Fundamentals of Structural Dynamics

✍ Scribed by Craig, Roy R

• Publisher: Wiley
• Year: 2006
• Tongue: English
• Leaves: 746
• Edition: 2
• Category: Library

✦ Synopsis

From theory and fundamentals to the latest advances in computational and experimental modal analysis, this is the definitive, updated reference on structural dynamics.

This edition updates Professor Craig's classic introduction to structural dynamics, which has been an invaluable resource for practicing engineers and a textbook for undergraduate and graduate courses in vibrations and/or structural dynamics. Along with comprehensive coverage of structural dynamics fundamentals, finite-element-based computational methods, and dynamic testing methods, this Second Edition includes new and expanded coverage of computational methods, as well as introductions to more advanced topics, including experimental modal analysis and "active structures." With a systematic approach, it presents solution techniques that apply to various engineering disciplines. It discusses single degree-of-freedom (SDOF) systems, multiple degrees-of-freedom (MDOF) systems, and continuous systems in depth; and includes numeric evaluation of modes and frequency of MDOF systems; direct integration methods for dynamic response of SDOF systems and MDOF systems; and component mode synthesis.

Numerous illustrative examples help engineers apply the techniques and methods to challenges they face in the real world. MATLAB(r) is extensively used throughout the book, and many of the .m-files are made available on the book's Web site. Fundamentals of Structural Dynamics, Second Edition is an indispensable reference and "refresher course" for engineering professionals; and a textbook for seniors or graduate students in mechanical engineering, civil engineering, engineering mechanics, or aerospace engineering.

