k k A Assume the kenel to have the fom: a s,σ = a s  σ. By i Fouie tansfoming the motion equation, ii applying the window W, and iii shifting the esult towad the oigin by k : Invese Fouie Tansfom h k k hk p u A DMA Univesità di Roma La Sapienza
18 Reconsideing its discete countepat N n1 a j k s mn mn e un pm with a a DMA Univesità di Roma La Sapienza How to build A M, K fom the physical matix A M, K cont d s e A u j k s k h hk h k sampling inteval of the dummy vaialble s p This expession pemits to ecove the envelope matix A M, K fom the physical matix A M, K
19 CEV EQUATION summay Fom the discete equation of a consevative dynamic poblem Au p by: load tansfomation: i Fouie tansfom F, ii application of bandpass windows W, iii wave numbe shift opeation towad the oigin S, iv invese Fouie tansfom F 1 : p F 1 S W F p p E p matix tansfomation DMA Univesità di Roma La Sapienza A u p CEV Equation
20 LIMITS OF CEV AND REMARKS The condition as,σ = asσ is stictly valid fo infinite systems. Fo finite systems it is not tue. Howeve it can be shown that it holds in an aveage sense, i.e. if the esponse is spatially aveaged.
21 CEV EQUATIONS FOR NON CONSERVATIVE SYSTEMS DMA Univesità di Roma La Sapienza Fo non consevative systems A and u ae complex, the steps pesented above can be maintained povided that u, p and A ae witten diffeently, as follows: 0 p p A A A A A u u u R I I R I R p u A p u A CEV
22 UNDERSAMPLIG Fo example, fo a 6 x 6 matix A, and a eduction atio = 2, we may  The new poblem, poviding the complex envelope, has size NxN, identical to choose the oiginal one and has the same eigenvalues of the oiginal one Each spectal window has a low wavenumbe spectum, thus a fine mesh is unnecessay and actually non 1 0convenient 0 fo the CEV application A suitable expansion matix R is intoduced to solve the poblem at a low computational cost. By omitting 0the 1 0supescipt fo the sake of simplicity: u Ru ed R is ectangula and admits a pseudoinvese R + such that so that, in this case it is R + = R T / R + R=I while RR + I The opeation A ed R AR p ed R p obtained A Rby AR aveaging ; its u elements R u ed ed DMA Univesità di Roma La Sapienza implies a patition of the oiginal matix into squae submatices, eplacing each submatix with a single value A ed u ed p ed
23 RECOVERING THE PHYSICAL SOLUTION The invese elationship povides the physical solution u Ru ed
24 Steps in CEV: summay DMA Univesità di Roma La Sapienza A M and K is detemined by a standad FEM The windowed envelop matix is detemined fom A is not affected by the filteing opeation The windowed envelope load is obtained by FT of the focing vecto, windowing the wavenumbe component by W, and shifting the spectum by The IFT povides p A is detemined by A ed R A R ed p is detemined by ed p R p ed k. Fom the CEV equation, u is detemined, and the physical esponse ecoveed
25 LIMITS OF CEV AND REMARKS DMA Univesità di Roma La Sapienza Looking at the spectum of a point load flat in the fequency domain, the Leakage filteed effect spectum of the is filteing not shaply pocess, ectangula, implying due that to CEV the use acts of coectly a finite numbe on the foced of points, pat i.e. of the a tuncated solution FT but of does the not signal tackle leakage efficiently the homogeneus pat A A If the matix is not educed, the eigenvalues of ae equal to those of the physical poblem A and the Filte envelope spectum solution shifted matches to the pefectly the physical solution. wavenumbe oigin This is a dawback especially fo low damping. Howeve the contibution of diffeent windows having diffeent phases, educes significantly When the envelope matix is educed, the eigenvalues of the educed poblem ae diffeent lowe fom those of the physical poblem: an eo is intoduced mistuning such spead. Response of the filteed load it is not Howeve: the eigenvalues of the educed stictly confined poblem ae in the a subset filte of the eigenvalues of the non educed poblem, bandwidth unde the assumption that the CEV solution is smooth. Using a set of windows in the wavenumbe domain, it is possible to appoximate sufficiently well the eigenvalues of the oiginal poblem thus obtaining a easonable esponse.
26
27 LIMITS OF CEV AND REMARKS CEV can be consideed successful when the modes of the system do not play a key ole. Paticulaly: when the damping is elatively high when a diect field is pepondeant with espect to the evebeant field fo high fequency poblems with an acceptable damping when an extenal acoustic poblem no modes is consideed*.
