BIFURCATION ANALYSIS FOR A QUASI-LINEAR CENTRIFUGAL PENDULUM ABSORBER
|
|
- Philomena Susanna Clark
- 5 years ago
- Views:
Transcription
1 11 th Intenational Confeence on Vibation Poblems Z. Dimitovová et al. (eds.) Lisbon, Potugal, 9-12 Septembe 213 BIFURCATION ANALYSIS FOR A QUASI-LINEAR CENTRIFUGAL PENDULUM ABSORBER Eugen B. Keme* 1, Mikhail V. Zakzhevsky 2, Igo T. Schukin 3, Alexey V. Klokov 2 1 LuK GmbH & Co. OHG, Gemany eugen.keme@schaeffle.com 2 Institute of Mechanics of Riga Technical Univesity, Latvia mzak@latnet.lv alex_klokov@inbox.lv 3 Daugavpils banch of Riga Technical Univesity, Latvia igo@df.tu.lv Keywods: Centifugal Pendulum Absobe, Complete Bifucation Analysis, Dynamical Stability. Abstact. A vibational pendulum absobe with tapezoidal suspension is a modification of the classical pendulum absobe, which allows not only its tanslational motion but some complex 2D-motion of the pendulum. It povides not only highe pefomances of the absobe, but also some new inteesting featues. About them it is a possibility fo patial compensation of non-lineaity. It allows avoiding the paasite supe-hamonical espond of the pendulum. The bifucation analysis of such a pendulum make possible to estimate effectiveness of a new type pendulum absobe. This pape is a continuation of pevious investigations [1,2] devoted to a pendulum absobe poblem. Main methods used hee ae methods based on the bifucation theoy [3-11] of nonlinea dynamical systems. Among them ae the method of complete bifucation goups with paamete (obit) continuation, concepts of peiodic skeletons with passpots of stable and unstable obits, unstable peiodic infinitiums, detemined chaotic egions and ae attactos. Fo numeical ealization of the bifucation theoy fo pendulum absobe poblem, oiginal softwae is used.
2 1 INTRODUCTION The diect global bifucation analysis of pendulum-like systems is pesented by the main featues and components of a new so-called bifucation theoy of nonlinea dynamics and chaos and its applications. The descibed pat of bifucation theoy uses dynamical peiodic systems, descibed by a model of ODE equations. Ou appoach is based on ideas of Poincaé, Andonov and othe scientists' esults concening stuctual stability and bifucations of diffeent dynamical nonlinea systems and thei topological popeties [3-8]. Fo illustation of the advantages of the new bifucation theoy we use in this pape the pendulum vibation absobe model [1,2] with soft impact (Figue 1,a). We have found impotant unknown egula o chaotic attactos and new bifucation goups with ae attactos. The method of complete bifucation goups gives obust stability to the pendulum vibation absobe by changing the system paametes, that allows saving chaacteistics of the vibation absobe system and excluding othe amazing egimes. Recent effots in nonlinea dynamics of pendulum systems show, that the behaviou of the diven damped pendula may be complex and sometimes with the unexpected phenomena such as stable hilltop vibations, complex subhamonical and quasi-peiodical vibations, diffeent otations and othe [9-11]. Ou aim is doing complete bifucation analysis fo impotant paamete of pendulum vibation absobe systems by using the fundamental concepts of the bifucation theoy: a peiodic skeleton, complete bifucation goup nt, subgoup of unstable peiodic infinitium (UPI), concepts of ae attactos, complex potubeances, typical bifucation topological goups and the topological stuctue of chaotic attactos and chaotic tansients [3-8]. All esults wee obtained numeically, using softwae NLO [3] and SPRING [5], ceated in Riga Technical Univesity. 2 MODEL OF THE PENDULUM ABSORBER The studied nonlinea dynamical model of the pendulum vibation absobe [1,2] with soft impact (see Figue 1,a) is epesented. System has tilinea dissipation and estoing foces (Figue 1,b). The equation of motion fo studied pendulum system is such: f f h cost 1 d 1 2hsint sin, 1 whee angle of the pendulum elative to basic disk (flywheel); angula velocity of the pendulum elative to basic disk, whee d / dt ; b 1, b 2 linea dissipation coefficients, accodingly to linea subegions of visco-elastic chaacteistic; c stiffness coefficient of linea elastic chaacteistic at soft impact in coodinate = ±15º: f b2 1 b2 if b if ; if f 1 (1) c if if, (2) c if atio of moments of inetia of the pendulum and disk (<1); h moment fom the moto (oscillating component) (h 1.5); excitation ode ( = 2 o 3, espectively fo 4-cylinde and 6-cylinde engine); d eo in setting up the pendulum vibation absobe at antiesonance (-.1 d.1). The vaiable paamete of the pendulum system Eq.1 is moment fom the moto h = and excitation ode = The base paametes fo analysis ae: =.1, b 1 =.2, b 2 = 5, c = 5, d =, h =.5. 2
