Exercise 11 ISOLATION OF MACHINE VIBRATIONS


 Merryl Waters
 1 years ago
 Views:
Transcription
1 Exercise 11 ISOLATION OF MACHINE VIBRATIONS 1. Aim of the exercise Isolatio of the vibratig device from its foudatio. Experimetal determiatio of the trasfer factor of vibratios.. Theoretical itroductio Rotatig machies with ubalace are typical sources of vibratios. If these devices are mouted rigidly o their foudatio, vibratios will trasfer to the eviromet. Trasferred vibratios may cause oise, a harmful ifluece o the huma body, or overloadig of the istrumets which are earby. Isolatio of vibratios ca miimize such udesirable iteractios. Usually, viscoelastic elemets are placed betwee the vibratig machie ad its foudatio. This is the socalled active isolatio, or forced isolatio whe we wat to prevet the force from beig trasferred to the foudatio. I the case whe we wat to isolate a device from the vibratig foudatio, we say this is passive isolatio, or displacemet isolatio..1. Admissible vibratios actig o the huma body To provide suitable coditios for people who work earby machies, the isolatio of machie vibratios is carried out amog others. Techical stadards describe the rules of mechaical vibratio measuremets to estimate their ifluece o the huma body. Admissible values of vibratio parameters are preseted also i these stadards. Admissible acceleratios of total vibratios (actig o the whole body), local vibratios (actig o hads) ad admissible work time whe these limits are exceeded are these vibratio parameters. O the basis of the Polish Stadard PN91/N0135 show i Table 11.1, the admissible values of acceleratio of vibratios which act o the huma body durig 80 miutes are preseted. The spectral method has bee used to estimate the risk. The spectral aalyses of acceleratio of vibratios i 1/3 octave frequecy bads i the rages 1 80 Hz (for total vibratios) ad Hz (for local vibratios) are carried out i this method. Table Admissible values of acceleratio of vibratios Middle frequecy of the 1/3octave bad [Hz] Admissible effective value of acceleratio [m/s ] Vertical compoet Horizotal compoet
2 Rubber as a vibroisolatig material Rubber is widely used as a viscoelastic isolatig elemet. I compariso with steel, rubber has high iteral dampig, a ability of soud absorptio ad very good shape elasticity. The stiffess coefficiet of the rubber vibroisolator depeds o its hardess ad chages i a oliear way with a icrease i the static load. The stiffess coefficiet is defied as: d Q N k = d y m, (11.1) where: Q static load of vibroisolator, y deflectio of vibroisolator. 600 Q [N] Q P 1 Q s P y st y y Fig Noliear characteristic curve of rubber Figure 11.1 shows the socalled hard characteristic curve. I this case, the k value icreases whe the loadig elarges. If the static load does ot exceed a certai value Q s, (poit P s i Fig. 11.1), the characteristic curve is liear. I this loadig rage, the stiffess coefficiet k has a costat value. If the static load elarges, for example to the value Q 1 (poit P 1 ), the stiffess coefficiet icreases i a oliear way. The slope i the poit P 1 determies the k value i this loadig rage.
3 For the isolatio purposes, vibratio dampig properties of rubber are very importat. They cause the absorptio of vibratio eergy ad facilitate a getle passage through resoace. Depedig o the rubber type, the value of dimesioless dampig coefficiet h/α is i the rage from 0.0 to 0.1 (where: h viscous dampig coefficiet referred to the mass i [rad s 1 ], α  atural frequecy i [rad s 1 ]). Cotrary to steel, rubber does ot corrode ad has high fatigue resistace. This does ot apply uder low temperatures, because rubber pads may be used i temperatures from 30 o to +75 o C..3. Trasfer factor A oedegreeoffreedom vibratig system is cosidered. The excitig harmoic force F sit acts o the mass m (Fig. 11.). Betwee the vibratig mass ad its foudatio, there is a sprig with the stiffess coefficiet k ad a viscous dashpot with the dampig coefficiet c. m F si t x k c Fig Model of the vibratig system The equatio of motio of the cosidered model ca be expressed i the followig form: m& x + c x& + k x = F si t. (11.) After some trasformatios, equatio of motio (11.) takes the form: & x&+ h x& + x = q si t, (11.3) where: c k F = h; = ; = q. (11.) m m m The particular solutio to Eq. (11.3) ca be predicted as: x = Asi( t ϕ), (11.5) where the amplitude of displacemet A is expressed by: q, (11.6) A= h ( ) + ad the phase shift agle ϕ betwee excitatio ad displacemet is determied by the followig depedece: h ϕ = arc tg. (11.7) The force which acts o the foudatio cosists of a force i the sprig ad a force i the damper. The force i the sprig is as follows: S = kx = kasi( t ϕ). (11.8) The force i the damper is equal to: R = cx& = ca cos( t ϕ). (11.9) The maximal total force actig o the foudatio is expressed as:
4 P max = S + R = ( ka) + ( ca). (11.10) max max Substitutig Eq. (11.) ad Eq. (11.6) ito Eq. (11.10), oe receives: P max h F 1+ = (11.11) h 1 + The ratio of the maximal total force actig o the foudatio P max to the excitig force amplitude F is called the trasfer factor ad will be deoted by ν i further cosideratios. Usig Eq. (11.11), the trasfer factor ca be determied i the form: ν h 1+ Pmax = = (11.1) F 1 h + Figure 11.3 shows plots of the trasfer factor ν versus the excitig frequecy γ = / (the ratio of the dimesioal excitig frequecy to the atural frequecy ) for differet values of the dimesioless dampig coefficiet h/. Depedig o the rubber type, the value of the dimesioless dampig coefficiet h/ is i the rage from 0.0 to 0.1. To receive the trasfer factor plot value of about 0.1 o the basis of Fig for these dampig values, the dimesioless excitig frequecy γ = / should be higher tha 3. 5 ν h / = 0 3 h / = 0. 1 h / = 0. h / = / Fig Plot of the trasfer factor
5 .. Example of the isolator selectio for active vibroisolatio o the basis its static characteristics I this umerical example, a system cosistig of a fa ad a drivig motor is cosidered. The total mass of the system is m 1 = 00 kg. The rotatioal speed of the motor is = 150 rev/mi. The system is mouted i a supportig structure of the mass m = 100 kg. The foudatio should be isolated from vertical vibratios of the system by meas of four rubber isolators. After the isolatio, the trasfer factor value should ot be higher tha 0.1. Solutio The excitig frequecy is equal to: π = = [rad/s] (a) 60 The gravitatioal force actig o oe isolator is as follows: m1 + m Q = g = [N] (b) It is assumed that rubber isolators will work i the liear part of their static characteristics (Fig. 11.1). Two kids of M00type isolators deoted by A ad B, depedig o their hardess, have bee selected to isolate the foudatio of the system. The static characteristics of M00type isolators are show i Fig Q [N] Hardess B Max force Q = 00 N Hardess A Max force Q = 1300 N Fig Static characteristics of M00type isolators From the characteristic curve of the M00type isolator of the hardess A, oe ca read the static deflectio uder the Q load. This deflectio is y st = 5.89 mm. The, oe ca determie the value of the atural frequecy of such a isolator: k mg g 9.81 = = = = 0.81 [rad/s] = (c) m y m y st st The ratio of the excitig frequecy to the atural frequecy is equal to: γ = = = 3.7 (d) y [mm] 1
6 Still, oe ought to check the trasfer factor value for the limitig value of the h/ ratio of rubber isolators. ν = h Measuremet device lim h + lim = 1+ 0,1 3,7 ( 1 3,7 ) + 0,1 3,7 = 0,097 < 0,1 A scheme of the measuremet device is show i Fig Loudspeaker device 1 is mouted o its foudatio, represeted by rigid plate 3. Oe should isolate the foudatio from vertical vibratios of the loudspeaker device by meas of four rubber isolators. Plate 3 is coected with the buildig costructio by meas of four supportig pads of the kow stiffess. Vibratios of loudspeaker device 1 ad plate 3 are measured with piezoelectric sesors 5 ad 6, respectively. The sesors are coected with a set of vibratio meters ad arrowbad aalyser 7. (e) y x Fig Scheme of the measuremet device. Course of the exercise The active isolatio of loudspeaker device vibratios should be performed. After the isolatio, the trasfer factor betwee the maximal total force actig o the plate ad the excitig force amplitude should ot be higher tha 0.1. The followig operatios are to be performed: 1) mout rigidly the loudspeaker device o the plate modellig the foudatio, ) tur o the loudspeaker device, 3) measure the vibratio frequecy ad the acceleratio amplitude alog the vertical directio, ) switch off the loudspeaker device, 5) calculate the amplitude of the excitig force, 6) o the basis of the example, select four rubber isolators, 7) calculate the value of the theoretical trasfer factor, 8) locate the selected isolators i the loudspeaker device support, 9) tur o the device, 10) measure the vibratio frequecy ad the acceleratio amplitude of the plate alog the vertical directio, 11) switch off the device, 1) calculate values of the force actig of the plate ad the trasfer factor.
