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Cover Art for Vibration of Discrete and Continuous Systems
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Vibration of Discrete and Continuous Systems
Edition: 2nd
Author(s): Shabana, Ahmed A.
ISBN10:  0387947442
ISBN13:  9780387947440
Format:  Hardcover
Pub. Date:  6/1/1997
Publisher(s): Springer Verlag

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Table of Contents
Series Preface vii(2)
Preface ix
CHAPTER 1 Introduction
1(52)
1.1 Kinematics of Rigid Bodies
1(6)
1.2 Dynamic Equations
7(4)
1.3 Single Degree of Freedom Systems
11(5)
1.4 Oscillatory and Nonoscillatory Motion
16(8)
1.5 Other Types of Damping
24(5)
1.6 Forced Vibration
29(9)
1.7 Impulse Response
38(3)
1.8 Response to an Arbitrary Forcing Function
41(3)
Problems
44(9)
CHAPTER 2 Lagrangian Dynamics
53(45)
2.1 Generalized Coordinates
53(4)
2.2 Virtual Work and Generalized Forces
57(5)
2.3 Lagrange's Equation
62(9)
2.4 Kinetic Energy
71(8)
2.5 Strain Energy
79(3)
2.6 Hamilton's Principle
82(4)
2.7 Conservation Theorems
86(4)
2.8 Concluding Remarks
90(3)
Problems
93(5)
CHAPTER 3 Multi-Degree of Freedom Systems
98(90)
3.1 Equations of Motion
99(12)
3.2 Undamped Free Vibration
111(5)
3.3 Orthogonality of the Mode Shapes
116(10)
3.4 Rigid-Body Modes
126(7)
3.5 Conservation of Energy
133(4)
3.6 Forced Vibration of the Undamped Systems
137(2)
3.7 Viscously Damped Systems
139(6)
3.8 General Viscous Damping
145(10)
3.9 Approximation and Numerical Methods
155(4)
3.10 Matrix-Iteration Methods
159(14)
3.11 Method of Transfer Matrices
173(9)
Problems
182(6)
CHAPTER 4 Vibration of Continuous Systems
188(80)
4.1 Free Longitudinal Vibrations
189(12)
4.2 Free Torsional Vibrations
201(5)
4.3 Free Transverse Vibrations of Beams
206(14)
4.4 Orthogonality of the Eigenfunctions
220(7)
4.5 Forced Vibrations
227(8)
4.6 Inhomogeneous Boundary Conditions
235(3)
4.7 Viscoelastic Materials
238(3)
4.8 Energy Methods
241(4)
4.9 Approximation Methods
245(11)
4.10 Galerkin's Method
256(3)
4.11 Assumed-Modes Method
259(3)
Problems
262(6)
CHAPTER 5 The Finite-Element Method
268(64)
5.1 Assumed Displacement Field
270(6)
5.2 Comments on the Element Shape Functions
276(4)
5.3 Connectivity Between Elements
280(6)
5.4 Formulation of the Mass Matrix
286(4)
5.5 Formulation of the Stiffness Matrix
290(10)
5.6 Equations of Motion
300(3)
5.7 Convergence of the Finite-Element Solution
303(7)
5.8 Higher-Order Elements
310(4)
5.9 Spatial Elements
314(9)
5.10 Large Rotations and Deformations
323(5)
Problems
328(4)
CHAPTER 6 Methods for the Eigenvalue Analysis
332(35)
6.1 Similarity Transformation
333(2)
6.2 Polynomial Matrices
335(4)
6.3 Equivalence of the Characteristic Matrices
339(4)
6.4 Jordan Matrices
343(4)
6.5 Elementary Divisors
347(3)
6.6 Generalized Eigenvectors
350(3)
6.7 Jacobi Method
353(3)
6.8 Householder Transformation
356(4)
6.9 QR Decomposition
360(4)
Problems
364(3)
APPENDIX A Linear Algebra
367(20)
A.1 Matrices
367(2)
A.2 Matrix Operations
369(5)
A.3 Vectors
374(9)
A.4 Eigenvalue Problem
383(1)
Problems
384(3)
References 387(2)
Index 389

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