3 3 CONSTRUCTION OF PERIODIC SKELETON FOR BASE PARAMETERS OF THE PENDULUM ABSORBER Befoe the constuction of complete bifucation diagams, peiodic skeleton fo base paametes of the pendulum vibation absobe was build. (a) (b) Figue 1: (a) A flywheel with pendulum vibation absobe with soft impact; (b) elastic dissipation foces chaacteistics and dependence of dissipation coefficient on state of system. Fom the gid of 2 2 = 4 initial conditions inside the ectangle (-/12; -1/ /12; 1) we have obtained peiodic skeleton [2] consisted fom 17 egimes (one unstable egime; one unstable P2 egime; fou P4 egimes two of them ae stable; two unstable P5 egimes; two unstable P6 egimes; one unstable P7 egime; one unstable P8 egime; thee unstable P9 egimes; one unstable 1 egime and one unstable) fo h =.5 and = 3 with egime scanning fo peiod fom 1 till 16 by using the Newton-Kantoovich method. By using the Poincaé map founded egimes can be specified by data of the solution (obit) ode, by the numbe of loops in the pojection of the phase tajectoies, the coodinates of the fixed point and stability chaacteistics. Fo example, 1 (1/1), Fixed point ( , ), 1 = -.781, 2 = This is the main passpot of peiodic egime (at a given point of the paamete space of the system). The examples of extended passpot of peiodic egimes with phase pojections and time histoies ae shown in [2,11]. 4 COMPLETE BIFURCATION ANALYSIS OF PENDULUM VIBRATION ABSORBER HEADINGS The constuction of bifucation diagams was done by the Runge-Kutta 4-th ode with constant integation step: t = T /2 k, whee the peiod of extenal foce is T = 2/ and coefficient k = 7. The esults of complete bifucation analysis of the pendulum vibation absobe model ae epesented in bifucation diagams of the fixed peiodic points of the coodinates p, p and Am vesus paamete h (Figue 2). Thee ae two 1T bifucations goups: 1T (with depth - P2) with complex potubeances and 1T isle. The pendulum system has many RA of diffeent kinds. In this figue stable solutions ae plotted by solid lines and unstable - by thin lines (eddish online). The banches of bifucation diagam ae not completed, because of poblem of high instability. 3
4 p (a) =.1, b 1 =.2, b 2 = 5, c = 5, = 3, d =, h = va. 1T bifucation goups P2 P2 isle stable egimes unstable egimes.28 Am.27 (b) Fagment P2 isle h =.1, b 1 =.2, b 2 = 5, c = 5, = 3, d =, h = va. h Figue 2: Pendulum vibation absobe with soft impact (see Eq.1 and Figue 1,a). Bifucation diagams of the fixed peiodic points of the coodinates p, p and Am vesus paamete h. Thee ae two 1T bifucations goups: 1T (with depth -P2) with complex potubeances and 1T isle. The pendulum system has many ae attactos of diffeent kinds. Paametes: =.1, b 1 =.2, b 2 = 5, c = 5, = 3, d =, h = va. (a) h = (b) h = isle NT = 3T NT = 3T Figue 3: Coexistence of ae attacto and isle fo h = Phase pojections with NT = 3T. 4
5 (a) b 1 =.2, b 2 = 5, = 3, h = 1.47 NT = (5-1)T ChA Cm 4 1Q 1T (b) h = 1.47 NT = 3T (c) h = 1.47 NT = 3T = -.12, = = -.12, = t Figue 4: Chaotic attacto in pendulum absobe fo h = 1.47: () Poincaé map fom a contou Cm 4 1Q (5-1)T; (b)-(c) phase pojection and time histoies with fom initial conditions = -.12, = -1.26;. The example of coexistence of ae attacto () with peiod-1 and isle attacto fo coss-section h = of bifucation diagam (Figue 2) on phases pojections is shown in Figue 3. Sometimes oscillation amplitudes of ae attactos ae tenfold bigge than oscillating amplitudes of stable egimes [2,1,11]. Rae attacto has highe velocity of oscillations than isle. In ou case oscillation amplitudes ae limited by two elastic detents, which ealise soft impacts. The example of globally stable chaotic attacto fo coss-section h = 1.47 of bifucation diagam (Figue 2) obtained using the contou mapping Cm 4 1Q (5-1)T fom a contou (-.4,-3/.4,2), phase pojection and time histoies with NT = 3T fom initial conditions = -.12, = -1.26, is shown in Figue 4. 