Engineering vibrations

Başlık:

Yazar:

Bottega, William J.

ISBN:

9780849334207

Ek Yazar:

Bottega, William J.

Yayım Bilgisi:

Boca Raton : CRC/Taylor & Francis, 2006.

Fiziksel Tanım:

xix, 726 s. : şkl. ; 23 cm.

Konu Terimleri:

Titreşim.

Vibration.

Mevcut:*

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0063340	TA355.B635 2006	Searching... Unknown

A resource on vibration that imparts a deep physical as well as mathematical understanding is critical to students who first encounter the subject. Books with an overly mathematical focus can leave them without a grasp of the underlying physics and mechanics. Those that attempt to be reader-friendly often oversimplify the mathematics and mechanics, leaving them with a lack of depth and unprepared for advanced work and complex problems. With a carefully balanced approach, Engineering Vibrations provides a systematic and unified treatment of mechanical and structural vibrations along with rigorous yet approachable mathematical development.

This text advances abstract concepts from first principles. The author weaves together the physical interpretation and fundamental principles with applied problem solving and uses illustrative examples and case studies to reinforce the concepts, encourage effective interpretation of results, and assist in learning the techniques and procedures. Accompanied by more than 500 two- and three-dimensional drawings, the book offers tabulated results of case studies and a table of operators of various one-dimensional continua. It also contains problem-solving flowcharts for solving forced vibration problems for discrete and continuous systems. For each class of system, it explores the fundamental dynamics and studies free and forced vibrations under various conditions.

Buildinga solid understanding of the principles and bases for mechanical and structural vibration, Engineering Vibrations offers a comprehensive and accessible introduction to the subject of vibrations and progresses systematically to advanced topics.

