كتاب Mechanical Vibrations Sixth Edition
منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Mechanical Vibrations Sixth Edition

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تاريخ التسجيل : 01/07/2009
العمر : 29
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مُساهمةموضوع: كتاب Mechanical Vibrations Sixth Edition   الثلاثاء 22 مايو 2018, 10:53 am

أخوانى فى الله
أحضرت لكم الكتاب الأشهر في مجال اهتزازات الماكينات بأحد اصداراته كامل
كتاب
Mechanical Vibrations Sixth Edition in SI Units
Singiresu S. Rao
University of Miami
SI Conversion by
Philip Griffin
University of Limerick, Ireland


ويتناول الموضوعات الأتية :

Contents
Preface 16
Acknowledgments 21
List of Symbols 23
ChAPtEr 1
Fundamentals of Vibration 29
1.1 Preliminary Remarks 30
1.2 Brief History of the Study of Vibration 31
1.2.1 Origins of the Study of Vibration 31
1.2.2 From Galileo to Rayleigh 33
1.2.3 Recent Contributions 36
1.3 Importance of the Study of Vibration 38
1.3.1 Conversion of Vibrations to
Sound by the Human Ear 40
1.4 Basic Concepts of Vibration 43
1.4.1 Vibration 43
1.4.2 Elementary Parts of
Vibrating Systems 43
1.4.3 Number of Degrees of Freedom 44
1.4.4 Discrete and Continuous Systems 46
1.5 Classification of Vibration 46
1.5.1 Free and Forced Vibration 46
1.5.2 Undamped and Damped Vibration 47
1.5.3 Linear and Nonlinear Vibration 47
1.5.4 Deterministic and
Random Vibration 47
1.6 Vibration Analysis Procedure 48
1.7 Spring Elements 52
1.7.1 Nonlinear Springs 53
1.7.2 Linearization of a Nonlinear Spring 55
1.7.3 Spring Constants of Elastic Elements 57
1.7.4 Combination of Springs 60
1.7.5 Spring Constant Associated with the
Restoring Force due to Gravity 68
1.8 Mass or Inertia Elements 69
1.8.1 Combination of Masses 70
1.9 Damping Elements 74
1.9.1 Construction of Viscous Dampers 75
1.9.2 Linearization of a Nonlinear Damper 81
1.9.3 Combination of Dampers 81
1.10 Harmonic Motion 83
1.10.1 Vectorial Representation of
Harmonic Motion 85
1.10.2 Complex-Number Representation
of Harmonic Motion 86
1.10.3 Complex Algebra 87
1.10.4 Operations on Harmonic Functions 87
1.10.5 Definitions and Terminology 90
1.11 Harmonic Analysis 93
1.11.1 Fourier Series Expansion 93
1.11.2 Complex Fourier Series 95
1.11.3 Frequency Spectrum 96
1.11.4 Time- and Frequency-Domain
Representations 97
1.11.5 Even and Odd Functions 98
1.11.6 Half-Range Expansions 100
1.11.7 Numerical Computation
of Coefficients 101
1.12 Examples Using MATLAB 105
1.13 Vibration Literature 109
Chapter Summary 110
References 110
Review Questions 112
Problems 116
Design Projects 14910 ContEntS
ChAPtEr 2
Free Vibration of Single-Degree-of-Freedom
Systems 153
2.1 Introduction 155
2.2 Free Vibration of an Undamped
Translational System 158
2.2.1 Equation of Motion Using Newton’s
Second Law of Motion 158
2.2.2 Equation of Motion Using Other
Methods 159
2.2.3 Equation of Motion of a Spring-Mass
System in Vertical Position 161
2.2.4 Solution 162
2.2.5 Harmonic Motion 163
2.3 Free Vibration of an Undamped
Torsional System 176
2.3.1 Equation of Motion 177
2.3.2 Solution 178
2.4 Response of First-Order Systems
and Time Constant 181
2.5 Rayleigh’s Energy Method 183