5 CONCLUSIONS The pendulum systems ae widely used in the engineeing, but thei qualitative behavio hasn t been investigated enough. Theefoe in this wok the new nonlinea effects in pendulum vibation absobe, which can be used in dynamics of the machines and mechanisms, wee shown. MCBG gives obust stability to the studied vibation absobe system by changing the system paametes, which allows saving chaacteistics of the vibation absobe system and excluding othe amazing egimes, which can lead to small beakages of machine and mechanisms and may be to global technical catastophes, because they ae unexpected and usually have lage amplitudes. This wok is peliminay, because it will be continued fo the nonlinea dynamical systems with two o seveal degees of feedom. 5
6 ACKNOWLEDGMENT This wok has been suppoted by the Euopean Social Fund within the poject Suppot fo the implementation of doctoal studies at Riga Technical Univesity and by the Latvian Council of Science unde the gants (21-212). REFERENCES [1] Kause T., Keme E., Movlazada P., Theoy and Simulation of Centifugal Pendulum Absobe with Tapezoidal Suspension, Poceedings of the 1th Intenational Confeence on Vibation Poblems, Pague, Czech Republic (211) [2] Keme E., Zakzhevsky M., Klokov, Complete Bifucation Analysis with Rae Attactos of a Pendulum Vibation Absobe, The 4th IEEE Intenational Confeence on Nonlinea Science and Complexity NSC 212, Budapest, Hungay (212) [3] Zakzhevsky M., Ivanov Y. and Folov V. NLO: Univesal Softwae fo Global Analysis of Nonlinea Dynamics and Chaos. // In Poceeding of the 2nd ENOC, Pague, Septembe , pp [4] Zakzhevsky M., New concepts of nonlinea dynamics: complete bifucation goups, potubeances, unstable peiodic infinitiums and ae attactos. // Jounal of Viboengineeing - JVE 1, Issue 4, 12 (28), [5] Schukin I., Development of the methods and algoithms of simulation of nonlinea dynamics poblems. Bifucations, chaos and ae attactos. // PhD Thesis), Riga - Daugavpils, Latvia (25), 25 p. [6] Zakzhevsky M., Global Nonlinea Dynamics Based on the Method of Complete Bifucation Goups and Rae Attactos. // Poceedings of the ASME 29 (IDETC/CIE 29), CD, San Diego, USA (29), 8 p. [7] Zakzhevsky M., How to Find Rae Peiodic and Rae Chaotic Attactos? Abstacts of the 8th AIMS Intenational Confeence, Desden, Gemany (21), 9 p. [8] Zakzhevsky M. Bifucation Theoy of Nonlinea Dynamics and Chaos. Peiodic Skeletons and Rae Attactos. // Poceedings of the 2nd Intenational Symposium RA 11 on Rae Attactos and Rae Phenomena in Nonlinea Dynamics, May 16-2, 211, Riga - Jumala, Latvia, pp [9] Klokov A., Zakzhevsky M. Nonlinea Dynamics and Rae Attactos of the Pendulum with the Vetical Vibating Point of Suspension // Poceedings of the 2nd Intenational Symposium RA 11 on Rae Attactos and Rae Phenomena in Nonlinea Dynamics, May 16-2, 211, Riga - Jumala, Latvia, pp [1] Klokov A., Zakzhevsky M., Paametically excited pendulum systems with seveal equilibium positions. Bifucation analysis and ae attactos. // Intenational Jounal of Bifucation and Chaos, - Vol. 21, No. 1 (211) pp [11] Zakzhevsky M.V. and Klokov A.V., How to find ae attactos in nonlinea dynamical systems by the method of complete bifucation goups. The collection of the pendulum diven systems. Riga, p. 6
A NEW VARIABLE STIFFNESS SPRING USING A PRESTRESSED MECHANISM
Poceedings of the ASME 2010 Intenational Design Engineeing Technical Confeences & Computes and Infomation in Engineeing Confeence IDETC/CIE 2010 August 15-18, 2010, Monteal, Quebec, Canada DETC2010-28496
More informationSAMPLING DELAY AND BACKLASH IN BALANCING SYSTEMS
PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 44, NO., PP. 77 84 () SAMPLING DELAY AND BACKLASH IN BALANCING SYSTEMS László E. KOLLÁR, Gáo STÉPÁN and S. John HOGAN Depatment of Applied Mechanics Technical
More informationHydroelastic Analysis of a 1900 TEU Container Ship Using Finite Element and Boundary Element Methods
TEAM 2007, Sept. 10-13, 2007,Yokohama, Japan Hydoelastic Analysis of a 1900 TEU Containe Ship Using Finite Element and Bounday Element Methods Ahmet Egin 1)*, Levent Kaydıhan 2) and Bahadı Uğulu 3) 1)
More informationDuality between Statical and Kinematical Engineering Systems
Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.