28 Application 1: 2D cavity with a point souce DMA Univesità di Roma La Sapienza FE discetization: gid 64x DOF CEV discetization: gid 16x DOF Damping 0.01
29 Application 2: bending plate 1x1x0.002 m with a point souce FE gid: 64x DOF. CEV DOFS: 384 Reduction ate 32 Damping 0.01
30 Application 3: foam plate 1x1x0.05 m with a point souce FE discetization: gid 64x DOF CEV discetization: gid 16x DOF Damping 0.17
31 A benchmak fo the Maie Cuie ITN 4 6
32 BENCHMARK FOR A PRIN NATIONAL PROJECT DMA Univesità di Roma La Sapienza Reduction fom dofs to 786 dofs atio 41 Plate dimensions: 1600x400x3 mm, 2300x400x3, 3400x400x3. 60 Damping Damping 0.04
33 Fomulation of the extenal poblem DMA Univesità di Roma La Sapienza APPLICATION OF CEV TO BEM FORMULATION FEM Velocity field on the bounday Pessue on the Bounday BEM Radiation into the field
34 APPLICATION OF CEV TO BEM FORMULATION Integal fomulation of a viboacoustic poblem, unde steady conditions, by the feespace Geen function Whateve the type of elements used, in matix fom one has This poblem can be solved by following the same steps shown befoe, i.e.:  a FEM is used to detemine the esponse v CEV can be used but not convenient  a BEM is used to detemine the matix T o  a BEM is used to detemine the matix T  a BEM is used to compute c c c ed T T ed T ed T ed moe convenient computationally
35 APPLICATION OF CEV TO BEM FORMULATION The CEV method applied to the bounday element fomulation povides The mistuning does not affect the BEMCEV fomulation because the opeato T is not diectly elated to the stuctual opeato: thus thee is no eo in the natual fequencies location. NO MISTUNING
36 TEST CASES: pulsating sphee = 0.1m, v n = 0.01 m/s Extenal field. Reduction facto 8: fom 1016 to 127 DOFS Pessue field on the suface f = 800 Hz Extenal field Intenal field
37 TEST CASES: extenal field geneated by a loaded box Foce specta ae flat between 700 and 2500 Hz Pessue spectum at a distance d=15m fom the box Reduction facto 21: fom 1176 to 112 DOFS Point spectum at 15 m fom the box: Compaison between efeence solution and CEV fo diffeent eduction factos Note that fo eduction facto 168, the CEV Dofs ae only 14
38 TEST CASES: extenal field adiated by a benchmak Flat specta foces Pessue spectum at a efeence point of the field Reduction facto 19: fom 855 to 45 DOFS
39 TEST CASES: extenal field adiated by a benchmak
40 TEST CASES: extenal field adiated by a benchmak
41 A efeence model fo futue developments WKB* Possible connections with CEV, VTCR, DEA, WBM, WIA? WKB Eikonal establishes a elationship between the exact equations of waves and the ay tacing appoximation. Consideing the wave equation with a hamonic excitation, it is: whee nx is the efaction index: c 0 /cx By factoizing ψ into amplitude and phase ψx = Ax e jsx, substituting into the wave equation and getting eal and imaginay pats: * Wenzel, Kames and Billouin
42 WKB cont. DMA Univesità di Roma La Sapienza Let ε = 1/k 2 : By expessing the solution in the fom and using a petubation appoach up the fist ode:
43 WKB cont. At ode zeo, i.e. λ 0, i.e. k DMA Univesità di Roma La Sapienza ay tacing Equal phase sufaces ae those ove which Sx ae constant: ays ae those lines intesecting othogonally equal phase sufaces. The unit vecto along the ay is: poducing: that can be solved iteatively.
44 WKB cont. Tuning this appoach to discete fom: with: i.e. L S a = p LS acts on the wave opeato by modulating exponentially its coefficients, just as CEV and othes methods do.