2.6 Free Vibration with Viscous Damping 188
2.6.1 Equation of Motion 188
2.6.2 Solution 189
2.6.3 Logarithmic Decrement 198
2.6.4 Energy Dissipated in Viscous
Damping 199
2.6.5 Torsional Systems with Viscous
Damping 201
2.7 Graphical Representation of Characteristic Roots
and Corresponding Solutions 207
2.7.1 Roots of the Characteristic Equation 207
2.7.2 Graphical Representation of Roots and
Corresponding Solutions 208
2.8 Parameter Variations and Root Locus
Representations 209
2.8.1 Interpretations of vn, vd, z, and t in the
s-plane 209
2.8.2 Root Locus and Parameter
Variations 212
2.9 Free Vibration with Coulomb Damping 218
2.9.1 Equation of Motion 219
2.9.2 Solution 220
2.9.3 Torsional Systems with Coulomb
Damping 223
2.10 Free Vibration with Hysteretic Damping 225
2.11 Stability of Systems 231
2.12 Examples Using MATLAB 235
Chapter Summary 241
References 242
Review Questions 242
Problems 247
Design Projects 294
ChAPtEr 3
harmonically Excited Vibration 297
3.1 Introduction 299
3.2 Equation of Motion 299
3.3 Response of an Undamped System Under
Harmonic Force 301
3.3.1 Total Response 305
3.3.2 Beating Phenomenon 305
3.4 Response of a Damped System Under Harmonic
Force 309
3.4.1 Total Response 312
3.4.2 Quality Factor and Bandwidth 316
3.5 Response of a Damped System Under
F1t2 = F0eiVt 317
3.6 Response of a Damped System Under
the Harmonic Motion of the Base 320
3.6.1 Force Transmitted 322
3.6.2 Relative Motion 323
3.7 Response of a Damped System Under Rotating
Unbalance 326
3.8 Forced Vibration with Coulomb Damping 332
3.9 Forced Vibration with Hysteresis Damping 337
3.10 Forced Motion with Other Types
of Damping 339
3.11 Self-Excitation and Stability Analysis 340
3.11.1 Dynamic Stability Analysis 340
3.11.2 Dynamic Instability Caused by Fluid
Flow 344
3.12 Transfer-Function Approach 352
3.13 Solutions Using Laplace Transforms 356
3.14 Frequency Transfer Functions 359
3.14.1 Relation between the General Transfer
Function T(s) and the Frequency Transfer
Function T1iv2 361
3.14.2 Representation of Frequency-Response
Characteristics 362ContEntS 11
3.15 Examples Using MATLAB 365
Chapter Summary 371
References 371
Review Questions 372
Problems 375
Design Projects 402
ChAPtEr 4
Vibration Under General Forcing
Conditions 403
4.1 Introduction 404
4.2 Response Under a General
Periodic Force 405
4.2.1 First-Order Systems 406
4.2.2 Second-Order Systems 412
4.3 Response Under a Periodic Force
of Irregular Form 418
4.4 Response Under a Nonperiodic Force 420
4.5 Convolution Integral 421
4.5.1 Response to an Impulse 422
4.5.2 Response to a General Forcing
Condition 425
4.5.3 Response to Base Excitation 426
4.6 Response Spectrum 434
4.6.1 Response Spectrum for Base
Excitation 436
4.6.2 Earthquake Response Spectra 439
4.6.3 Design Under a Shock Environment 443
4.7 Laplace Transforms 446
4.7.1 Transient and Steady-State
Responses 446
4.7.2 Response of First-Order Systems 447
4.7.3 Response of Second-Order
Systems 449
4.7.4 Response to Step Force 454
4.7.5 Analysis of the Step Response 460
4.7.6 Description of Transient Response 461
4.8 Numerical Methods 467
4.8.1 Runge-Kutta Methods 469
4.9 Response to Irregular Forcing Conditions Using