1 Preliminaries	p. 1
1.1 Degrees of Freedom	p. 2
1.2 Equivalent Systems	p. 6
1.2.1 Extension/Contraction of Elastic Rods	p. 6
1.2.2 Bending of Elastic Beams	p. 8
1.2.3 Torsion of Elastic Rods	p. 16
1.2.4 Floating Bodies	p. 20
1.2.5 The Viscous Damper	p. 22
1.2.6 Aero/Hydrodynamic Damping (Drag)	p. 24
1.3 Springs Connected in Parallel and in Series	p. 25
1.3.1 Springs in Parallel	p. 26
1.3.2 Springs in Series	p. 26
1.4 A Brief Review of Complex Numbers	p. 28
1.5 A Review of Elementary Dynamics	p. 30
1.5.1 Kinematics of Particles	p. 31
1.5.2 Kinetics of a Single Particle	p. 38
1.5.3 Dynamics of Particle Systems	p. 49
1.5.4 Kinematics of Rigid Bodies	p. 56
1.5.5 (Planar) Kinetics of Rigid Bodies	p. 60
1.6 Concluding Remarks	p. 66
Bibliography	p. 67
Problems	p. 67
2 Free Vibration of Single Degree of Freedom Systems	p. 75
2.1 Free Vibration of Undamped Systems	p. 75
2.1.1 Governing Equation and System Response	p. 76
2.1.2 The Effect of Gravity	p. 87
2.1.3 Work and Energy	p. 93
2.1.4 The Simple Pendulum	p. 94
2.2 Free Vibration of Systems with Viscous Damping	p. 109
2.2.1 Equation of Motion and General System Response	p. 109
2.2.2 Underdamped Systems	p. 111
2.2.3 Logarithmic Decrement	p. 115
2.2.4 Overdamped Systems	p. 119
2.2.5 Critically Damped Systems	p. 121
2.3 Coulomb (Dry Friction) Damping	p. 127
2.3.1 Stick-Slip Condition	p. 127
2.3.2 System Response	p. 129
2.4 Concluding Remarks	p. 133
Bibliography	p. 135
Problems	p. 135
3 Forced Vibration of Single Degree of Freedom Systems &3- 1: Periodic Excitation	p. 143
3.1 Standard Form of the Equation of Motion	p. 143
3.2 Superposition	p. 144
3.3 Harmonic Forcing	p. 147
3.3.1 Formulation	p. 147
3.3.2 Steady State Response of Undamped Systems	p. 149
3.3.3 Steady State Response of Systems with Viscous Damping	p. 162
3.3.4 Force Transmission and Vibration Isolation	p. 179
3.4 Structural Damping	p. 184
3.4.1 Linear Hereditary Materials	p. 185
3.4.2 Steady State Response of Linear Hereditary Materials	p. 186
3.4.3 Steady State Response of Single Degree of Freedom Systems	p. 189
3.5 Selected Applications	p. 192
3.5.1 Harmonic Motion of the Support	p. 192
3.5.2 Unbalanced Motor	p. 201
3.5.3 Synchronous Whirling of Rotating Shafts	p. 206
3.6 Response to General Periodic Loading	p. 211
3.6.1 General Periodic Excitation	p. 211
3.6.2 Steady State Response	p. 213
3.7 Concluding Remarks	p. 219
Bibliography	p. 220
Problems	p. 220
4 Forced Vibration of Single Degree of Freedom Systems - 2: Nonperiodic Excitation	p. 229
4.1 Two Generalized Functions	p. 229
4.1.1 The Dirac Delta Function (Unit Impulse)	p. 230
4.1.2 The Heaviside Step Function (Unit Step)	p. 232
4.1.3 Relation Between the Unit Step and the Unit Impulse	p. 233
4.2 Impulse Response	p. 234
4.2.1 Impulsive and Nonimpulsive Forces	p. 234
4.2.2 Response to an Applied Impulse	p. 235
4.3 Response to Arbitrary Excitation	p. 239
4.4 Response to Step Loading	p. 241
4.5 Response to Ramp Loading	p. 246
4.6 Transient Response by Superposition	p. 248
4.6.1 The Rectangular Pulse	p. 249
4.6.2 Linear Transition to Constant Load Level	p. 255
4.7 Shock Spectra	p. 257
4.8 Concluding Remarks	p. 268
Bibliography	p. 269
Problems	p. 269
5 Operational Methods	p. 273
5.1 The Laplace Transform	p. 273
5.1.1 Laplace Transforms of Basic Functions	p. 274
5.1.2 Shifting Theorem	p. 276
5.1.3 Laplace Transforms of the Derivatives of Functions	p. 277
5.1.4 Convolution	p. 278
5.2 Free Vibrations	p. 279
5.3 Forced Vibrations	p. 281
5.3.1 The Governing Equations	p. 281
5.3.2 Steady State Response	p. 282
5.3.3 Transient Response	p. 283
5.4 Concluding Remarks	p. 285
Bibliography	p. 285
Problems	p. 285
6 Dynamics of Multi-Degree of Freedom Systems	p. 287
6.1 Newtonian Mechanics of Discrete Systems	p. 288
6.1.1 Mass-Spring Systems	p. 288
6.1.2 The Double Pendulum	p. 296
6.1.3 Two-Dimensional Motion of a Rigid Frame	p. 300
6.2 Lagrange's Equations	p. 303
6.2.1 Virtual Work	p. 304
6.2.2 The Canonical Equations	p. 306
6.2.3 Implementation	p. 309
6.2.4 The Rayleigh Dissipation Function	p. 321
6.3 Symmetry of the System Matrices	p. 324
6.3.1 The Stiffness Matrix	p. 324
6.3.2 The Mass Matrix	p. 327
6.3.3 The Damping Matrix	p. 328
6.4 Concluding Remarks	p. 329
Bibliography	p. 330
Problems	p. 330