More informationBifurcation Analysis for the Delay Logistic Equation with Two Delays
IOSR Jounal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 5 Ve. IV (Sep. - Oct. 05), PP 53-58 www.iosjounals.og Bifucation Analysis fo the Delay Logistic Equation with Two Delays
More informationANALYSIS OF QUANTUM EIGENSTATES IN A 3-MODE SYSTEM
AAYSIS OF QUATUM EIGESTATES I A 3-MODE SYSTEM SRIHARI KESHAVAMURTHY AD GREGORY S. EZRA Depatment of Chemisty, Bake aboatoy Conell Univesity, Ithaca, Y 14853, USA. Abstact. We study the quantum eigenstates
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationME 3600 Control Systems Frequency Domain Analysis
ME 3600 Contol Systems Fequency Domain Analysis The fequency esponse of a system is defined as the steady-state esponse of the system to a sinusoidal (hamonic) input. Fo linea systems, the esulting steady-state
More informationyou of a spring. The potential energy for a spring is given by the parabola U( x)
Small oscillations The theoy of small oscillations is an extemely impotant topic in mechanics. Conside a system that has a potential enegy diagam as below: U B C A x Thee ae thee points of stable equilibium,
More informationSTABILITY AND PARAMETER SENSITIVITY ANALYSES OF AN INDUCTION MOTOR
HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY VESZPRÉM Vol. 42(2) pp. 109 113 (2014) STABILITY AND PARAMETER SENSITIVITY ANALYSES OF AN INDUCTION MOTOR ATTILA FODOR 1, ROLAND BÁLINT 1, ATTILA MAGYAR 1, AND
More informationtime [s] time [s]
ROBUST ATTITUDE STABILIZATION OF AN UNDERACTUATED AUV K. Y. Pettesen and O. Egeland Depatment of Engineeing Cybenetics Nowegian Univesity of Science and Technology N- Tondheim, Noway Fax: + 9 99 E-mail:
More informationBifurcation Routes and Economic Stability Miloslav S. Vosvrda
Bifucation Routes and Economic Stability Miloslav S. Vosvda Institute of Infomation Theoy and Automation, Academy of Sciences of the Czech Republic Institute of Economic Studies, Faculty of Social Sciences,
More informationUsing Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu
Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of
More informationCOUPLED MODELS OF ROLLING, SLIDING AND WHIRLING FRICTION
ENOC 008 Saint Petesbug Russia June 30-July 4 008 COUPLED MODELS OF ROLLING SLIDING AND WHIRLING FRICTION Alexey Kieenkov Ins ti tu te fo P ob le ms in Me ch an ic s Ru ss ia n Ac ad em y of Sc ie nc es
More informationMATH 415, WEEK 3: Parameter-Dependence and Bifurcations
MATH 415, WEEK 3: Paamete-Dependence and Bifucations 1 A Note on Paamete Dependence We should pause to make a bief note about the ole played in the study of dynamical systems by the system s paametes.
More informationDesigning a Sine-Coil for Measurement of Plasma Displacements in IR-T1 Tokamak
Designing a Sine-Coil fo Measuement of Plasma Displacements in IR-T Tokamak Pejman Khoshid, M. Razavi, M. Ghoanneviss, M. Molaii, A. TalebiTahe, R. Avin, S. Mohammadi and A. NikMohammadi Dept. of Physics,
More informationUNKNOWN BIFURCATION GROUPS WITH CHAOTIC AND RARE ATTRACTORS IN THE DUFFING-UEDA AND DUFFING - VAN DER POL ARCHETYPAL OSCILLATORS
11 th International Conference on Vibration Problems Z. Dimitrovová et al. (eds.) Lisbon, Portugal, 9-12 September 2013 UNKNOWN BIFURCATION GROUPS WITH CHAOTIC AND RARE ATTRACTORS IN THE DUFFING-UEDA AND
More informationIdentification of the degradation of railway ballast under a concrete sleeper
Identification of the degadation of ailway ballast unde a concete sleepe Qin Hu 1) and Heung Fai Lam ) 1), ) Depatment of Civil and Achitectual Engineeing, City Univesity of Hong Kong, Hong Kong SAR, China.
More informationChapter 7-8 Rotational Motion
Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,
More informationTHE INFLUENCE OF TEMPERATURE S CHANGE ALONG THE RADIUS ON THE MEMBRANE STRESSES FIELD AT ROTATING DISKS
6 th Intenational Confeence Computational Mechanics and Vitual Engineeing COMEC 015 15-16 Octobe 015, Başov, Romania HE INFLUENCE OF EMPERAURE S CHANGE ALONG HE RADIUS ON HE MEMBRANE SRESSES FIELD A ROAING
More informationELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS
THE 9 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS ELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS R. Sbulati *, S. R. Atashipou Depatment of Civil, Chemical and Envionmental Engineeing,
More informationChaos and bifurcation of discontinuous dynamical systems with piecewise constant arguments
Malaya Jounal of Matematik ()(22) 4 8 Chaos and bifucation of discontinuous dynamical systems with piecewise constant aguments A.M.A. El-Sayed, a, and S. M. Salman b a Faculty of Science, Aleandia Univesity,
More informationResidual Modes on Non-linear Resonant Decay Method
Residual Modes on Non-linea Resonant Decay Method D Mehdi Samast, Pofesso Jan R. Wight ABSRAC Non-linea Resonant Decay method (NL-RDM) addesses the identification of multi-degee of feedom non-linea systems.
