Dynamics of Multibody Systems

by Ahmed A. Shabana

• ISBN13: 9780521154222
• ISBN10: 0521154227
• Edition: 3rd
• Format: Paperback
• Copyright: 2010-08-30
• Publisher: Cambridge University Press

Summary

Dynamics of Multibody Systems, Third Edition, introduces multibody dynamics, with an emphasis on flexible body dynamics. Many common mechanisms such as automobiles, space structures, robots, and micromachines have mechanical and structural systems that consist of interconnected rigid and deformable components. The dynamics 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 implementation. This revised third edition now includes important new developments relating to the problem of large deformations and numerical algorithms as applied to flexible 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.

Author Biography

Ahmed A. Shabana is a Professor in the Department of Mechanical and Industrial Engineering at the University of Illinois, Chicago. Dr. Shabana received his Ph.D. in mechanical engineering from the University of Iowa. 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 five other works, Theory of Vibration: An Introduction, Vibration of Discrete and Continuous Systems, Computational Dynamics (Third Edition), Railroad Vehicle Dynamics, and Computational Continuum Mechanics.

Table of Contents

Preface	p. ix
Introduction	p. 1
Multibody Systems	p. 1
Reference Frames	p. 3
Particle Mechanics	p. 6
Rigid Body Mechanics	p. 11
Deformable Bodies	p. 15
Constrained Motion	p. 18
Computer Formulation and Coordinate Selection	p. 22
Objectives and Scope of This Book	p. 25
Reference Kinematics	p. 28
Rotation Matrix	p. 29
Properties of the Rotation Matrix	p. 35
Successive Rotations	p. 39
Velocity Equations	p. 47
Accelerations and Important Identities	p. 55
Rodriguez Parameters	p. 59
Euler Angles	p. 63
Direction Cosines	p. 68
The 4 × 4 Transformation Matrix	p. 72
Relationship between Different Orientation Coordinates	p. 80
Problems	p. 82
Analytical Techniques	p. 85
Generalized Coordinates and Kinematic Constraints	p. 86
Degrees of Freedom and Generalized Coordinate Partitioning	p. 94
Virtual Work and Generalized Forces	p. 102
Lagrangian Dynamics	p. 115
Application to Rigid Body Dynamics	p. 123
Calculus of Variations	p. 129
Euler's Equation in the Case of Several Variables	p. 135
Equations of Motion of Rigid Body Systems	p. 142
Newton-Euler Equations	p. 150
Concluding Remarks	p. 154
Problems	p. 156
Mechanics of Deformable Bodies	p. 159
Kinematics of Deformable Bodies	p. 160
Strain Components	p. 164
Physical Interpretation of Strains	p. 168
Rigid Body Motion	p. 169
Stress Components	p. 172
Equations of Equilibrium	p. 175
Constitutive Equations	p. 178
Virtual Work of the Elastic Forces	p. 183
Problems	p. 186
Floating Frame of Reference Formulation	p. 188
Kinematic Description	p. 189
Inertia of Deformable Bodies	p. 200
Generalized Forces	p. 213
Kinematic Constraints	p. 219
Equations of Motion	p. 223
Coupling between Reference and Elastic Displacements	p. 228
Application to a Multibody System	p. 231
Use of Independent Coordinates	p. 241
Dynamic Equations with Multipliers	p. 244
Generalized Coordinate Partitioning	p. 248
Organization of Multibody Computer Programs	p. 251
Numerical Algorithms	p. 254
Problems	p. 263
Finite-Element Formulation	p. 267
Element Shape Functions	p. 268
Reference Conditions	p. 276
Kinetic Energy	p. 278
Generalized Elastic Forces	p. 287
Characterization of Planar Elastic Systems	p. 288
Characterization of Spatial Elastic Systems	p. 294
Coordinate Reduction	p. 300
The Floating Frame of Reference and Large Deformation Problem	p. 304
Problems	p. 307
The Large Deformation Problem	p. 309
Background	p. 310
Absolute Nodal Coordinate Formulation	p. 314
Formulation of the Stiffness Matrix	p. 318
Equations of Motion	p. 322
Relationship to the Floating Frame of Reference Formulation	p. 323
Coordinate Transformation	p. 325
Consistent Mass Formulation	p. 328
The Velocity Transformation Matrix	p. 331
Lumped Mass Formulation	p. 332
Extension of the Method	p. 335
Comparison with Large Rotation Vector Formulation	p. 339
Problems	p. 342
Appendix: Linear Algebra	p. 345
Matrix Algebra	p. 345
Eigenvalue Analysis	p. 349
Vector Spaces	p. 350
Chain Rule of Differentiation	p. 353
Principle of Mathematical Induction	p. 354
Problems	p. 355
References	p. 357
Index	p. 369
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