45 Compaison between WKB and CEV WKB CEV  It uses diffeent odes of petubation  It uses seveal windows centeed on to appoximate the solution k to shift the HF components and appoximate the solution  Sx is unknown  The phase modulating tem is assigned } 2Re{ 1 s k j P e s u s u } { } { 1 1 k k W k k U F k U F s u DMA Univesità di Roma La Sapienza
46 Compaison between WKB and VTCR/WBM* WKB VTCR/WBM In WKB the solution is epesented by Both VTCR and WBM use shape waves amplitudes modulated by phase functions that ae exact solution of the functions, and diffeent petubation govening diffeential equations  odes ae used to appoximate the modes epesented by a supeposition solution. of wave shape functions in WBM, local modes, supeposition of appopiate waves in VTCR. In VTCR a twoscale appoximation is used in the weak fomulation. Only the slow scale wave amplitude is discetized while the fast vaying scale spatial shape of the wave is analytically descibed. * WBM: Wave based method, VTCR: Vaiational theoy of complex ays
47 Compaison between WKB and DEA/WIA* WKB DEA/WIA In WKB the zeoth ode appoximation povides the ay tacing technique. Using highe odes of petubation it is possible to efine the solution. In DEA the ay dynamics is descibed by a set of basis functions. When using the lowest basis function the ay tacing appoximation, and SEA, is obtained In WIA the displacement field is obtained by a supeposition of tavelling waves. By neglecting phase dependencies, only an enegy beam is associated to each wave. By expanding each beam by a Fouie seies, an enegy balance equations is obtained. It povides the SEA equations if the seies is aested to the fist tem. *DEA: Dynamic Enegy analysis, WIA: Wave intensity appoach
48 CONCLUDING REMARKS 1 CEV does not use an enegy fomulation, but pefoms a tansfomation leading to a new vaiable that has a low wavenumbe content and capable of accounting coectly fo the bounday conditions. As such, it is paticulaly appopiate to deal with high fequency poblems. The envelope mass and stiffness matices ae detemined diectly fom the FE matices, so that any commecial FE o BE code can be used. A eduction technique is applied to these matices to get a new poblem whose dimensions ae much smalle than the oiginal one, with a elevant saving of time computation. The appoach is paticulaly convenient when the modes do not play a elevant ole: e.g. extenal acoustic poblems
49 CONCLUDING REMARKS 2 CEV can be applied to both extenal and intenal viboacoustic poblems, with eos bounded within 3 db fom the efeence solution. Unlike the application of CEV with FEM, in the application to BEM the mistuning poblem is absent. Thus, CEV can be efficiently used to detemine the intenal acoustic field. The eduction facto can be inceased at will, without affecting significantly the quality of the solution: howeve, inceasing the eduction facto it is necessay to incease the numbe of spectal filtes. Shall we define a common goal and tasks to addess pedictive methods, with clea tasks and goals?
50 Time aveage? Fequency aveage? Ensemble aveage? Diect field? Revebeant field? Wave intefeence? Thank you fo you attention Any question?
51 Weak fom of the kenel Fo an infinite system as,σ = asσ feee space Geen function Fo finite systems it does geneally hold. Howeve it can hold in a weak o aveage fom, i.e. By FT as,σ By FT asσ a s, σ = as σ a s, σ a s σ e ik xx ds = Ak x,σ e ik xx ds = Ak x e ik xσ i.e., to satisfy the convolution condition it must be Ak x,σ = Ak x e ik xσ Ak x = Ak x,σ e ik xσ By IFT, it is possible to detemine as as: as = F 1 Ak x, σ e ik xσ
52 SPECTRAL WINDOW DECOMPOSITION DMA Univesità di Roma La Sapienza W 1 W 2 W 3 W 4 W 5 W 6 W 1 LOW FREQUENCY SOLUTION N W 6.. LOW FREQUENCY SOLUTION N. 6 FORWARD SHIFTING MOVE THE SOLUTIONS AT THE RIGTH WN +
53 HIGH FREQUENCY PROBLEMS & SPECTRAL CHARACTERISTICS δs FOURIER TRANSFORM space step a k MAX maximum wavenumbe
54 CEDV SOLUTION: DMA Univesità di Roma La Sapienza DESCRIBE THE RESPONSE BY A SET OF NARROW BAND SIGNALS LOW FREQUENCY SIGNAL HIGH FREQUENCY SIGNAL WAVENUMBER AXIS ORIGIN
55 NUMERICAL RESULTS 34x34 DMA Univesità di Roma La Sapienza
56 NUMERICAL RESULTS, PLATE 34x34 vs 16x16 COMPARISON BETWEEN VECTORIZED SOLUTIONS ENVELOPE PHYSICAL
57 CEV: GOVERNING EQUATIONS d s x s x 1 ~ ~ ˆ s jx s x s x x jk e s x s x 0 ˆ New equation of motion, 0 s f d x e s I a s jk Equation of motion fo the discete countepat 0 i j l jk ij ij e M M 0 i j l jk ij ij e K K f x K M 2
58 CEV: ENVELOPE VECTORIZATION 2 M K w f ~ jk0x w E[ w] w jw e 2 M K w f M K ij ij M K ij ij e e jk0l ji jk0l ji