More informationDonnishJournals
DonnishJounals 041-1189 Donnish Jounal of Educational Reseach and Reviews. Vol 1(1) pp. 01-017 Novembe, 014. http:///dje Copyight 014 Donnish Jounals Oiginal Reseach Pape Vecto Analysis Using MAXIMA Savaş
More informationAnalysis of high speed machining center spindle dynamic unit structure performance Yuan guowei
Intenational Confeence on Intelligent Systems Reseach and Mechatonics Engineeing (ISRME 0) Analysis of high speed machining cente spindle dynamic unit stuctue pefomance Yuan guowei Liaoning jidian polytechnic,dan
More informationReliability analysis examples
Reliability analysis examples Engineeing Risk Analysis Goup, Technische Univesität München. Acisst., 80 Munich, Gemany. May 8, 08 Intoduction In the context of eliability analysis and ae event estimation,
More informationA scaling-up methodology for co-rotating twin-screw extruders
A scaling-up methodology fo co-otating twin-scew extudes A. Gaspa-Cunha, J. A. Covas Institute fo Polymes and Composites/I3N, Univesity of Minho, Guimaães 4800-058, Potugal Abstact. Scaling-up of co-otating
More informationNUMERICAL SIMULATION OF FLUID FLOW IN ENCLOSED ROTATING FILTER AND DISK
VOL., NO. 9, SEPTEMBER 010 ISSN 1819-6608 ARPN Jounal of Engineeing and Applied Sciences 006-010 Asian Reseach Publishing Netwok (ARPN). All ights eseved. www.apnjounals.com NUMERICAL SIMULATION OF FLUID
More informationLINEAR AND NONLINEAR ANALYSES OF A WIND-TUNNEL BALANCE
LINEAR AND NONLINEAR ANALYSES O A WIND-TUNNEL INTRODUCTION BALANCE R. Kakehabadi and R. D. Rhew NASA LaRC, Hampton, VA The NASA Langley Reseach Cente (LaRC) has been designing stain-gauge balances fo utilization
More informationUniversity of Huddersfield Repository
Univesity of Huddesfield Repositoy Kolla, László E., Stepan, Gao and Hogan, S.J. Backlash in alancing systems using appoximate sping chaacteistics Oiginal Citation Kolla, László E., Stepan, Gao and Hogan,
More informationHigh precision computer simulation of cyclotrons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D.
High pecision compute simulation of cyclotons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D. Abstact Effective and accuate compute simulations ae highly impotant in acceleatos design and poduction.
More informationarxiv:physics/ v2 [physics.soc-ph] 11 Mar 2005
Heide Balance in Human Netwoks P. Gawoński and K. Ku lakowski axiv:physics/5385v2 [physics.soc-ph] 11 Ma 25 Depatment of Applied Compute Science, Faculty of Physics and Applied Compute Science, AGH Univesity
More informationA Three-Dimensional Magnetic Force Solution Between Axially-Polarized Permanent-Magnet Cylinders for Different Magnetic Arrangements
Poceedings of the 213 Intenational Confeence on echanics, Fluids, Heat, Elasticity Electomagnetic Fields A Thee-Dimensional agnetic Foce Solution Between Axially-Polaied Pemanent-agnet Cylindes fo Diffeent
More informationJ. Electrical Systems 1-3 (2005): Regular paper
K. Saii D. Rahem S. Saii A Miaoui Regula pape Coupled Analytical-Finite Element Methods fo Linea Electomagnetic Actuato Analysis JES Jounal of Electical Systems In this pape, a linea electomagnetic actuato
More informationSteady State and Transient Performance Analysis of Three Phase Induction Machine using MATLAB Simulations
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9 Steady State and Tansient Pefomance Analysis of Thee Phase Induction Machine using MATAB Simulations Pof. Himanshu K. Patel Assistant
More informationPearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms
Peason s Chi-Squae Test Modifications fo Compaison of Unweighted and Weighted Histogams and Two Weighted Histogams Univesity of Akueyi, Bogi, v/noduslód, IS-6 Akueyi, Iceland E-mail: nikolai@unak.is Two
More informationAPPLICATION OF MAC IN THE FREQUENCY DOMAIN
PPLICION OF MC IN HE FREQUENCY DOMIN D. Fotsch and D. J. Ewins Dynamics Section, Mechanical Engineeing Depatment Impeial College of Science, echnology and Medicine London SW7 2B, United Kingdom BSRC he
More informationApplication of homotopy perturbation method to the Navier-Stokes equations in cylindrical coordinates
Computational Ecology and Softwae 5 5(): 9-5 Aticle Application of homotopy petubation method to the Navie-Stokes equations in cylindical coodinates H. A. Wahab Anwa Jamal Saia Bhatti Muhammad Naeem Muhammad
More informationThree-dimensional Quantum Cellular Neural Network and Its Application to Image Processing *
Thee-dimensional Quantum Cellula Neual Netwok and Its Application to Image Pocessing * Sen Wang, Li Cai, Huanqing Cui, Chaowen Feng, Xiaokuo Yang Science College, Ai Foce Engineeing Univesity Xi an 701,
