Advanced Vibration Analysis / Edition 1 available in Hardcover, Paperback
- ISBN-10:
- 0367389657
- ISBN-13:
- 9780367389659
- Pub. Date:
- 09/05/2019
- Publisher:
- Taylor & Francis
- ISBN-10:
- 0367389657
- ISBN-13:
- 9780367389659
- Pub. Date:
- 09/05/2019
- Publisher:
- Taylor & Francis
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$82.99Overview
The book begins with a discussion of the physics of dynamic systems comprised of particles, rigid bodies, and deformable bodies and the physics and mathematics for the analysis of a system with a single-degree-of-freedom. It develops mathematical models using energy methods and presents the mathematical foundation for the framework. The author illustrates the development and analysis of linear operators used in various problems and the formulation of the differential equations governing the response of a conservative linear system in terms of self-adjoint linear operators, the inertia operator, and the stiffness operator. The author focuses on the free response of linear conservative systems and the free response of non-self-adjoint systems. He explores three method for determining the forced response and approximate methods of solution for continuous systems.
The use of the mathematical foundation and the application of the physics to build a framework for the modeling and development of the response is emphasized throughout the book. The presence of the framework becomes more important as the complexity of the system increases. The text builds the foundation, formalizes it, and uses it in a consistent fashion including application to contemporary research using linear vibrations.
Product Details
| ISBN-13: | 9780367389659 |
|---|---|
| Publisher: | Taylor & Francis |
| Publication date: | 09/05/2019 |
| Pages: | 664 |
| Product dimensions: | 6.00(w) x 9.00(h) x (d) |
Table of Contents
Chapter 1 Introduction and Vibration of Single-Degree-of-Freedom Systems 1
1.1 Introduction 1
1.1.1 Degrees of Freedom and Generalized Coordinates 1
1.1.2 Scope of Study 7
1.2 Newton's Second Law, Angular Momentum, and Kinetic Energy 8
1.2.1 Particles 8
1.2.2 Systems of Particles 9
1.2.3 Rigid Bodies 13
1.3 Components of Vibrating Systems 17
1.3.1 Inertia Elements 17
1.3.2 Stiffness Elements 22
1.3.3 Energy Dissipation 30
1.3.4 External Energy Sources 34
1.4 Modeling of One-Degree-of-Freedom Systems 38
1.4.1 Introduction and Assumptions 38
1.4.2 Static Spring Forces 39
1.4.3 Derivation of Differential Equations 42
1.4.4 Model Systems 48
1.4.5 One-Degree-of-Freedom Models of Continuous Systems 49
1.5 Qualitative Aspects of One-Degree-of-Freedom Systems 56
1.6 Free Vibrations of Linear Single-Degree-of-Freedom Systems 63
1.7 Response of a Single-Degree-of-Freedom System Due to Harmonic Excitation 70
1.7.1 General Theory 70
1.7.2 Frequency-Squared Excitation 73
1.7.3 Motion Input 75
1.7.4 General Periodic Input 80
1.8 Transient Response of a Single-Degree-of-Freedom System 82
Chapter 2 Derivation of Differential Equations Using Variational Methods 87
2.1 Functional 87
2.2 Variations 91
2.3 Euler-Lagrange Equation 93
2.4 Hamilton's Principle 100
2.5 Lagrange's Equations for Conservative Discrete Systems 104
2.6 Lagrange's Equations for Non-Conservative Discrete Systems 112
2.7 Linear Discrete Systems 122
2.7.1 Quadratic Forms 122
2.7.2 Differential Equations for Linear Systems 125
2.7.3 Linearization of Differential Equations 127
