Lecture 8 Modal Analysis
|
|
- Mark Ramsey
- 6 years ago
- Views:
Transcription
1 Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal ANSYS, Inc. February 27, 2015
2 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal wll be covered. Chapter Contents: A. Bascs of Free Vbraton B. Theory and Assumpton C. Geometry D. Contact E. Soluton Setup F. Modal Results G. Vbraton Wth Prestress H. Workshop 8.1, Free Vbraton Machne Frame 2
3 A. Bascs of Free Vbraton The free vbraton analyss procedure s very smlar to performng a lnear statc analyss, so not all steps wll be covered n detal. The schematc setup for modal (free vbraton) s shown here. Later a prestressed modal setup wll be covered. 3
4 B. Theory and Assumptons The lnear equaton of moton for free, un-damped vbraton s Assume harmonc moton: M u K u 0 u sn t 2 u sn t Substtutng {u} and {u} In the governng equaton gves an egenvalue equaton: 2 K M 0 4
5 Theory and Assumptons As shown on prevous slde, for vbraton analyss, the natural crcular frequences and mode shapes are calculated from: Assumptons for modal analyss: [K] and [M] are constant: Lnear elastc materal behavor s assumed K 2 M 0 Small deflecton theory s used, and no nonlneartes ncluded [C] s not present, so dampng s not ncluded {F} s not present, so no exctaton of the structure s assumed The structure can be constraned or unconstraned Mode shapes { } are relatve values, not absolute 5
6 C. Geometry Modal analyss can employ any type of geometry: Sold bodes, surface bodes and lne bodes. The Pont Mass feature can be used: A pont mass adds mass wthout addtonal flexblty to the structure thus reducng the natural frequency (K/M)^0.5. Materal propertes: Young s Modulus, Posson s Rato, and Densty are requred. Structural and thermal loads are not avalable n free vbraton: If no supports (or partal) are present, rgd-body modes wll occur at or near 0 Hz. The choce of boundary condtons wll affect the mode shapes and frequences of the part. Carefully consder how the model s constraned. 6
7 D. Contact Contact regons are avalable n free vbraton analyses however contact behavor wll dffer for the nonlnear contact types: Contact Type Modal Analyss Intally Touchng Insde Pnball Regon Outsde Pnball Regon Bonded Bonded Bonded Free No Separaton No Separaton No Separaton Free Rough Bonded Free Free Frctonless No Separaton Free Free Frctonal Bonded Free Free All contact wll behave as bonded or no separaton n a modal analyss: If a gap s present: Nonlnear contacts wll be free (no contact). Bonded and no separaton contact wll depend on the pnball sze. 7
8 E. Soluton Setup Wthn Mechancal Analyss Settngs: Specfy the number of modes to fnd (default s 6). Optonally specfy a frequency search range (defaults from 0Hz to 1e+08Hz). Note: damped modal analyss s covered n the dynamcs course. Request addtonal result output f desred. 8
9 Soluton Setup When a soluton s complete, the soluton branch wll dsplay a bar chart and table lstng frequences and mode numbers. RMB to request the modes to be dsplayed (or select all). Indvdual mode shapes can be anmated. 9
10 F. Modal Results Modal Results: Because there s no exctaton appled to the structure the mode shapes are relatve values not actual ones. Mode shape results are mass normalzed. The same s true for other results (stress, stran, etc.). Because a modal result s based on the model s propertes and not a partcular nput, we can nterpret where the maxmum or mnmum results wll occur for a partcular mode shape but not the actual value. 10
11 G. Vbraton wth Pre-Stress Whle many prestressed modal examples appear n muscal nstruments (gutar strngs, drum heads, etc.), there are numerous engneerng applcatons where the ncluson of prestress effects are crtcal. Note: whle prestressng n tenson wll cause frequences to ncrease, compressve states can decrease natural frequences. 11
12 ... Vbraton wth Pre-Stress Setup a pre-stressed modal analyss n the schematc by lnkng a statc structural system to a modal system at the soluton level. Notce n the modal branch, the structural analyss result becomes an ntal condton. 12
13 ... Vbraton wth Pre-Stress The stress state of a structure under nfluences the modal soluton by modfyng the stffness of the structure. K x F o A lnear statc analyss s performed S o A stress stffness matrx s calculated from the structural analyss K S 2 M 0 The orgnal free vbraton equaton s modfed to nclude the [S] term 13
14 H. Workshop 8.1 Free Vbraton Workshop 8.1 Free Vbraton Analyss Goal: Investgate the vbraton characterstcs of the machne frame shown here by testng 2 sets of constrants. 14
MEEM 3700 Mechanical Vibrations
MEEM 700 Mechancal Vbratons Mohan D. Rao Chuck Van Karsen Mechancal Engneerng-Engneerng Mechancs Mchgan echnologcal Unversty Copyrght 00 Lecture & MEEM 700 Multple Degree of Freedom Systems (ext: S.S.