Numerical Methods 471
4.10 Examples Using MATLAB 476
Chapter Summary 480
References 480
Review Questions 481
Problems 484
Design Projects 506
ChAPtEr 5
two-Degree-of-Freedom Systems 509
5.1 Introduction 510
5.2 Equations of Motion for Forced
Vibration 514
5.3 Free-Vibration Analysis of an Undamped
System 516
5.4 Torsional System 525
5.5 Coordinate Coupling and Principal
Coordinates 530
5.6 Forced-Vibration Analysis 536
5.7 Semidefinite Systems 539
5.8 Self-Excitation and Stability Analysis 542
5.9 Transfer-Function Approach 544
5.10 Solutions Using Laplace Transform 546
5.11 Solutions Using Frequency Transfer
Functions 554
5.12 Examples Using MATLAB 557
Chapter Summary 564
References 565
Review Questions 565
Problems 568
Design Projects 594
ChAPtEr 6
Multidegree-of-Freedom Systems 596
6.1 Introduction 598
6.2 Modeling of Continuous Systems as Multidegreeof-Freedom Systems 598
6.3 Using Newton’s Second Law to Derive Equations
of Motion 600
6.4 Influence Coefficients 605
6.4.1 Stiffness Influence Coefficients 605
6.4.2 Flexibility Influence Coefficients 610
6.4.3 Inertia Influence Coefficients 615
6.5 Potential and Kinetic Energy Expressions in
Matrix Form 617
6.6 Generalized Coordinates and Generalized
Forces 619
6.7 Using Lagrange’s Equations to Derive Equations
of Motion 62012 ContEntS
6.8 Equations of Motion of Undamped Systems in
Matrix Form 624
6.9 Eigenvalue Problem 626
6.10 Solution of the Eigenvalue Problem 628
6.10.1 Solution of the Characteristic (Polynomial)
Equation 628
6.10.2 Orthogonality of Normal Modes 634
6.10.3 Repeated Eigenvalues 637
6.11 Expansion Theorem 639
6.12 Unrestrained Systems 639
6.13 Free Vibration of Undamped Systems 644
6.14 Forced Vibration of Undamped Systems Using
Modal Analysis 646
6.15 Forced Vibration of Viscously Damped
Systems 653
6.16 Self-Excitation and Stability Analysis 660
6.17 Examples Using MATLAB 662
Chapter Summary 670
References 670
Review Questions 671
Problems 675
Design Projects 696
ChAPtEr 7
Determination of natural Frequencies
and Mode Shapes 699
7.1 Introduction 700
7.2 Dunkerley’s Formula 701
7.3 Rayleigh’s Method 703
7.3.1 Properties of Rayleigh’s Quotient 704
7.3.2 Computation of the Fundamental Natural
Frequency 706
7.3.3 Fundamental Frequency of Beams and
Shafts 708
7.4 Holzer’s Method 711
7.4.1 Torsional Systems 711
7.4.2 Spring-Mass Systems 714
7.5 Matrix Iteration Method 715
7.5.1 Convergence to the Highest Natural
Frequency 717
7.5.2 Computation of Intermediate Natural
Frequencies 718
7.6 Jacobi’s Method 723
7.7 Standard Eigenvalue Problem 725
7.7.1 Choleski Decomposition 726
7.7.2 Other Solution Methods 728
7.8 Examples Using MATLAB 728
Chapter Summary 731
References 731
Review Questions 733
Problems 735
Design Projects 744
ChAPtEr 8
Continuous Systems 745
8.1 Introduction 746
8.2 Transverse Vibration of a String or Cable 747
8.2.1 Equation of Motion 747
8.2.2 Initial and Boundary Conditions 749
8.2.3 Free Vibration of a Uniform String 750
8.2.4 Free Vibration of a String with Both Ends
Fixed 751
8.2.5 Traveling-Wave Solution 755
8.3 Longitudinal Vibration of a Bar or Rod 756
8.3.1 Equation of Motion and Solution 756
