Dynamics Of Multibody Systems---Shabana

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多体动力学方面,国外的经典书籍 作者Ahmed A. Shabana
Dynamics of Multibody systems Third edition ynamics of Multibody Systems, Third Edition, introduces multibody dynamics, with an emphasis on flexible body dynamics many common mechanisms such as auto mobiles, space structures, robots, and micromachines have mechanical and structural systens that consist of interconnected rigid and deformable components. The dynaIn- ics of these large-scale, multibody systems are highly nonlinear, presenting complex problems that in most cases can only be solved with computer-based techniques. The book begins with a review of the basic ideas of kinematics and the dynamics of rigid and deformable bodies before moving on to more advanced topics and computer im plementation. This revised third edition now includes important new developments relating to the problem of large deformations and numerical algorithms as applied to fexible multibody systems. The book's wealth of examples and practical applications will be useful to graduate students, researchers, and practicing engineers working on a wide variety of flexible multibody systems Ahmed A. Shabana is a Professor in the Department of Mechnical and Industrial Engineering at the University of Illinois, Chicago. Dr. Shabana received his Ph D in mechanical engineering from the University of lowa. His active areas of research interest are in dynamics, vibration, and control of mechanical systems consisting of rigid and deformable interconnected bodies He is also the author of three other works Theory of Vibration: An Introduction, Vibration of Discrete and Continuous Systems, nd Computational dynamics. DYNAMICS OF MULTIBODY SYSTEMS Third edition Ahmed a shabana University of lllinois at Chicago W CAMBRIDGE 多 UNIVERSITY PRESS To my father and to the memory of my mother CAMBRIDGE UNIVERSITY PRESS CaInbridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitlewww.cambridge.org/9780521850117 o Cambridge University Press 2005 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take pl without the written permission of Cambridge University Press First published in print format 2005 ISBN-I3978-0-5II-II583-7 eBook(Netlibrary ISBN-I0 O-SII-1IS83-0 eBook(NetLibrary) ISBN-13 978-0-52T-8SOTT- hardback ISBN-IO 0-521-85O1I-8 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface 1 INTRODUCTION 1.1 Multibody systems 1 1.2 Reference frames Particle mechanics 1. Rigid Body Mechanics 11 1.5 Deformable bodies 15 1.6 Constrained motion 18 1.7 Computer Formulation and Coordinate Selection 22 8 Objectives and Scope of This Book 25 2 REFERENCE KINEMATICS 28 2.1 Rotation matrix 29 2.2 Properties of the rotation matrix 35 2. 3 Successive rotations 39 2. 4 Velocity Equations 47 2.5 Accelerations and Important Identities 55 2.6 Rodriguez parameters 59 2. 7 Euler Angles 63 2. 8 Direction Cosines 68 2. 9 The 4x 4 Transformation matrix 72 2.10 Relationship between Different Orientation Coordinates 80 Problems 82 CONTENTS 3 ANALYTICAL TECHNIQUES 85 3.1 Generalized coordinates and Kinematic Constraints 86 3.2 Degrees of Freedom and Generalized Coordinate partitioning 94 3.3 Virtual Work and generalized forces 102 3.4 Lagrangian dynamics 115 3.5 Application to Rigid Body Dynamics 123 3. 6 Calculus of variations 129 3.7 Eulers Equation in the Case of Several Variables 135 3.8 Equations of Motion of Rigid Body Systems 142 3.9 Newton-Euler Equations 150 3.10 Concluding Remarks 154 Problems 156 4 MECHANICS OF DEFORMABLE BODIES 159 41 Kinematics of deformable bodies 160 4.2 Strain Components 164 4.3 Physical Interpretation of Strains 4. 4 Rigid Body Motion 169 4.5 Stress Components 172 4.6 Equations of equilibrium 175 4.7 Constitutive equations 178 4. 8 Virtual Work of the elastic forces 183 Problems 186 5 FLOATING FRAME OF REFERENCE FORMULATION 188 5.1 Kinematic Description 189 5.2 Inertia of deformable bodies 200 5.3 Generalized forces 213 5.4 Kinematic Constraints 219 5.5 Equations of Motion 223 5.6 Coupling between Reference and Elastic Displacements 228 5.7 application to a multibody system 231 5.8 Use of Independent coordinates 241 5.9 Dynamic Equations with Multipliers 244 5.10 Generalized Coordinate Partitioning 248 5.11 Organization of Multibody Computer Programs 251 5.12 Numerical algorithms 254 Problems 263 6 FINITE-ELEMENT FORMULATION 267 6.1 Element Shape Functions 268 6.2 Reference Conditions 276 CONTENTS 6.3 Kinetic Energy 278 6.4 Generalized Elastic Forces 287 6.5 Characterization of Planar Elastic Systems 288 6.6 Characterization of Spatial elastic systems 294 6.7 Coordinate Reduction 30 6. 8 The Floating Frame of Reference and Large Deformation problem 304 Problems 307 7 THE LARGE DEFORMATION PROBLEM 309 7.1 Background 310 7.2 Absolute nodal coordinate formulation 314 7. 3 Formulation of the Stiffness matrix 318 7.4 Equations of motion 322 7.5 Relationship to the Floating Frame of Reference Formulation 323 7. 6 Coordinate Transformation 325 7. 7 Consistent Mass Formulation 328 7. 8 The Velocity Transformation Matrix 331 7.9 Lumped Mass Formulation 332 7. 10 Extension of the Method 335 7.11 Comparison with Large Rotation Vector Formulation 339 Problems 342 APPENDIX: LINEAR ALGEBRA 345 A1 Matrix Algebra 345 A 2 Eigenvalue Analysis 349 A3 Vector Spaces 350 A 4 Chain rule of differentiation 353 A.5 Principle of mathematical Induction 354 Problems 355 REFERENCES 357 IINDEX 369 yIlI

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