More informationPhysics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
More informationCalculation of Quark-antiquark Potential Coefficient and Charge Radius of Light Mesons
Applied Physics Reseach ISSN: 96-9639 Vol., No., May E-ISSN: 96-9647 Calculation of Quak-antiquak Potential Coefficient and Chage Radius of Light Mesons M.R. Shojaei (Coesponding autho ) Depatment of Physics
More informationFuzzy Sliding Mode Speed Controller Design of Induction Motor Drives
Poceedings of the Intenational Confeence on Industial Engineeing and Opeations Management Istanbul, Tukey, July 3 6, Fuzzy Sliding Mode Speed Contolle Design of Induction Moto Dives F. Nacei, T. Laamayad
More informationStress, Cauchy s equation and the Navier-Stokes equations
Chapte 3 Stess, Cauchy s equation and the Navie-Stokes equations 3. The concept of taction/stess Conside the volume of fluid shown in the left half of Fig. 3.. The volume of fluid is subjected to distibuted
More informationHandout: IS/LM Model
Econ 32 - IS/L odel Notes Handout: IS/L odel IS Cuve Deivation Figue 4-4 in the textbook explains one deivation of the IS cuve. This deivation uses the Induced Savings Function fom Chapte 3. Hee, I descibe
More informationDynamics of Rotating Discs
Dynamics of Rotating Discs Mini Poject Repot Submitted by Subhajit Bhattachaya (0ME1041) Unde the guidance of Pof. Anivan Dasgupta Dept. of Mechanical Engineeing, IIT Khaagpu. Depatment of Mechanical Engineeing,
More informationQUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER
QUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER Jey N. Baham Anand B. Shetty Mechanical Kinesiology Laboatoy Depatment of Kinesiology Univesity of Nothen Coloado Geeley, Coloado Muscle powe is one
More informationThermo-Mechanical Model for Wheel Rail Contact using Coupled. Point Contact Elements
IM214 28-3 th July, ambidge, England hemo-mechanical Model fo heel Rail ontact using oupled Point ontact Elements *J. Neuhaus¹ and. Sexto 1 1 hai of Mechatonics and Dynamics, Univesity of Padebon, Pohlweg
More informationRigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining
More informationPARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER
ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA PARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER S. Kuz*,
More informationEffect of Downstream Flapping Plate on the Flow Field Characteristics behind a Circular Cylinder
Poceedings of the 3 d Intenational Confeence on Fluid Flow, Heat and Mass Tansfe (FFHMT 16) Ottawa, Canada May 2 3, 2016 Pape No. 169 Effect of Downsteam Flapping Plate on the Flow Field Chaacteistics
More informationInternational Journal of Mathematical Archive-3(12), 2012, Available online through ISSN
Intenational Jounal of Mathematical Achive-3(), 0, 480-4805 Available online though www.ijma.info ISSN 9 504 STATISTICAL QUALITY CONTROL OF MULTI-ITEM EOQ MOEL WITH VARYING LEAING TIME VIA LAGRANGE METHO
More informationAH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion
AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed
More information7.2.1 Basic relations for Torsion of Circular Members
Section 7. 7. osion In this section, the geomety to be consideed is that of a long slende cicula ba and the load is one which twists the ba. Such poblems ae impotant in the analysis of twisting components,
More informationAn Adaptive Neural-Network Model-Following Speed Control of PMSM Drives for Electric Vehicle Applications
Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp412-417) An Adaptive Neual-Netwo Model-Following Speed Contol of PMSM Dives fo Electic Vehicle
More informationConservative Averaging Method and its Application for One Heat Conduction Problem
Poceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING and ENVIRONMENT Elounda Geece August - 6 (pp6-) Consevative Aveaging Method and its Application fo One Heat Conduction Poblem
More informationParticle Systems. University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell
Paticle Systems Univesity of Texas at Austin CS384G - Compute Gaphics Fall 2010 Don Fussell Reading Requied: Witkin, Paticle System Dynamics, SIGGRAPH 97 couse notes on Physically Based Modeling. Witkin
More informationLevitation force analysis of ring and disk shaped permanent magnet-high temperature superconductor
Inn Jounal of Pue & Applied Physics Vol. 55, Apil 017, pp. 61-68 Levitation foce analysis of ing and disk shaped pemanent magnet-high tempeatue supeconducto Sinan Basaan & Selim Sivioglu* Depatment of
More informationPhysics 161 Fall 2011 Extra Credit 2 Investigating Black Holes - Solutions The Following is Worth 50 Points!!!