8.3.2 Orthogonality of Normal Functions 759
8.4 Torsional Vibration of a Shaft or Rod 764
8.5 Lateral Vibration of Beams 767
8.5.1 Equation of Motion 767
8.5.2 Initial Conditions 769
8.5.3 Free Vibration 769
8.5.4 Boundary Conditions 770
8.5.5 Orthogonality of Normal
Functions 772
8.5.6 Forced Vibration 776
8.5.7 Effect of Axial Force 778
8.5.8 Effects of Rotary Inertia and Shear
Deformation 780
8.5.9 Beams on Elastic Foundation 785
8.5.10 Other Effects 788
8.6 Vibration of Membranes 788
8.6.1 Equation of Motion 788
8.6.2 Initial and Boundary Conditions 790
8.7 Rayleigh’s Method 791
8.8 The Rayleigh-Ritz Method 794
8.9 Examples Using MATLAB 797
Chapter Summary 800
References 800
Review Questions 802
Problems 805
Design Project 818ContEntS 13
ChAPtEr 9
Vibration Control 819
9.1 Introduction 820
9.2 Vibration Nomograph and Vibration
Criteria 821
9.3 Reduction of Vibration at the Source 825
9.4 Balancing of Rotating Machines 826
9.4.1 Single-Plane Balancing 826
9.4.2 Two-Plane Balancing 829
9.5 Whirling of Rotating Shafts 835
9.5.1 Equations of Motion 835
9.5.2 Critical Speeds 837
9.5.3 Response of the System 838
9.5.4 Stability Analysis 840
9.6 Balancing of Reciprocating Engines 842
9.6.1 Unbalanced Forces Due to Fluctuations in
Gas Pressure 842
9.6.2 Unbalanced Forces Due to Inertia of the
Moving Parts 843
9.6.3 Balancing of Reciprocating Engines 846
9.7 Control of Vibration 848
9.8 Control of Natural Frequencies 848
9.9 Introduction of Damping 849
9.10 Vibration Isolation 851
9.10.1 Vibration Isolation System with Rigid
Foundation 854
9.10.2 Vibration Isolation System with Base
Motion 864
9.10.3 Vibration Isolation System with Flexible
Foundation 872
9.10.4 Vibration Isolation System with Partially
Flexible Foundation 874
9.10.5 Shock Isolation 875
9.10.6 Active Vibration Control 878
9.11 Vibration Absorbers 883
9.11.1 Undamped Dynamic Vibration
Absorber 884
9.11.2 Damped Dynamic Vibration
Absorber 891
9.12 Examples Using MATLAB 895
Chapter Summary 903
References 903
Review Questions 905
Problems 907
Design Project 922
ChAPtEr 10
Vibration Measurement and
Applications 924
10.1 Introduction 925
10.2 Transducers 927
10.2.1 Variable-Resistance Transducers 927
10.2.2 Piezoelectric Transducers 930
10.2.3 Electrodynamic Transducers 931
10.2.4 Linear Variable Differential Transformer
Transducer 932
10.3 Vibration Pickups 933
10.3.1 Vibrometer 935
10.3.2 Accelerometer 936
10.3.3 Velometer 940
10.3.4 Phase Distortion 942
10.4 Frequency-Measuring Instruments 944
10.5 Vibration Exciters 946
10.5.1 Mechanical Exciters 946
10.5.2 Electrodynamic Shaker 947
10.6 Signal Analysis 949
10.6.1 Spectrum Analyzers 950
10.6.2 Bandpass Filter 951
10.6.3 Constant-Percent Bandwidth and
Constant-Bandwidth Analyzers 952
10.7 Dynamic Testing of Machines and
Structures 954
10.7.1 Using Operational Deflection-Shape
Measurements 954
10.7.2 Using Modal Testing 954
10.8 Experimental Modal Analysis 954
10.8.1 The Basic Idea 954
10.8.2 The Necessary Equipment 954
10.8.3 Digital Signal Processing 957
10.8.4 Analysis of Random Signals 959
10.8.5 Determination of Modal Data from
Observed Peaks 961
10.8.6 Determination of Modal Data from