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationChapter 5. Vibration Analysis. Workbench - Mechanical Introduction ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.
Workbench - Mechanical Introduction 12.0 Chapter 5 Vibration Analysis 5-1 Chapter Overview In this chapter, performing free vibration analyses in Simulation will be covered. In Simulation, performing a
More informationNovember 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project
SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationPhysics 111: Mechanics Lecture 11
Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 Rgd-Body Rotaton
More informationMECHANICS OF MATERIALS
Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationOne Dimensional Axial Deformations
One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The -as s taken as the
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationGEO-SLOPE International Ltd, Calgary, Alberta, Canada Vibrating Beam
GEO-SLOPE Internatonal Ltd, Calgary, Alberta, Canada www.geo-slope.com Introducton Vbratng Beam Ths example looks at the dynamc response of a cantlever beam n response to a cyclc force at the free end.
More information11. Dynamics in Rotating Frames of Reference
Unversty of Rhode Island DgtalCommons@URI Classcal Dynamcs Physcs Course Materals 2015 11. Dynamcs n Rotatng Frames of Reference Gerhard Müller Unversty of Rhode Island, gmuller@ur.edu Creatve Commons
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.
Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -
More informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationNONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM
Advanced Steel Constructon Vol. 5, No., pp. 59-7 (9) 59 NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM M. Abdel-Jaber, A.A. Al-Qasa,* and M.S. Abdel-Jaber Department of Cvl Engneerng, Faculty
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationIdentification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model
Identfcaton of Instantaneous Modal Parameters of A Nonlnear Structure Va Ampltude-Dependent ARX Model We Chh Su(NCHC), Chung Shann Huang(NCU), Chng Yu Lu(NCU) Outlne INRODUCION MEHODOLOGY NUMERICAL VERIFICAION
More informationPHYS 705: Classical Mechanics. Newtonian Mechanics
1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: -An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]
More informationDelay equations with engineering applications Gábor Stépán Department of Applied Mechanics Budapest University of Technology and Economics
Delay equatons wth engneerng applcatons Gábor Stépán Department of Appled Mechancs Budapest Unversty of Technology and Economcs Contents Delay equatons arse n mechancal systems by the nformaton system
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationModal Identification of Non-Linear Structures and the Use of Modal Model in Structural Dynamic Analysis
Modal Identfcaton of Non-Lnear Structures and the Use of Modal Model n Structural Dynamc Analyss Özge Arslan and H. Nevzat Özgüven Department of Mechancal Engneerng Mddle East Techncal Unversty Ankara
More informationGrover s Algorithm + Quantum Zeno Effect + Vaidman
Grover s Algorthm + Quantum Zeno Effect + Vadman CS 294-2 Bomb 10/12/04 Fall 2004 Lecture 11 Grover s algorthm Recall that Grover s algorthm for searchng over a space of sze wors as follows: consder the
More informationCopyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data
More informationSOME ASPECTS OF THE EXISTENCE OF COULOMB VIBRATIONS IN A COMPOSITE BAR
SISOM 006, Bucharest 7-9 May SOME ASPECTS OF THE EXISTECE OF COULOMB VIBRATIOS I A COMPOSITE BAR Ştefana DOESCU Techncal Unversty of Cvl Engneerng, Dept. of Mathematcs, emal: stefa05@rdsln.ro. In ths paper,
More informationModeling and Simulation of a Hexapod Machine Tool for the Dynamic Stability Analysis of Milling Processes. C. Henninger, P.