Physics 161 Fall 011 Exta Cedit Investigating Black Holes - olutions The Following is Woth 50 Points!!! This exta cedit assignment will investigate vaious popeties of black holes that we didn t have time
More informationPeriodic Skeletons of Nonlinear Dynamical Systems in the Problems of Global Bifurcation Analysis
Periodic Skeletons of Nonlinear Dynamical Systems in the Problems of Global Bifurcation Analysis M Zakrzhevsky, I Schukin, A Klokov and E Shilvan PERIODIC SKELETONS OF NONLINEAR DYNAMICAL SYSTEMS IN THE
More informationRight-handed screw dislocation in an isotropic solid
Dislocation Mechanics Elastic Popeties of Isolated Dislocations Ou study of dislocations to this point has focused on thei geomety and thei ole in accommodating plastic defomation though thei motion. We
More informationTransverse Wakefield in a Dielectric Tube with Frequency Dependent Dielectric Constant
ARDB-378 Bob Siemann & Alex Chao /4/5 Page of 8 Tansvese Wakefield in a Dielectic Tube with Fequency Dependent Dielectic Constant This note is a continuation of ARDB-368 that is now extended to the tansvese
More informationModeling of High Temperature Superconducting Tapes, Arrays and AC Cables Using COMSOL
Except fom the Poceedings of the COMSOL Confeence 2010 Pais Modeling of High Tempeatue Supeconducting Tapes, Aays and AC Cables Using COMSOL Oleg Chevtchenko * Technical Univesity of Delft, The Nethelands
More informationSafety variations in steel designed using Eurocode 3
JCSS Wokshop on eliability Based Code Calibation Safety vaiations in steel designed using Euocode 3 Mike Byfield Canfield Univesity Swindon, SN6 8LA, UK David Nethecot Impeial College London SW7 2BU, UK
More informationAnalytical time-optimal trajectories for an omni-directional vehicle
Analytical time-optimal tajectoies fo an omni-diectional vehicle Weifu Wang and Devin J. Balkcom Abstact We pesent the fist analytical solution method fo finding a time-optimal tajectoy between any given
More informationNATURAL CONVECTION HEAT TRANSFER WITHIN VERTICALLY ECCENTRIC DOMED SKYLIGHTS CAVITIES
Poceedings: Building Simulation 007 NATURAL CONVECTION HEAT TRANSFER WITHIN VERTICALLY ECCENTRIC DOMED SKYLIGHTS CAVITIES A. Satipi, A. Laouadi, D. Naylo 3, R. Dhib 4 Depatment of Mechanical and Industial
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationAn Exact Solution of Navier Stokes Equation
An Exact Solution of Navie Stokes Equation A. Salih Depatment of Aeospace Engineeing Indian Institute of Space Science and Technology, Thiuvananthapuam, Keala, India. July 20 The pincipal difficulty in
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights
More informationIdentification of the Hardening Curve Using a Finite Element Simulation of the Bulge Test
Manuscipt No.72 Abdessalem Chamekh, Hédi Bel Hadj Salah, Mohamed Amen Gahbiche, Abdelmejid Ben Amaa & Abdelwaheb Dogui Identification of the Hadening Cuve Using a Finite Element Simulation of the Bulge
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to
More informationAnalytical Solutions for Confined Aquifers with non constant Pumping using Computer Algebra
Poceedings of the 006 IASME/SEAS Int. Conf. on ate Resouces, Hydaulics & Hydology, Chalkida, Geece, May -3, 006 (pp7-) Analytical Solutions fo Confined Aquifes with non constant Pumping using Compute Algeba
More informationExplosive Contagion in Networks (Supplementary Information)
Eplosive Contagion in Netwoks (Supplementay Infomation) Jesús Gómez-Gadeñes,, Laua Loteo, Segei N. Taaskin, and Fancisco J. Péez-Reche Institute fo Biocomputation and Physics of Comple Systems (BIFI),
More informationRelating Branching Program Size and. Formula Size over the Full Binary Basis. FB Informatik, LS II, Univ. Dortmund, Dortmund, Germany
Relating Banching Pogam Size and omula Size ove the ull Binay Basis Matin Saueho y Ingo Wegene y Ralph Wechne z y B Infomatik, LS II, Univ. Dotmund, 44 Dotmund, Gemany z ankfut, Gemany sauehof/wegene@ls.cs.uni-dotmund.de
More informationFREE TRANSVERSE VIBRATIONS OF NON-UNIFORM BEAMS
Please cite this aticle as: Izabela Zamosa Fee tansvese vibations of non-unifom beams Scientific Reseach of the Institute of Mathematics and Compute Science Volume 9 Issue pages 3-9. The website: http://www.amcm.pcz.pl/
More informationOn the ratio of maximum and minimum degree in maximal intersecting families
On the atio of maximum and minimum degee in maximal intesecting families Zoltán Lóánt Nagy Lale Özkahya Balázs Patkós Máté Vize Septembe 5, 011 Abstact To study how balanced o unbalanced a maximal intesecting
More informationThe evolution of the phase space density of particle beams in external fields
The evolution of the phase space density of paticle beams in extenal fields E.G.Bessonov Lebedev Phys. Inst. RAS, Moscow, Russia, COOL 09 Wokshop on Beam Cooling and Related Topics August 31 Septembe 4,
More informationVECTOR MECHANICS FOR ENGINEERS: STATICS
4 Equilibium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Fedinand P. Bee E. Russell Johnston, J. of Rigid Bodies Lectue Notes: J. Walt Ole Texas Tech Univesity Contents Intoduction Fee-Body Diagam
More informationPrecessing Ball Solitons as Self-Organizing Systems during a Phase Transition in a Ferromagnet
Applied Mathematics,, 4, 78-8 http://dxdoiog/46/am4a Published Online Octobe (http://wwwscipog/jounal/am) Pecessing Ball Solitons as Self-Oganiing Systems duing a Phase Tansition in a Feomagnet V V Niet