2.8 Gyroscopic Systems 130
2.9 Continuous Systems 136
2.10 Bars, Strings, and Shafts 138
2.11 Euler-Bernoulli Beams 150
2.12 Timoshenko Beams 166
2.13 Membranes 170
Chapter 3 Linear Algebra 173
3.1 Introduction 173
3.2 Three-Dimensional Space 174
3.3 Vector Spaces 177
3.4 Linear Independence 182
3.5 Basis and Dimension 185
3.6 Inner Products 189
3.7 Norms 193
3.8 Gram-Schmidt Orthonormalization Method 197
3.9 Orthogonal Expansions 202
3.10 Linear Operators 206
3.11 Adjoint Operators 212
3.12 Positive Definite Operators 219
3.13 Energy Inner Products 222
Chapter 4 Operators Used in Vibration Problems 225
4.1 Summary of Basic Theory 225
4.2 Differential Equations for Discrete Systems 227
4.3 Stiffness Matrix 227
4.4 Mass Matrix 233
4.5 Flexibility Matrix 234
4.6 M-1 K and AM 240
4.7 Formulation of Partial Differential Equations for Continuous Systems 242
4.8 Second-Order Problems 245
4.9 Euler-Bernoulli Beam 253
4.10 Timoshenko Beams 262
4.11 Systems with Multiple Deformable Bodies 266
4.12 Continuous Systems with Attached Inertia Elements 272
4.13 Combined Continuous and Discrete Systems 278
4.14 Membranes 283
Chapter 5 Free Vibrations of Conservative Systems 287
5.1 Normal Mode Solution 287
5.2 Properties of Eigenvalues and Eigenvectors 292
5.2.1 Eigenvalues of Self-Adjoint Operators 292
5.2.2 Positive Definite Operators 297
5.2.3 Expansion Theorem 298
5.2.4 Summary 302
5.3 Rayleigh's Quotient 303
5.4 Solvability Conditions 306
5.5 Free Response Using the Normal Mode Solution 309
5.5.1 General Free Response 309
5.5.2 Principal Coordinates 314
5.6 Discrete Systems 316
5.6.1 The Matrix Eigenvalue Problem 317
5.7 Natural Frequency Calculations Using Flexibility Matrix 326
5.8 Matrix Iteration 330
5.9 Continuous Systems 341
5.10 Second-Order Problems (Wave Equation) 342
5.11 Euler-Bernoulli Beams 360
5.12 Repeated Structures 375
5.13 Timoshenko Beams 398
5.14 Combined Continuous and Discrete Systems 409
5.15 Membranes 414
5.16 Green's Functions 430
Chapter 6 Non Self-Adjoint Systems 437
6.1 Non-Self-Adjoint Operators 437
6.2 Discrete Systems with Proportional Damping 441
6.3 Discrete Systems with General Damping 446
6.4 Discrete Gyroscopic Systems 452
6.5 Continuous Systems with Viscous Damping 458
Chapter 7 Forced Response 465
7.1 Response of Discrete Systems for Harmonic Excitations 465
7.1.1 General Theory 465
7.1.2 Vibration Absorbers 470
7.2 Harmonic Excitation of Continuous Systems 480
7.3 Laplace Transform Solutions 490
7.3.1 Discrete Systems 491
7.3.2 Continuous Systems 497
7.4 Modal Analysis for Undamped Discrete Systems 501
7.5 Modal Analysis for Undamped Continuous Systems 504
7.6 Discrete Systems with Damping 516
7.6.1 Proportional Damping 516
7.6.2 General Viscous Damping 517
Chapter 8 Rayleigh-Ritz and Finite-Element Methods 525
8.1 Fourier Best Approximation Theorem 525
8.2 Rayleigh-Ritz Method 528
8.3 Galerkin Method 531
8.4 Rayleigh-Ritz Method for Natural Frequencies and Mode Shapes 532
8.5 Rayleigh-Ritz Methods for Forced Response 551
8.6 Admissible Functions 556
8.7 Assumed Modes Method 560
8.8 Finite-Element Method 570
8.9 Assumed Modes Development of Finite-Element Method 575
8.10 Bar Element 577
8.11 Beam Element 584
Chapter 9 Exercises 595
9.1 Chapter 1 595
9.2 Chapter 2 602
9.3 Chapter 3 611
9.4 Chapter 4 614
9.5 Chapter 5 617
9.6 Chapter 6 620
9.7 Chapter 7 622
9.8 Chapter 8 625
References 627
Index 629