✦ Table of Contents

Fundamentals of Structural Dynamics......Page 3
Contents......Page 9
Preface to Structural Dynamics—An Introduction to Computer Methods......Page 13
Preface to Fundamentals of Structural Dynamics......Page 15
About the Authors......Page 17
1.1 Introduction to Structural Dynamics......Page 19
1.2 Modeling of Structural Components and Systems......Page 20
1.3 Prototype Spring–Mass Model......Page 25
1.5 Scope of the Book......Page 30
1.6 Computer Simulations; Supplementary Material on the Website......Page 33
Problems......Page 34
Part I Single-Degree-of-Freedom Systems......Page 37
2.1 Brief Review of the Dynamics of Particles and Rigid Bodies......Page 39
2.2 Elements of Lumped-Parameter Models......Page 42
2.3 Application of Newton’s Laws to Lumped-Parameter Models......Page 45
2.4 Application of the Principle of Virtual Displacements to Lumped-Parameter Models......Page 52
2.5 Application of the Principle of Virtual Displacements to Continuous Models: Assumed-Modes Method......Page 59
References......Page 68
Problems......Page 69
3 Free Vibration of SDOF Systems......Page 74
3.1 Free Vibration of Undamped SDOF Systems......Page 76
3.2 Free Vibration of Viscous-Damped SDOF Systems......Page 79
3.3 Stability of Motion......Page 84
3.4 Free Vibration of an SDOF System with Coulomb Damping......Page 88
3.5 Experimental Determination of the Natural Frequency and Damping Factor of an SDOF System......Page 90
References......Page 95
Problems......Page 96
4 Response of SDOF Systems to Harmonic Excitation......Page 99
4.1 Response of Undamped SDOF Systems to Harmonic Excitation......Page 100
4.2 Response of Viscous-Damped SDOF Systems to Harmonic Excitation: Frequency-Response Functions......Page 105
4.3 Complex Frequency Response......Page 111
4.4 Vibration Isolation: Force Transmissibility and Base Motion......Page 114
4.5 Vibration Measuring Instruments: Accelerometers and Vibrometers......Page 119
4.6 Use of Frequency-Response Data to Determine the Natural Frequency and Damping Factor of a Lightly Damped SDOF System......Page 122
4.7 Equivalent Viscous Damping......Page 125
4.8 Structural Damping......Page 129
References......Page 130
Problems......Page 131
5.1 Response of a Viscous-Damped SDOF System to an Ideal Step Input......Page 135
5.2 Response of Undamped SDOF Systems to Rectangular Pulse and Ramp Loadings......Page 137
5.3 Response of Undamped SDOF Systems to a Short-Duration Impulse: Unit Impulse Response......Page 141
5.4 Response of SDOF Systems to General Dynamic Excitation: Convolution Integral Method......Page 143
5.5 Response Spectra......Page 146
5.6 System Response by the Laplace Transform Method: System Transfer Function......Page 154
References......Page 160
Problems......Page 161
6 Numerical Evaluation of the Dynamic Response of SDOF Systems......Page 165
6.1 Integration of Second-Order Ordinary Differential Equations......Page 166
6.2 Integration of First-Order Ordinary Differential Equations......Page 177
6.3 Nonlinear SDOF Systems......Page 189
References......Page 199
Problems......Page 200
7.1 Response to Periodic Excitation: Real Fourier Series......Page 202
7.2 Response to Periodic Excitation: Complex Fourier Series......Page 207
7.3 Response to Nonperiodic Excitation: Fourier Integral......Page 213
7.4 Relationship Between Complex Frequency Response and Unit Impulse Response......Page 217
7.5 Discrete Fourier Transform and Fast Fourier Transform......Page 218
Problems......Page 223
Part II Multiple-Degree-of-Freedom Systems—Basic Topics......Page 227
8 Mathematical Models of MDOF Systems......Page 229
8.1 Application of Newton’s Laws to Lumped-Parameter Models......Page 230
8.2 Introduction to Analytical Dynamics: Hamilton’s Principle and Lagrange’s Equations......Page 236
8.3 Application of Lagrange’s Equations to Lumped-Parameter Models......Page 241
8.4 Application of Lagrange’s Equations to Continuous Models: Assumed-Modes Method......Page 246
8.5 Constrained Coordinates and Lagrange Multipliers......Page 256
References......Page 258
Problems......Page 259
9 Vibration of Undamped 2-DOF Systems......Page 266
9.1 Free Vibration of 2-DOF Systems: Natural Frequencies and Mode Shapes......Page 267
9.2 Beat Phenomenon......Page 272
9.3 Additional Examples of Modes and Frequencies of 2-DOF Systems: Assumed-Modes Models......Page 276
9.4 Free Vibration of Systems with Rigid-Body Modes......Page 284
9.5 Introduction to Mode Superposition: Frequency Response of an Undamped 2-DOF System......Page 286
9.6 Undamped Vibration Absorber......Page 290
Problems......Page 293
10 Vibration Properties of MDOF Systems: Modes, Frequencies, and Damping......Page 299
10.1 Some Properties of Natural Frequencies and Natural Modes of Undamped MDOF Systems......Page 300
10.2 Model Reduction: Rayleigh, Rayleigh–Ritz, and Assumed-Modes Methods......Page 316
10.3 Uncoupled Damping in MDOF Systems......Page 320
10.4 Structures with Arbitrary Viscous Damping: Complex Modes......Page 325
10.5 Natural Frequencies and Mode Shapes of Damped Structures with Rigid-Body Modes......Page 334