Smpack User Meetng 27 Modelng and Smulaton of a Heapod Machne Tool for the Dynamc Stablty Analyss of Mllng Processes C. Hennnger, P. Eberhard Insttute of Engneerng project funded by the DFG wthn the framework
More informationHashing. Alexandra Stefan
Hashng Alexandra Stefan 1 Hash tables Tables Drect access table (or key-ndex table): key => ndex Hash table: key => hash value => ndex Man components Hash functon Collson resoluton Dfferent keys mapped
More informationEconomics 101. Lecture 4 - Equilibrium and Efficiency
Economcs 0 Lecture 4 - Equlbrum and Effcency Intro As dscussed n the prevous lecture, we wll now move from an envronment where we looed at consumers mang decsons n solaton to analyzng economes full of
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More information[Kumar*, 5(3): March, 2016] ISSN: (I2OR), Publication Impact Factor: 3.785
[Kumar*, 5(3): March, 016] ISSN: 77-9655 (IOR), Publcaton Impact Factor: 3.785 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY ANALYSIS OF VIBRATION DAMPING IN PROPELLER SHAFT
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationFrame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments.
CE7 Structural Analyss II PAAR FRAE EEET y 5 x E, A, I, Each node can translate and rotate n plane. The fnal dsplaced shape has ndependent generalzed dsplacements (.e. translatons and rotatons) noled.
More informationLinear Feature Engineering 11
Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19
More informationSIMULATION OF WAVE PROPAGATION IN AN HETEROGENEOUS ELASTIC ROD
SIMUATION OF WAVE POPAGATION IN AN HETEOGENEOUS EASTIC OD ogéro M Saldanha da Gama Unversdade do Estado do o de Janero ua Sào Francsco Xaver 54, sala 5 A 559-9, o de Janero, Brasl e-mal: rsgama@domancombr
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationPARTICIPATION FACTOR IN MODAL ANALYSIS OF POWER SYSTEMS STABILITY
POZNAN UNIVE RSITY OF TE CHNOLOGY ACADE MIC JOURNALS No 86 Electrcal Engneerng 6 Volodymyr KONOVAL* Roman PRYTULA** PARTICIPATION FACTOR IN MODAL ANALYSIS OF POWER SYSTEMS STABILITY Ths paper provdes a
More informationModifying the Shear Buckling Loads of Metal Shear Walls for Improving Their Energy Absorption Capacity
Modfyng the Shear Bucklng Loads of Metal Shear Walls for Improvng Ther Energy Absorpton Capacty S. Shahab, M. Mrtaher, R. Mrzaefa and H. Baha 3,* George W. Woodruff School of Mechancal Engneerng, Georga
More informationLecture 14: Forces and Stresses
The Nuts and Bolts of Frst-Prncples Smulaton Lecture 14: Forces and Stresses Durham, 6th-13th December 2001 CASTEP Developers Group wth support from the ESF ψ k Network Overvew of Lecture Why bother? Theoretcal
More informationDynamic Analysis Based On ANSYS of Turning and Grinding Compound Machine Spindle Box Zanhui Shu and Qiushi Han
Advanced Materals Research Onlne: 2012-01-03 ISSN: 1662-8985, Vols. 433-440, pp 524-529 do:10.4028/www.scentfc.net/amr.433-440.524 2012 Trans Tech Publcatons, Swtzerland Dynamc Analyss Based On ANSYS of
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationChapter 3. Estimation of Earthquake Load Effects
Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationPHYS 705: Classical Mechanics. Canonical Transformation II
1 PHYS 705: Classcal Mechancs Canoncal Transformaton II Example: Harmonc Oscllator f ( x) x m 0 x U( x) x mx x LT U m Defne or L p p mx x x m mx x H px L px p m p x m m H p 1 x m p m 1 m H x p m x m m
More information( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
More informationModeling of Dynamic Systems
Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how
More informationHow Strong Are Weak Patents? Joseph Farrell and Carl Shapiro. Supplementary Material Licensing Probabilistic Patents to Cournot Oligopolists *
How Strong Are Weak Patents? Joseph Farrell and Carl Shapro Supplementary Materal Lcensng Probablstc Patents to Cournot Olgopolsts * September 007 We study here the specal case n whch downstream competton
More informationTechnical Report TR05
Techncal Report TR05 An Introducton to the Floatng Frame of Reference Formulaton for Small Deformaton n Flexble Multbody Dynamcs Antono Recuero and Dan Negrut May 11, 2016 Abstract Ths techncal report
More informationEffects of Boundary Conditions on Cross-Ply Laminated Composite Beams
Internatonal Journal of Engneerng Research And Advanced Technology (IJERAT) DOI: http://dx.do.org/0.734/ijerat.344 E-ISSN : 454-635 Vol.3 (0) Oct -07 Effects of Boundary Condtons on Cross-Ply Lamnated
More information5.04, Principles of Inorganic Chemistry II MIT Department of Chemistry Lecture 32: Vibrational Spectroscopy and the IR
5.0, Prncples of Inorganc Chemstry II MIT Department of Chemstry Lecture 3: Vbratonal Spectroscopy and the IR Vbratonal spectroscopy s confned to the 00-5000 cm - spectral regon. The absorpton of a photon