7 5. Laboratory report should cotai: 1) Aim of the exercise. ) Experimetal ad calculatio results preseted i the followig table: Table 1 Loudspeaker device mouted rigidly o the plate Vibratio frequecy: f = [Hz] Agular excitig frequecy: =... [rad/s] Acceleratio amplitude alog the vertical directio: A y =... [mm/s ] Excitig force amplitude: F y = [N]. 3) Isolator selectio  calculatio results. The gravitatioal force actig o oe isolator: Q =...[N]. The selected isolator type: The static deflectio uder the Q load: y st =... [mm]. The atural frequecy of the isolator: ν =... [rad/s]. The ratio of the excitig frequecy to the atural frequecy: γ = / =... The trasfer factor value for the limitig value of the ratio of rubber isolators (h / = 0.1): ν =.... ) Experimetal ad calculatio results preseted i the followig table: Table Loudspeaker device supported o isolators Vibratio frequecy: f = [Hz] Agular excitig frequecy: =..... [rad/s] Vibratio amplitude of the plate alog the y directio: A y = [mm/s ] Force actig o the plate: F y = [N] Trasfer factor value: ν y =... [] 5) Coclusios.
8 Refereces 1. Goliński J.: Wibroizolacja maszy i urządzeń, WNT Warszawa Parszewski Z.: Drgaia i dyamika maszy, WNT Warszawa Iformatio o isolatig materials of the Swedish compay Trelleborg AB.. PN91/N Admissible values of acceleratios of vibratios which act o the huma body. 5. Rao S.S.: Mechical Vibratios, 3rd ed., Pretice Hall, NY, 1995.
Cantilever Beam Experiment
Mechaical Egieerig Departmet Uiversity of Massachusetts Lowell Catilever Beam Experimet Backgroud A disk drive maufacturer is redesigig several disk drive armature mechaisms. This is the result of evaluatio
More informationPartial Di erential Equations
Partial Di eretial Equatios Partial Di eretial Equatios Much of moder sciece, egieerig, ad mathematics is based o the study of partial di eretial equatios, where a partial di eretial equatio is a equatio
More informationDesign and Development of Experimental setup for Identification of SDoF with Harmonic Excitation
Iteratioal Joural of Egieerig ad Techical Research (IJETR) ISSN: 30869, Volume, Issue, February 04 Desig ad Developmet of Experimetal setup for Idetificatio of SDoF with Harmoic Excitatio Prof. Dr.
More informationSOLID MECHANICS DYNAMICS TUTORIAL DAMPED VIBRATIONS. On completion of this tutorial you should be able to do the following.
SOLID MECHANICS DYNAMICS TUTORIAL DAMPED VIBRATIONS This work overs elemets of the syllabus for the Egieerig Couil Eam D5 Dyamis of Mehaial Systems, C05 Mehaial ad Strutural Egieerig ad the Edeel HNC/D
More informationA Theoretical and Experimental Analysis of the Acoustic Guitar. Eric Battenberg ME 173 51809
A Theoretical ad Experimetal Aalysis of the Acoustic Guitar Eric Batteberg ME 173 51809 1 Itroductio ad Methods The acoustic guitar is a striged musical istrumet frequetly used i popular music. Because
More informationOPTIMIZATION OF AN ENGINE MOUNTING SYSTEM FOR VIBROACOUSTIC COMFORT IMPROVEMENT
OPTIMIZATION OF AN ENGINE MOUNTING SYSTEM FOR VIBROACOUSTIC COMFORT IMPROVEMENT Marco La Civita ad Aldo Sestieri Departmet of Mechaics ad Aeroautics Uiversity of Rome "La Sapieza" 184 Rome, ITALY ABSTRACT
More information19. LINEAR VISCOUS DAMPING. Linear Viscous Damping Is a Property of the Computational Model And is not a Property of a Real Structure
19. LINEAR VISCOUS DAMPING Liear Viscous Dampig Is a Property of the Computatioal Model Ad is ot a Property of a Real Structure 19.1 INRODUCION { XE "Viscous Dampig" }I structural egieerig, viscous velocitydepedet
More informationStudy on the application of the software phaselocked loop in tracking and filtering of pulse signal
Advaced Sciece ad Techology Letters, pp.3135 http://dx.doi.org/10.14257/astl.2014.78.06 Study o the applicatio of the software phaselocked loop i trackig ad filterig of pulse sigal Sog Wei Xia 1 (College
More informationThe influence of the carriage speed on the compliance of the toolholder.