7 Free Vibration of Multi-Degree of Freedom Systems	p. 341
7.1 The General Free Vibration Problem and Its Solution	p. 341
7.2 Unrestrained Systems	p. 371
7.3 Properties of Modal Vectors	p. 374
7.3.1 The Scalar Product	p. 375
7.3.2 Orthogonality	p. 377
7.3.3 Normalization	p. 384
7.4 Systems with Viscous Damping	p. 387
7.4.1 System Response	p. 387
7.4.2 State Space Representation	p. 394
7.5 Evaluation of Amplitudes and Phase Angles	p. 400
7.5.1 Undamped Systems	p. 401
7.5.2 Systems with General Viscous Damping	p. 403
7.6 Concluding Remarks	p. 404
Bibliography	p. 405
Problems	p. 405
8 Forced Vibration of Multi-Degree of Freedom Systems	p. 415
8.1 Introduction	p. 416
8.1.1 Steady State Response to Harmonic Excitation	p. 416
8.1.2 The Simple Vibration Absorber	p. 418
8.2 Modal Coordinates	p. 422
8.2.1 Principal Coordinates	p. 422
8.2.2 Coordinate Transformations	p. 424
8.2.3 Modal Coordinates	p. 427
8.3 General Motion in Terms of the Natural Modes	p. 431
8.3.1 Linear Independence of the Set of Modal Vectors	p. 431
8.3.2 Modal Expansion	p. 432
8.4 Decomposition of the Forced Vibration Problem	p. 433
8.5 Solution of Forced Vibration Problems	p. 440
8.6 Mode Isolation	p. 468
8.7 Rayleigh Damping	p. 474
8.8 Systems with General Viscous Damping	p. 479
8.8.1 Steady State Response to Harmonic Excitation	p. 480
8.8.2 Eigenvector Expansion	p. 483
8.8.3 Decomposition of the Forced Vibration Problem	p. 484
8.8.4 Solution of Forced Vibration Problems	p. 487
8.9 Concluding Remarks	p. 498
Bibliography	p. 500
Problems	p. 500
9 Dynamics of One-Dimensional Continua	p. 511
9.1 Mathematical Description of 1-D Continua	p. 511
9.1.1 Correspondence Between Discrete and Continuous Systems	p. 512
9.1.2 The Scalar Product and Orthogonality	p. 517
9.2 Characterization of Local Deformation	p. 520
9.2.1 Relative Extension of a Material Line Element	p. 521
9.2.2 Distortion	p. 524
9.3 Longitudinal Motion of Elastic Rods	p. 525
9.4 Torsional Motion of Elastic Rods	p. 530
9.5 Transverse Motion of Strings and Cables	p. 534
9.6 Transverse Motion of Elastic Beams	p. 539
9.6.1 Kinematical and Constitutive Relations	p. 539
9.6.2 Kinetics	p. 543
9.6.3 Euler-Bernoulli Beam Theory	p. 544
9.6.4 Rayleigh Beam Theory	p. 549
9.6.5 Timoshenko Beam Theory	p. 552
9.7 Geometrically Nonlinear Beam Theory	p. 558
9.8 Translating 1-D Continua	p. 562
9.8.1 Kinematics of a Material Particle	p. 562
9.8.2 Kinetics	p. 565
9.9 Concluding Remarks	p. 569
Bibliography	p. 570
Problems	p. 571
10 Free Vibration of One-Dimensional Continua	p. 579
10.1 The General Free Vibration Problem	p. 579
10.2 Free Vibration of Uniform Second Order Systems	p. 581
10.2.1 The General Free Vibration Problem and Its Solution	p. 581
10.2.2 Longitudinal Vibration of Elastic Rods	p. 582
10.2.3 Torsional Vibration of Elastic Rods	p. 591
10.2.4 Transverse Vibration of Strings and Cables	p. 595
10.3 Free Vibration of Euler-Bernoulli Beams	p. 599
10.4 Free Vibration of Euler-Bernoulli Beam-Columns	p. 617
10.5 Free Vibration of Rayleigh Beams	p. 622
10.6 Free Vibration of Timoshenko Beams	p. 627
10.7 Normalization of the Modal Functions	p. 634
10.8 Orthogonality of the Modal Functions	p. 636
10.8.1 Systems Whose Mass Operators Are Scalar Functions	p. 637
10.8.2 Second Order Systems	p. 639
10.8.3 Euler-Bernoulli Beams and Beam-Columns	p. 646
10.8.4 Rayleigh Beams	p. 652
10.8.5 Timoshenko Beams	p. 656
10.9 Evaluation of Amplitudes and Phase Angles	p. 660
10.9.1 Systems Possessing a Single Scalar Mass Operator	p. 660
10.9.2 Rayleigh Beams	p. 666
10.9.3 Timoshenko Beams	p. 669
10.10 Concluding Remarks	p. 673
Bibliography	p. 675
Problems	p. 675
11 Forced Vibration of One-Dimensional Continua	p. 683
11.1 Modal Expansion	p. 684
11.1.1 Linear Independence of the Modal Functions	p. 684
11.1.2 Generalized Fourier Series	p. 685
11.2 Decomposition of the Forced Vibration Problem	p. 686
11.3 Solution of Forced Vibration Problems	p. 690
11.3.1 Axially Loaded Elastic Rods	p. 690
11.3.2 Torsion of Elastic Rods	p. 692
11.3.3 Strings and Cables	p. 694
11.3.4 Euler-Bernoulli Beams	p. 697
11.3.5 Rayleigh Beams	p. 708
11.3.6 Timoshenko Beams	p. 711
11.4 Concluding Remarks	p. 714
Bibliography	p. 714
Problems	p. 715
Index	p. 721

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