59 Spectum of the vectoized displacement of high dimensional poblems
The Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationSTABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION
Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More information12.1. FÖRSTER RESONANCE ENERGY TRANSFER
ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 11 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationDYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES
DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation
More informationEpdf Sulf petroleum, Eflecti and Eeflecti
ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9075585846; F: +90755848470; E: fossi@unipg.it
More informationPessu Behavior Analysis for Autologous Fluidations
EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049001 Lisboa Email: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB30 AIRCRAFT  PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
More informationCRRC1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationGravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationTracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors
Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationModal Characteristics study of CEM1 SingleLayer Printed Circuit Board Using Experimental Modal Analysis
Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM1 SingleLaye
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More information12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
More informationExcitation energies for molecules by TimeDependent. based on Effective Exact Exchange KohnSham potential
Excitation enegies fo molecules by TimeDependent DensityFunctional Theoy based on Effective Exact Exchange KohnSham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationPHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationFIRST EXPERIENCES WITH THE DEFORMATION ANALYSIS OF A LARGE DAM COMBINING LASERSCANNING AND HIGHACCURACY SURVEYING
FIRST EXPERIENCES WITH THE DEFORMATION ANALYSIS OF A LARGE DAM COMBINING LASERSCANNING AND HIGHACCURACY SURVEYING Diego González Aguilea a*, Javie Gómez Lahoz a and José Antonio Sánchez Seano b a Land
More informationStructure and evolution of circumstellar disks during the early phase of accretion from a parent cloud
Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The
More informationDisplacement, Velocity And Acceleration
Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,
More informationChapter 4: Fluid Kinematics
Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More informationTiming Synchronization in High Mobility OFDM Systems
Timing Synchonization in High Mobility OFDM Systems Yasamin Mostofi Depatment of Electical Engineeing Stanfod Univesity Stanfod, CA 94305, USA Email: yasi@wieless.stanfod.edu Donald C. Cox Depatment of
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationINVESTIGATION OF FLOW INSIDE AN AXIALFLOW PUMP OF GV IMP TYPE
1 INVESTIGATION OF FLOW INSIDE AN AXIALFLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of
More informationModel Question Paper Mathematics Class XII
Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat
More informationElectricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system
Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system MiaoSheng Chen a ChienLiang Wang b,c, ShengChuan Wang d,e a Taichung Banch Gaduate
More informationMining Relatedness Graphs for Data Integration
Mining Relatedness Gaphs fo Data Integation Jeemy T. Engle (jtengle@indiana.edu) Ying Feng (yingfeng@indiana.edu) Robet L. Goldstone (goldsto@indiana.edu) Indiana Univesity Bloomington, IN. 47405 USA Abstact
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk  Risk to shaeholdes esulting fom the use of debt. Financial Leveage  Incease in the vaiability of shaeholde etuns that
More informationMultiband Microstrip Patch Antenna for Microwave Applications
IOSR Jounal of Electonics and Communication Engineeing (IOSRJECE) ISSN: 22782834, ISBN: 22788735. Volume 3, Issue 5 (Sep.  Oct. 2012), PP 4348 Multiband Micostip Patch Antenna fo Micowave Applications
More informationReduced Pattern Training Based on Task Decomposition Using Pattern Distributor
> PNN05P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto ShengUei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task
More informationUNIVERSIDAD DE CANTABRIA TESIS DOCTORAL
UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationSUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA
Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 677 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L.