techische hogeschool eidhove laboratorium voor mec:haisc:he tec:hojogie e werkplaatstec:hiek rapport va de sectie: Verspaigstechologie titel: The ifluece of the carriage speed o the compliace of the toolholder
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 007 MARKS: 50 TIME: 3 hours This questio paper cosists of pages, 4 diagram sheets ad a page formula sheet. Please tur over Mathematics/P DoE/Exemplar
More information1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
More informationVladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT
Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee
More informationModified Line Search Method for Global Optimization
Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o
More informationConvention Paper 6764
Audio Egieerig Society Covetio Paper 6764 Preseted at the 10th Covetio 006 May 0 3 Paris, Frace This covetio paper has bee reproduced from the author's advace mauscript, without editig, correctios, or
More informationThe analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection
The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity
More informationThermodynamic Laws/Definition of Entropy
This is a review of Thermodyamics ad Statistical Mechaics. Thermodyamic Laws/Defiitio of Etropy st law of thermodyamics, the coservatio of eergy: du = dq dw = Q W, ( where dq is heat eterig the system
More informationCHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationHCL Dynamic Spiking Protocol
ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7
More informationThe second difference is the sequence of differences of the first difference sequence, 2
Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for
More informationAP Calculus AB 2006 Scoring Guidelines Form B
AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a otforprofit membership associatio whose missio is to coect studets to college success
More informationTHREE DIMENSIONAL EXPERIMENTAL MODAL ANALYSIS ON A WATER FILLED CYLINDRICAL SHELL
Proceedigs of the IMACXXVII February 912, 29 Orlado, Florida USA 29 Society for Experimetal Mechaics Ic. THREE DIMENSIONAL EXPERIMENTAL MODAL ANALYSIS ON A WATER FILLED CYLINDRICAL SHELL William K. Boess,
More informationAutomatic Tuning for FOREX Trading System Using Fuzzy Time Series
utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which
More information3. Covariance and Correlation
Virtual Laboratories > 3. Expected Value > 1 2 3 4 5 6 3. Covariace ad Correlatio Recall that by takig the expected value of various trasformatios of a radom variable, we ca measure may iterestig characteristics
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationMeasuring Magneto Energy Output and Inductance Revision 1
Measurig Mageto Eergy Output ad Iductace evisio Itroductio A mageto is fudametally a iductor that is mechaically charged with a iitial curret value. That iitial curret is produced by movemet of the rotor
More informationCase Piezoelectric Vibration Monitor Specifications
Case Piezoelectric Vibratio Moitor Specificatios The Case Piezoelectric Vibratio Moitor is desiged for high reliability for your plat s most critical rotatig machiery moitorig case vibratio from accelerometer
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationData Analysis and Statistical Behaviors of Stock Market Fluctuations
44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:
More informationStat 104 Lecture 2. Variables and their distributions. DJIA: monthly % change, 2000 to Finding the center of a distribution. Median.
Stat 04 Lecture Statistics 04 Lecture (IPS. &.) Outlie for today Variables ad their distributios Fidig the ceter Measurig the spread Effects of a liear trasformatio Variables ad their distributios Variable:
More informationRepeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS
More informationUniversity of California, Los Angeles Department of Statistics. Distributions related to the normal distribution
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chisquare (χ ) distributio.
More informationSystems Design Project: Indoor Location of Wireless Devices
Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 6985295 Email: bcm1@cec.wustl.edu Supervised
More informationBasic Measurement Issues. Sampling Theory and AnalogtoDigital Conversion
Theory ad AalogtoDigital Coversio Itroductio/Defiitios Aalogtodigital coversio Rate Frequecy Aalysis Basic Measuremet Issues Reliability the extet to which a measuremet procedure yields the same results
More informationWhen the rate of heat transfer remains constant during a process
HERMODYNAMICS It has bee poited out that eergy ca either be created or destroyed; it ca oly chage forms. his priciple is the first law of thermodyamics or the coservatio of eergy priciple. Durig a iteractio
More informationChapter 7 Methods of Finding Estimators
Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of
More informationT R A N S F O R M E R A C C E S S O R I E S SAM REMOTE CONTROL SYSTEM
REMOTE CONTROL SYSTEM REMOTE CONTROL SYSTEM TYPE MRCS T R A N S F O R M E R A C C E S S O R I E S PLN.03.08 CODE NO: 720 (20A.) CODE NO: 72400 / 800 (400/800A.) CODE NO: 73000 (000A.). GENERAL This system
More information, a Wishart distribution with n 1 degrees of freedom and scale matrix.