Problems......Page 340
11.1 Mode-Superposition Method: Principal Coordinates......Page 343
11.2 Mode-Superposition Solutions for MDOF Systems with Modal Damping: Frequency-Response Analysis......Page 348
11.3 Mode-Displacement Solution for the Response of MDOF Systems......Page 360
11.4 Mode-Acceleration Solution for the Response of Undamped MDOF Systems......Page 367
11.5 Dynamic Stresses by Mode Superposition......Page 369
11.6 Mode Superposition for Undamped Systems with Rigid-Body Modes......Page 371
References......Page 377
Problems......Page 378
Part III Continuous Systems......Page 383
12.1 Applications of Newton’s Laws: Axial Deformation and Torsion......Page 385
12.2 Application of Newton’s Laws: Transverse Vibration of Linearly Elastic Beams (Bernoulli–Euler Beam Theory)......Page 392
12.3 Application of Hamilton’s Principle: Torsion of a Rod with Circular Cross Section......Page 397
12.4 Application of the Extended Hamilton’s Principle: Beam Flexure Including Shear Deformation and Rotatory Inertia (Timoshenko Beam Theory)......Page 400
Problems......Page 403
13.1 Free Axial and Torsional Vibration......Page 406
13.2 Free Transverse Vibration of Bernoulli–Euler Beams......Page 410
13.3 Rayleigh’s Method for Approximating the Fundamental Frequency of a Continuous System......Page 416
13.4 Free Transverse Vibration of Beams Including Shear Deformation and Rotatory Inertia......Page 418
13.5 Some Properties of Natural Modes of Continuous Systems......Page 419
13.6 Free Vibration of Thin Flat Plates......Page 423
Problems......Page 427
Part IV Computational Methods in Structural Dynamics......Page 433
14 Introduction to Finite Element Modeling of Structures......Page 435
14.1 Introduction to the Finite Element Method......Page 436
14.2 Element Stiffness and Mass Matrices and Element Force Vector......Page 437
14.3 Transformation of Element Matrices......Page 448
14.4 Assembly of System Matrices: Direct Stiffness Method......Page 456
14.5 Boundary Conditions......Page 463
14.6 Constraints: Reduction of Degrees of Freedom......Page 465
14.7 Systems with Rigid-Body Modes......Page 469
14.8 Finite Element Solutions for Natural Frequencies and Mode Shapes......Page 471
References......Page 480
Problems......Page 481
15.1 Introduction to Methods for Solving Algebraic Eigenproblems......Page 487
15.2 Vector Iteration Methods......Page 489
15.3 Subspace Iteration......Page 498
15.4 QR Method for Symmetric Eigenproblems......Page 501
15.5 Lanczos Eigensolver......Page 507
15.6 Numerical Case Study......Page 514
Problems......Page 516
16 Direct Integration Methods for Dynamic Response of MDOF Systems......Page 518
16.1 Damping in MDOF Systems......Page 519
16.2 Numerical Integration: Mathematical Framework......Page 522
16.3 Integration of Second-Order MDOF Systems......Page 528
16.4 Single-Step Methods and Spectral Stability......Page 534
16.5 Numerical Case Study......Page 543
References......Page 545
Problems......Page 546
17 Component-Mode Synthesis......Page 549
17.1 Introduction to Component-Mode Synthesis......Page 550
17.2 Component Modes: Normal, Constraint, and Rigid-Body Modes......Page 552
17.3 Component Modes: Attachment and Inertia-Relief Attachment Modes......Page 557
17.4 Flexibility Matrices and Residual Flexibility......Page 562
17.5 Substructure Coupling Procedures......Page 567
17.6 Component-Mode Synthesis Methods: Fixed-Interface Methods......Page 575
17.7 Component-Mode Synthesis Methods: Free-Interface Methods......Page 577
17.8 Brief Introduction to Multilevel Substructuring......Page 582
References......Page 589
Problems......Page 590
Part V Advanced Topics in Structural Dynamics......Page 595
18 Introduction to Experimental Modal Analysis......Page 597
18.1 Introduction......Page 598
18.2 Frequency-Response Function Representations......Page 602
18.3 Vibration Test Hardware......Page 608
18.4 Fourier Transforms, Digital Signal Processing, and Estimation of FRFs......Page 612
18.5 Modal Parameter Estimation......Page 622
18.6 Mode Shape Estimation and Model Verification......Page 630
References......Page 633
Problems......Page 634
19.1 Introduction to Piezoelectric Materials......Page 635
19.2 Constitutive Laws of Linear Piezoelectricity......Page 638
19.3 Application of Newton’s Laws to Piezostructural Systems......Page 642
19.4 Application of Extended Hamilton’s Principle to Piezoelectricity......Page 645
19.5 Active Truss Models......Page 648
19.6 Active Beam Models......Page 655
19.7 Active Composite Laminates......Page 659
References......Page 664
Problems......Page 665
20.1 Introduction......Page 668
20.2 Response of a SDOF System to Earthquake Excitation: Response Spectra......Page 670
20.3 Response of MDOF Systems to Earthquake Excitation......Page 678
20.4 Further Considerations......Page 682
References......Page 683
Problems......Page 684
A Units......Page 685
B Complex Numbers......Page 689
C Elements of Laplace Transforms......Page 692
D Fundamentals of Linear Algebra......Page 700
E Introduction to the Use of Matlab......Page 715
Index......Page 733