More informationMETHODOLOGICAL APPROACH TO STRATEGIC PERFORMANCE OPTIMIZATION
ETHODOOGICA APPOACH TO STATEGIC PEFOANCE OPTIIZATION ao Hell * Stjepan Vidačić ** Željo Gaača *** eceived: 4. 07. 2009 Peliminay communication Accepted: 5. 0. 2009 UDC 65.02.4 This pape pesents a matix
More informationMATHEMATICAL SIMULATION OF MASS SPECTRUM
MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationDIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION
DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION Mohammad Rashed Iqbal Fauque* #1, Mohammad Taiqul Islam* 2, Nobahiah Misan* #3 * Institute of Space Science
More informationRelativistic Quantum Mechanics
Chapte Relativistic Quantum Mechanics In this Chapte we will addess the issue that the laws of physics must be fomulated in a fom which is Loentz invaiant, i.e., the desciption should not allow one to
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationChapter 2 Modelling of Fluid Flow and Heat Transfer in RotatingDisk Systems
Chapte 2 Modelling of Fluid Flow and Heat Tansfe in RotatingDisk Systems 2.1 Diffeential and Integal Equations 2.1.1 Diffeential Navie Stokes and Enegy Equations We will conside hee stationay axisymmetic
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationChapter 2. Electrostatics
Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationUncertainty Associated with Microbiological Analysis
Appendix J STWG Pat 3 Uncetainty 7806 Page 1 of 31 Uncetainty Associated with Micobiological Analysis 1. Intoduction 1.1. Thee ae only two absolute cetainties in life: death and taxes! Whateve task we
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationNUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
More informationMULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION
MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION K.C. CHANG AND TAN ZHANG In memoy of Pofesso S.S. Chen Abstact. We combine heat flow method with Mose theoy, supe and subsolution method with
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More information10. Collisions. Before During After
10. Collisions Use conseation of momentum and enegy and the cente of mass to undestand collisions between two objects. Duing a collision, two o moe objects exet a foce on one anothe fo a shot time: F(t)
More informationA Web Application for Geothermal Borefield Design
Poceedings Wold Geothemal Congess 205 Melboune, Austalia, 925 Apil 205 A Web Application fo Geothemal Boefield Design Davide Rolando,2, José Acuna and Maco Fossa 2 KT Royal Institute of Technology, Binellvägen
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationThank you for participating in Teach It First!
Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Suppot Coach, Foundational Mathematics teache lesson followed by the coesponding student lesson. We ae confident
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationAn Infrastructure Cost Evaluation of Single and MultiAccess Networks with Heterogeneous Traffic Density
An Infastuctue Cost Evaluation of Single and MultiAccess Netwoks with Heteogeneous Taffic Density Andes Fuuskä and Magnus Almgen Wieless Access Netwoks Eicsson Reseach Kista, Sweden [andes.fuuska, magnus.almgen]@eicsson.com
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationDistributed Computing and Big Data: Hadoop and MapReduce
Distibuted Computing and Big Data: Hadoop and Map Bill Keenan, Diecto Tey Heinze, Achitect Thomson Reutes Reseach & Development Agenda R&D Oveview Hadoop and Map Oveview Use Case: Clusteing Legal Documents
More informationHeat transfer analysis of canned food sterilization in a still retort
Available online at www.sciencediect.com Jounal of Food Engineeing xxx (28) xxx xxx www.elsevie.com/locate/jfoodeng Heat tansfe analysis of canned food steilization in a still etot A. Kannan *, P.Ch. Gouisanka
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationMechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
More informationAntiLock Braking System Training Program
COVERST.EPS ac T to $2.50 BS A AntiLock Baking System Taining Pogam Student Manual TP9738 Revised 399 Module 1 ABS Components and System Opeation Module 2 ABS Diagnosis and Repai Module 3 ATC Opeation,
More informationA Hybrid DCTSVD Video Compression Technique (HDCTSVD)
A Hybid  Video Compession echnique (H) ong, Lin; Rao, K.R. Abstact A new hybid  (H) video compession technique is poposed in this pape. Discete cosine tansfom () is widely used in video coding due to
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo MatínezdeAlbéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationGraphs of Equations. A coordinate system is a way to graphically show the relationship between 2 quantities.
Gaphs of Equations CHAT PeCalculus A coodinate sstem is a wa to gaphicall show the elationship between quantities. Definition: A solution of an equation in two vaiables and is an odeed pai (a, b) such
More informationAn Efficient Group Key Agreement Protocol for Ad hoc Networks
An Efficient Goup Key Ageement Potocol fo Ad hoc Netwoks Daniel Augot, Raghav haska, Valéie Issany and Daniele Sacchetti INRIA Rocquencout 78153 Le Chesnay Fance {Daniel.Augot, Raghav.haska, Valéie.Issany,
More informationMemoryAware Sizing for InMemory Databases
MemoyAwae Sizing fo InMemoy Databases Kasten Molka, Giuliano Casale, Thomas Molka, Laua Mooe Depatment of Computing, Impeial College London, United Kingdom {k.molka3, g.casale}@impeial.ac.uk SAP HANA
More information