UMEÅ UNIVERSITET Matematiskstatistiska istitutioe Multivariat dataaalys D MSTD79 PA TENTAMEN 00409 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multivariat dataaalys D, 5 poäg.. Assume that
More informationZTEST / ZSTATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
ZTEST / ZSTATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large TTEST / TSTATISTIC: used to test hypotheses about
More informationCHAPTER 3 The Simple Surface Area Measurement Module
CHAPTER 3 The Simple Surface Area Measuremet Module I chapter 2, the quality of charcoal i each batch might chage due to traditioal operatio. The quality test shall be performed before usig it as a adsorbet.
More informationAQA STATISTICS 1 REVISION NOTES
AQA STATISTICS 1 REVISION NOTES AVERAGES AND MEASURES OF SPREAD www.mathsbox.org.uk Mode : the most commo or most popular data value the oly average that ca be used for qualitative data ot suitable if
More informationOverview on SBox Design Principles
Overview o SBox Desig Priciples Debdeep Mukhopadhyay Assistat Professor Departmet of Computer Sciece ad Egieerig Idia Istitute of Techology Kharagpur INDIA 721302 What is a SBox? SBoxes are Boolea
More informationThe Euler Totient, the Möbius and the Divisor Functions
The Euler Totiet, the Möbius ad the Divisor Fuctios Rosica Dieva July 29, 2005 Mout Holyoke College South Hadley, MA 01075 1 Ackowledgemets This work was supported by the Mout Holyoke College fellowship
More information4.1 Sigma Notation and Riemann Sums
0 the itegral. Sigma Notatio ad Riema Sums Oe strategy for calculatig the area of a regio is to cut the regio ito simple shapes, calculate the area of each simple shape, ad the add these smaller areas
More informationNUMERICAL VERIFICATION OF THE RELATIONSHIP BETWEEN THE INPLANE GEOMETRIC CONSTRAINTS USED IN FRACTURE MECHANICS PROBLEMS.
Marci Graba Numerical Verificatio of the Relatioship Betwee he IPlae Geometric CoStraits used i Fracture Mechaics Problems NUMERICAL VERIFICAION OF HE RELAIONSHIP BEWEEN HE INPLANE GEOMERIC CONSRAINS
More informationProblem Set 1 Oligopoly, market shares and concentration indexes
Advaced Idustrial Ecoomics Sprig 2016 Joha Steek 29 April 2016 Problem Set 1 Oligopoly, market shares ad cocetratio idexes 1 1 Price Competitio... 3 1.1 Courot Oligopoly with Homogeous Goods ad Differet
More informationADAPTIVE NETWORKS SAFETY CONTROL ON FUZZY LOGIC
8 th Iteratioal Coferece o DEVELOPMENT AND APPLICATION SYSTEMS S u c e a v a, R o m a i a, M a y 25 27, 2 6 ADAPTIVE NETWORKS SAFETY CONTROL ON FUZZY LOGIC Vadim MUKHIN 1, Elea PAVLENKO 2 Natioal Techical
More informationThe Dynamics of Tibetan Singing Bowls
Iácio, Herique & Atues: he Dyamics of ibeta Sigig Bowls he Dyamics of ibeta Sigig Bowls Octávio Iácio & Luís L. Herique Istituto Politécico do Porto, Escola Superior de Música e Artes do Espectáculo, Musical
More informationModule 2. The Science of Surface and Ground Water. Version 2 CE IIT, Kharagpur
Module The Sciece of Surface ad Groud Water Versio CE IIT, Kharagpur Lesso 8 Flow Dyamics i Ope Chaels ad Rivers Versio CE IIT, Kharagpur Istructioal Objectives O completio of this lesso, the studet shall
More informationNonlife insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
Nolife isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
More informationResearch Method (I) Knowledge on Sampling (Simple Random Sampling)
Research Method (I) Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact
More informationQueuing Systems: Lecture 1. Amedeo R. Odoni October 10, 2001
Queuig Systems: Lecture Amedeo R. Odoi October, 2 Topics i Queuig Theory 9. Itroductio to Queues; Little s Law; M/M/. Markovia BirthadDeath Queues. The M/G/ Queue ad Extesios 2. riority Queues; State
More information9.8: THE POWER OF A TEST
9.8: The Power of a Test CD91 9.8: THE POWER OF A TEST I the iitial discussio of statistical hypothesis testig, the two types of risks that are take whe decisios are made about populatio parameters based
More informationTruStore: The storage. system that grows with you. Machine Tools / Power Tools Laser Technology / Electronics Medical Technology
TruStore: The storage system that grows with you Machie Tools / Power Tools Laser Techology / Electroics Medical Techology Everythig from a sigle source. Cotets Everythig from a sigle source. 2 TruStore
