كتاب Vibration of Discrete and Continuous Systems

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Vibration of Discrete and Continuous Systems
Second Edition - With 147 Figures
A.A. Shabana
Mechanical Engineering Series
Frederick F. Ling
Series Editor

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Contents
Series Preface vii
Preface ix
CHAPTER 1
Introduction I
l.l Kinematics of Rigid Bodies 1
1.2 Dynamic Equations 7
1.3 Single Degree of Freedom Systems II
1.4 Oscillatory and Nonoscillatory Motion 16
1.5 Other Types of Damping 24
1.6 Forced Vibration 29
1.7 Impulse Response 38
1.8 Response to an Arbitrary Forcing Function 41
Problems 44
CHAPTER 2
Lagrangian Dynamics 53
2.1 Generalized Coordinates 53
2.2 Virtual Work and Generalized Forces 57
2.3 Lagrange's Equation 62
2.4 Kinetic Energy 71
2.5 Strain Energy 79
2.6 Hamilton's Principle 82
2.7 Conservation Theorems 86
2.8 Concluding Remarks 90
Problems 93
CHAPTER 3
Multi-Degree of Freedom Systems 98
3.1 Equations of Motion 99
3.2 Undamped Free Vibration III
3.3 Orthogonality of the Mode Shapes 116
3.4 Rigid-Body Modes 126
3.5 Conservation of Energy 133
xiiixiv Contents
3.6 Forced Vibration of the Undamped Systems 137
3.7 Viscously Damped Systems 139
3.8 General Viscous Damping 145
3.9 Approximation and Numerical Methods 155
3.10 Matrix-Iteration Methods 159
3.11 Method of Transfer Matrices 173
Problems 182
CHAPTER 4
Vibration of Continuous Systems 188
4.1 Free Longitudinal Vibrations 189
4.2 Free Torsional Vibrations 201
4.3 Free Transverse Vibrations of Beams 206
4.4 Orthogonality of the Eigenfunctions 220
4.5 Forced Vibrations 227
4.6 Inhomogeneous Boundary Conditions 235
4.7 Viscoelastic Materials 238
4.8 Energy Methods 241
4.9 Approximation Methods 245
4.10 Galerkin's Method 256
4.11 Assumed-Modes Method 259
Problems 262
CHAPTER 5
The Finite-Element Method 268
5.1 Assumed Displacement Field 270
5.2 Comments on the Element Shape Functions 276
5.3 Connectivity Between Elements 280
5.4 Formulation ofthe Mass Matrix 286
5.5 Formulation of the Stiffness Matrix 290
5.6 Equations of Motion 300
5.7 Convergence of the Finite-Element Solution 303
5.8 Higher-Order Elements 310
5.9 Spatial Elements 314
5.10 Large Rotations and Deformations 323
Problems 328
CHAPTER 6
Methods for the Eigenvalue Analysis 332
6.1 Similarity Transformation 333
6.2 Polynomial Matrices 335
6.3 Equivalence ofthe Characteristic Matrices 339
6.4 Jordan Matrices 343
6.5 Elementary Divisors 347
6.6 Generalized Eigenvectors 350
6.7 Jacobi Method 353
6.8 Householder Transformation 3566.9 QR Decomposition
Problems
APPENDIX A
Linear Algebra
A.l Matrices
A.2 Matrix Operations
AJ Vectors
A.4 Eigenvalue Problem
Problems
References
Index

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