More informationES 240 Solid Mechanics Z. Suo. Vibration
ES 4 Sold Mechancs Z Suo Vbraton Reference JP Den Hartog, Mechancal Vbratons, Dover Publcatons, New York hs eceptonal book, wrtten by a moshenko Medalst, s avalable on amazoncom at $6 When a bar s pulled,
More informationOPTIMAL DESIGN OF VISCOELASTIC COMPOSITES WITH PERIODIC MICROSTRUCTURES
OPTIMAL DESIN OF VISCOELASTIC COMPOSITES WITH PERIODIC MICROSTRUCTURES eong-moo 1, Sang-Hoon Park 2, and Sung-Ke oun 2 1 Space Technology Dvson, Korea Aerospace Research Insttute, usung P.O. Box 3, Taejon,
More informationDESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS
Munch, Germany, 26-30 th June 2016 1 DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School
More informationCHAPTER 6. LAGRANGE S EQUATIONS (Analytical Mechanics)
CHAPTER 6 LAGRANGE S EQUATIONS (Analytcal Mechancs) 1 Ex. 1: Consder a partcle movng on a fxed horzontal surface. r P Let, be the poston and F be the total force on the partcle. The FBD s: -mgk F 1 x O
More informationECEN 667 Power System Stability Lecture 21: Modal Analysis
ECEN 667 Power System Stablty Lecture 21: Modal Analyss Prof. Tom Overbye Dept. of Electrcal and Computer Engneerng Texas A&M Unversty, overbye@tamu.edu 1 Announcements Read Chapter 8 Homework 7 s posted;
More informationCHARACTERISATION OF VIBRATION ISOLATORS USING VIBRATION TEST DATA
Mustafa E. Levent, Page number 1 Abstract CHARACTERISATION OF VIBRATION ISOLATORS USING VIBRATION TEST DATA Mustafa E. Levent, KenanY. Sanlturk 1 Istanbul Techncal Unversty, Faculty of Mechancal Engneerng,
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationStart with the equation of motion for a linear multi-degree of freedom system with base ground excitation:
SE 80 Earthquake Enneern November 3, 00 STEP-BY-STEP PROCEDURE FOR SETTING UP A SPREADSHEET FOR USING NEWMARK S METHOD AND MODAL ANALYSIS TO SOLVE FOR THE RESPONSE OF A MULTI-DEGREE OF FREEDOM (MDOF) SYSTEM
More informationPlease initial the statement below to show that you have read it
EN0: Structural nalyss Exam I Wednesday, March 2, 2005 Dvson of Engneerng rown Unversty NME: General Instructons No collaboraton of any nd s permtted on ths examnaton. You may consult your own wrtten lecture
More information3 ENERGY CALCULATION ENERGY CALCULATION Introduction
ENERGY CALCULATION 3-1 3 ENERGY CALCULATION 3.1 Introducton Energy changes determned n UDEC are performed for the ntact rock, the jonts and for the work done on boundares. The energy terms calculated here
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationInvestigation of noise radiation from tire using experimental modal identification
Investgaton of nose radaton from tre usng expermental modal dentfcaton Atsush KITAHARA 1 ; Takuya YOSHIMURA 2 ; Shnsaku KATAYAMA 3 1 Brdgestone Corporaton, Japan 2 Tokyo Metropoltan Unversty, Japan 3 Brdgestone
More informationUniformity of Deformation in Element Testing
Woousng Km, Marc Loen, ruce hadbourn and Joseph Labu Unformt of Deformaton n Element Testng Abstract Unform deformaton s a basc assumpton n element testng, where aal stran tpcall s determned from dsplacement
More informationSpin-rotation coupling of the angularly accelerated rigid body
Spn-rotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 E-mal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationConsistency & Convergence
/9/007 CHE 374 Computatonal Methods n Engneerng Ordnary Dfferental Equatons Consstency, Convergence, Stablty, Stffness and Adaptve and Implct Methods ODE s n MATLAB, etc Consstency & Convergence Consstency
More informationTHE CURRENT BALANCE Physics 258/259
DSH 1988, 005 THE CURRENT BALANCE Physcs 58/59 The tme average force between two parallel conductors carryng an alternatng current s measured by balancng ths force aganst the gravtatonal force on a set
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationAdvanced Mechanical Elements
May 3, 08 Advanced Mechancal Elements (Lecture 7) Knematc analyss and moton control of underactuated mechansms wth elastc elements - Moton control of underactuated mechansms constraned by elastc elements
More informationVIBRATION FATIGUE DESIGN METHODOLOGY OF A LARGE SCALE HEAVY DUTY ROBOT
ICSV14 Carns Australa 9-12 July, 2007 VIBRATION FATIGUE DESIGN METHODOLOGY OF A LARGE SCALE HEAVY DUTY ROBOT Jong Hw Seo 1, Jae Chul Hwang 1, Yong Won Cho 1, Dong Il Km 1, Hong Jae Ym 2 1 Robotcs Technology
More informationAPPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam
APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More information1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys
More informationGouy-Chapman model (1910) The double layer is not as compact as in Helmholtz rigid layer.