More informationhp calculators HP 12C Statistics  average and standard deviation Average and standard deviation concepts HP12C average and standard deviation
HP 1C Statistics  average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics
More informationWindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12
WidWise Educatio T rasformig the Eergy of Wid ito Powerful Mids A Curriculum for Grades 6 12 Notice Except for educatioal use by a idividual teacher i a classroom settig this work may ot be reproduced
More informationUsing Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N)
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN  Usig Four Types Of Notches For Compariso Betwee Chezy s Costat(C) Ad Maig s Costat (N) Joyce Edwi Bategeleza, Deepak
More informationYour organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:
Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network
More informationLecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009)
18.409 A Algorithmist s Toolkit October 27, 2009 Lecture 13 Lecturer: Joatha Keler Scribe: Joatha Pies (2009) 1 Outlie Last time, we proved the BruMikowski iequality for boxes. Today we ll go over the
More informationMeasures of Central Tendency
Measures of Cetral Tedecy A studet s grade will be determied by exam grades ( each exam couts twice ad there are three exams, HW average (couts oce, fial exam ( couts three times. Fid the average if the
More informationEquation of a line. Line in coordinate geometry. Slopeintercept form ( 斜 截 式 ) Intercept form ( 截 距 式 ) Pointslope form ( 點 斜 式 )
Chapter : Liear Equatios Chapter Liear Equatios Lie i coordiate geometr I Cartesia coordiate sstems ( 卡 笛 兒 坐 標 系 統 ), a lie ca be represeted b a liear equatio, i.e., a polomial with degree. But before
More informationTrigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is
0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values
More informationSection 7: Free electron model
Physics 97 Sectio 7: ree electro model A free electro model is the simplest way to represet the electroic structure of metals. Although the free electro model is a great oversimplificatio of the reality,
More informationCS100: Introduction to Computer Science
Iclass Exercise: CS100: Itroductio to Computer Sciece What is a flipflop? What are the properties of flipflops? Draw a simple flipflop circuit? Lecture 3: Data Storage  Mass storage & represetig
More information7. Sample Covariance and Correlation
1 of 8 7/16/2009 6:06 AM Virtual Laboratories > 6. Radom Samples > 1 2 3 4 5 6 7 7. Sample Covariace ad Correlatio The Bivariate Model Suppose agai that we have a basic radom experimet, ad that X ad Y
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationKey Ideas Section 81: Overview hypothesis testing Hypothesis Hypothesis Test Section 82: Basics of Hypothesis Testing Null Hypothesis
Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, Pvalue Type I Error, Type II Error, Sigificace Level, Power Sectio 81: Overview Cofidece Itervals (Chapter 7) are
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More informationComplex Numbers. where x represents a root of Equation 1. Note that the ± sign tells us that quadratic equations will have
Comple Numbers I spite of Calvi s discomfiture, imagiar umbers (a subset of the set of comple umbers) eist ad are ivaluable i mathematics, egieerig, ad sciece. I fact, i certai fields, such as electrical
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio  Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationConvexity, Inequalities, and Norms
Covexity, Iequalities, ad Norms Covex Fuctios You are probably familiar with the otio of cocavity of fuctios. Give a twicedifferetiable fuctio ϕ: R R, We say that ϕ is covex (or cocave up) if ϕ (x) 0 for
More informationAP Calculus BC 2003 Scoring Guidelines Form B
AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet
More informationWeek 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable
Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5
More informationResearch Article Sign Data Derivative Recovery
Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov
More informationBaan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
More informationKinematic Synthesis of Multifingered Robotic Hands for Finite and Infinitesimal Tasks
Kiematic Sythesis of Multifigered Robotic Hads for Fiite ad Ifiitesimal Tasks E. SimoSerra, A. PerezGracia, H. Moo ad N. Robso Abstract I this paper we preset a ovel method of desigig multifigered
More informationSemiconductor Devices
emicoductor evices Prof. Zbigiew Lisik epartmet of emicoductor ad Optoelectroics evices room: 116 email: zbigiew.lisik@p.lodz.pl Uipolar devices IFE T&C JFET Trasistor Uipolar evices  Trasistors asic
More informationNEW HIGH PERFORMANCE COMPUTATIONAL METHODS FOR MORTGAGES AND ANNUITIES. Yuri Shestopaloff,
NEW HIGH PERFORMNCE COMPUTTIONL METHODS FOR MORTGGES ND NNUITIES Yuri Shestopaloff, Geerally, mortgage ad auity equatios do ot have aalytical solutios for ukow iterest rate, which has to be foud usig umerical
More informationMOLAR MASS of POLYMERS
MOLR MSS of POLYMERS Recogize the ifluece of molar mass (molecular weight) o polymer properties. Uderstad the relatioship betwee molecular weight ad degree of polymerizatio. Uderstad the sigificace of
More informationDOME ROOF OF ABOVEGROUND STEEL TANK WITH V=70000 m 3 CAPACITY. Lyubomir A. Zdravkov 1
DOME ROOF OF ABOVEGROUND STEEL TANK WITH V=70000 m 3 CAPACITY Lyubomir A. Zdrako 1 Abstract: Dome roos are the lightest structure to coer cylidrical taks. Whe they are steel made they could ot be used
More informationChapter 4 Volumetric Flux
Chapter 4 Volumetric Flux We have so far taled about Darcy's law as if it was oe of the fudametal laws of ature. Here we will first describe the origial experimet by Darcy i 856. We will the geeralize
More information1. Introduction. Scheduling Theory
. Itroductio. Itroductio As a idepedet brach of Operatioal Research, Schedulig Theory appeared i the begiig of the 50s. I additio to computer systems ad maufacturig, schedulig theory ca be applied to may
More informationThreedimensional transient and harmonic shearwave scattering by a soft cylinder for dynamic vascular elastography
Threedimesioal trasiet ad harmoic shearwave scatterig by a soft cylider for dyamic vascular elastography Ais Hadj Hei a,b Laboratory of Biorheology ad Medical Ultrasoics, Uiversity of Motreal Hospital
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationTHE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationNormal Distribution.
Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued
More informationVERIFICATION OF MECHANICAL PROPERTIES OF ABS MATERIALS USED IN FDM RAPID PROTOTYPING TECHNOLOGY
Proceedigs i Maufacturig Systems, Volume 8, Issue 2, 2013 ISSN 20679238 VERIFICATION OF MECHANICAL PROPERTIES OF ABS MATERIALS USED IN FDM RAPID PROTOTYPING TECHNOLOGY Ludmila NOVAKOVAMARCINCINOVA 1,*,
More informationStatistical Methods. Chapter 1: Overview and Descriptive Statistics
Geeral Itroductio Statistical Methods Chapter 1: Overview ad Descriptive Statistics Statistics studies data, populatio, ad samples. Descriptive Statistics vs Iferetial Statistics. Descriptive Statistics
More informationVolatility of rates of return on the example of wheat futures. Sławomir Juszczyk. Rafał Balina
Overcomig the Crisis: Ecoomic ad Fiacial Developmets i Asia ad Europe Edited by Štefa Bojec, Josef C. Brada, ad Masaaki Kuboiwa http://www.hippocampus.si/isbn/9789616832328/cotets.pdf Volatility of
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEITCST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal  Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationElementary Theory of Russian Roulette
Elemetary Theory of Russia Roulette iterestig patters of fractios Satoshi Hashiba Daisuke Miematsu Ryohei Miyadera Itroductio. Today we are goig to study mathematical theory of Russia roulette. If some
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More information3 Energy. 3.3. NonFlow Energy Equation (NFEE) Internal Energy. MECH 225 Engineering Science 2
MECH 5 Egieerig Sciece 3 Eergy 3.3. NoFlow Eergy Equatio (NFEE) You may have oticed that the term system kees croig u. It is ecessary, therefore, that before we start ay aalysis we defie the system that
More information