More informationAnalytical periodic motions and bifurcations in a nonlinear rotor system
Int. J. Dynam. Contol 4 2:425 459 DOI.7/s4435-3-55-4 nalytical peiodic motions and bifucations in a nonlinea oto system Jianzhe Huang lbet C. J. Luo Received: 5 Octobe 3 / Revised: 26 Decembe 3 / ccepted:
More informationChapter 12. Kinetics of Particles: Newton s Second Law
Chapte 1. Kinetics of Paticles: Newton s Second Law Intoduction Newton s Second Law of Motion Linea Momentum of a Paticle Systems of Units Equations of Motion Dynamic Equilibium Angula Momentum of a Paticle
More information1D2G - Numerical solution of the neutron diffusion equation
DG - Numeical solution of the neuton diffusion equation Y. Danon Daft: /6/09 Oveview A simple numeical solution of the neuton diffusion equation in one dimension and two enegy goups was implemented. Both
More informationANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE
THE p-adic VALUATION OF STIRLING NUMBERS ANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE Abstact. Let p > 2 be a pime. The p-adic valuation of Stiling numbes of the
More informationLocalization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix
Jounal of Sciences, Islamic Republic of Ian (): - () Univesity of Tehan, ISSN - http://sciencesutaci Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matix H Ahsani
More informationGraphs of Sine and Cosine Functions
Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the
More informationComplete bifurcation analysis of driven damped pendulum systems
Estonian Journal of Engineering, 0, 7,, 76 87 doi: 0.376/eng.0..08 Complete bifurcation analysis of driven damped pendulum systems Mikhail Zakrzhevsky, Alex Кlokov, Vladislav Yevstignejev and Eduard Shilvan
More informationDo Managers Do Good With Other People s Money? Online Appendix
Do Manages Do Good With Othe People s Money? Online Appendix Ing-Haw Cheng Haison Hong Kelly Shue Abstact This is the Online Appendix fo Cheng, Hong and Shue 2013) containing details of the model. Datmouth
More informationMagnetic Field. Conference 6. Physics 102 General Physics II
Physics 102 Confeence 6 Magnetic Field Confeence 6 Physics 102 Geneal Physics II Monday, Mach 3d, 2014 6.1 Quiz Poblem 6.1 Think about the magnetic field associated with an infinite, cuent caying wie.
More informationCentral Force Motion
Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More informationDiffusion and Transport. 10. Friction and the Langevin Equation. Langevin Equation. f d. f ext. f () t f () t. Then Newton s second law is ma f f f t.
Diffusion and Tanspot 10. Fiction and the Langevin Equation Now let s elate the phenomena of ownian motion and diffusion to the concept of fiction, i.e., the esistance to movement that the paticle in the
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions A ing of adius a has a chage distibution on it that vaies as l(q) l sin q, as shown in Figue -9. (a) What is the diection of the electic field
More informationEFFECTS OF GFRP REINFORCING REBARS ON SHRINKAGE AND THERMAL STRESSES IN CONCRETE
EFFECTS OF GFRP REINFORCING REBARS ON SHRINKAGE AND THERMAL STRESSES IN CONCRETE Roge H. L. Chen 1 and Jeong-Hoon Choi 2 ABSTRACT The use of Glass Fibe Reinfoced Polyme (GFRP) ebas instead of conventional
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation
More informationI. CONSTRUCTION OF THE GREEN S FUNCTION
I. CONSTRUCTION OF THE GREEN S FUNCTION The Helmohltz equation in 4 dimensions is 4 + k G 4 x, x = δ 4 x x. In this equation, G is the Geen s function and 4 efes to the dimensionality. In the vey end,
More informationLab 10: Newton s Second Law in Rotation
Lab 10: Newton s Second Law in Rotation We can descibe the motion of objects that otate (i.e. spin on an axis, like a popelle o a doo) using the same definitions, adapted fo otational motion, that we have
More informationStress Intensity Factor
S 47 Factue Mechanics http://imechanicaog/node/7448 Zhigang Suo Stess Intensity Facto We have modeled a body by using the linea elastic theoy We have modeled a cack in the body by a flat plane, and the
More informationSolving Some Definite Integrals Using Parseval s Theorem
Ameican Jounal of Numeical Analysis 4 Vol. No. 6-64 Available online at http://pubs.sciepub.com/ajna///5 Science and Education Publishing DOI:.69/ajna---5 Solving Some Definite Integals Using Paseval s
More information[2007] IEEE. Reprinted, with permission, from [Jiaxin Chen, Jianguo Zhu, Youguang Guo, A 2-D nonlinear FEA tool embedded in Matlab/Simulink
[2007] IEEE. Repinted, with pemission, fom [Jiaxin Chen, Jianguo Zhu, Youguang Guo, A 2-D nonlinea FEA tool embedded in Matlab/Simulin suounding fo application of electomagnetic field analysis in powe
More informationMagneto-Elastic Analysis of an Annular FGM Plate Based on Classical Plate Theory Using GDQ Method
736 Magneto-Elastic Analysis of an Annula FGM Plate Based on Classical Plate Theoy Using GDQ Method Abstact Using GDQ method, the adial and cicumfeential stesses in an annula FGM plate with a unifom thickness
More informationA dual-reciprocity boundary element method for axisymmetric thermoelastodynamic deformations in functionally graded solids
APCOM & ISCM 11-14 th Decembe, 013, Singapoe A dual-ecipocity bounday element method fo axisymmetic themoelastodynamic defomations in functionally gaded solids *W. T. Ang and B. I. Yun Division of Engineeing
More information