CHE465/865, 6-3, Lecture 1, 7 nd Sep., 6 Gouy-Chapman model (191) The double layer s not as compact as n Helmholtz rgd layer. Consder thermal motons of ons: Tendency to ncrease the entropy and make the
More informationStatic and Modal Analysis and Optimization of Cross- Sectional Area of the Manipulator Arm
Amercan Journal of Mechancal Engneerng, 2013, Vol. 1, No. 7, 236-240 Avalable onlne at http://pubs.scepub.com/ajme/1/7/17 Scence and Educaton Publshng DOI:10.12691/ajme-1-7-17 Statc and Modal Analyss and
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
More informationFlow Induced Vibration
Flow Induced Vbraton Project Progress Report Date: 16 th November, 2005 Submtted by Subhrajt Bhattacharya Roll no.: 02ME101 Done under the gudance of Prof. Anrvan Dasgupta Department of Mechancal Engneerng,
More informationTHE DYNAMIC ANALYSIS OF CATALYTIC CONVERTER
UNIVERSITY OF PITESTI FACULTY OF MECHANICS AND TECHNOLOGY SCIENTIFIC BULLETIN AUTOMOTIVE seres, year XX, no.24(1) THE DYNAMIC ANALYSIS OF CATALYTIC CONVERTER Ionel VIERU *, Vorel NICOLAE, Sebastan PÂRLAC
More informationAnswers Problem Set 2 Chem 314A Williamsen Spring 2000
Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationNumerical Modeling of Woven Carbon Composite Failure
8 th Internatonal LS-DYNA Users Conference Smulaton Technology (3) Numercal Modelng of Woven Carbon Composte Falure Paul F. Deslaurers, Duane S. Cronn Unversty of Waterloo Alex Duquette Multmatc Techncal
More informationADVANCED MACHINE LEARNING ADVANCED MACHINE LEARNING
1 ADVANCED ACHINE LEARNING ADVANCED ACHINE LEARNING Non-lnear regresson technques 2 ADVANCED ACHINE LEARNING Regresson: Prncple N ap N-dm. nput x to a contnuous output y. Learn a functon of the type: N
More informationPage 1. SPH4U: Lecture 7. New Topic: Friction. Today s Agenda. Surface Friction... Surface Friction...
SPH4U: Lecture 7 Today s Agenda rcton What s t? Systeatc catagores of forces How do we characterze t? Model of frcton Statc & Knetc frcton (knetc = dynac n soe languages) Soe probles nvolvng frcton ew
More informationNordic Insulation Symposium - Nord-IS 13 - Trondheim, Norway, June 9-12, 2013
Nordc Insulaton Symposum - Nord-IS - Trondhem, Norway, June 9-2, 2 Dpl.-Ing. D. Geßler (danel.gessler@kt.edu), Prof. Dr.-Ing. T. Lebfred Insttute of Electrc Energy Systems and Hgh Voltage Technology Karlsruhe
More informationQueueing Networks II Network Performance
Queueng Networks II Network Performance Davd Tpper Assocate Professor Graduate Telecommuncatons and Networkng Program Unversty of Pttsburgh Sldes 6 Networks of Queues Many communcaton systems must be modeled
More information