Nyquist Plot 964
10.8.7 Measurement of Mode Shapes 966
10.9 Machine-Condition Monitoring and
Diagnosis 969
10.9.1 Vibration Severity Criteria 969
10.9.2 Machine Maintenance Techniques 969
10.9.3 Machine-Condition Monitoring
Techniques 97014 ContEntS
10.9.4 Vibration Monitoring Techniques 972
10.9.5 Instrumentation Systems 978
10.9.6 Choice of Monitoring Parameter 978
10.10 Examples Using MATLAB 979
Chapter Summary 982
References 982
Review Questions 984
Problems 986
Design Projects 992
ChAPtEr 11
numerical Integration Methods in
Vibration Analysis 993
11.1 Introduction 994
11.2 Finite Difference Method 995
11.3 Central Difference Method for Single-Degree-ofFreedom Systems 996
11.4 Runge-Kutta Method for Single-Degree-ofFreedom Systems 999
11.5 Central Difference Method for Multidegree-ofFreedom Systems 1001
11.6 Finite Difference Method for Continuous
Systems 1005
11.6.1 Longitudinal Vibration of Bars 1005
11.6.2 Transverse Vibration of Beams 1009
11.7 Runge-Kutta Method for Multidegree-ofFreedom Systems 1014
11.8 Houbolt Method 1016
11.9 Wilson Method 1019
11.10 Newmark Method 1022
11.11 Examples Using MATLAB 1026
Chapter Summary 1032
References 1032
Review Questions 1033
Problems 1035
ChAPtEr 12
Finite Element Method 1041
12.1 Introduction 1042
12.2 Equations of Motion of an Element 1043
12.3 Mass Matrix, Stiffness Matrix, and Force
Vector 1045
12.3.1 Bar Element 1045
12.3.2 Torsion Element 1048
12.3.3 Beam Element 1049
12.4 Transformation of Element Matrices
and Vectors 1052
12.5 Equations of Motion of the Complete System
of Finite Elements 1055
12.6 Incorporation of Boundary Conditions 1057
12.7 Consistent- and Lumped-Mass Matrices 1066
12.7.1 Lumped-Mass Matrix for a Bar
Element 1066
12.7.2 Lumped-Mass Matrix for a Beam
Element 1066
12.7.3 Lumped-Mass Versus Consistent-Mass
Matrices 1067
12.8 Examples Using MATLAB 1069
Chapter Summary 1073
References 1073
Review Questions 1074
Problems 1076
Design Projects 1088
Chapters 13 and 14 are provided as downloadable
files on the Companion Website.
ChAPtEr 13
nonlinear Vibration 13-1
13.1 Introduction 13-2
13.2 Examples of Nonlinear Vibration Problems 13-3
13.2.1 Simple Pendulum 13-3
13.2.2 Mechanical Chatter, Belt Friction
System 13-5
13.2.3 Variable Mass System 13-5
13.3 Exact Methods 13-6
13.4 Approximate Analytical Methods 13-7
13.4.1 Basic Philosophy 13-8
13.4.2 Lindstedt’s Perturbation
Method 13-10
13.4.3 Iterative Method 13-13
13.4.4 Ritz-Galerkin Method 13-17
13.5 Subharmonic and Superharmonic
Oscillations 13-19
13.5.1 Subharmonic Oscillations 13-20
13.5.2 Superharmonic Oscillations 13-23ContEntS 15
13.6 Systems with Time-Dependent Coefficients
(Mathieu Equation) 13-24
13.7 Graphical Methods 13-29
13.7.1 Phase-Plane Representation 13-29
13.7.2 Phase Velocity 13-34
13.7.3 Method of Constructing
Trajectories 13-34
13.7.4 Obtaining Time Solution from Phase-Plane
Trajectories 13-36
13.8 Stability of Equilibrium States 13-37
13.8.1 Stability Analysis 13-37
13.8.2 Classification of Singular Points 13-40
13.9 Limit Cycles 13-41
13.10 Chaos 13-43
13.10.1 Functions with Stable Orbits 13-45
13.10.2 Functions with Unstable Orbits 13-45
13.10.3 Chaotic Behavior of Duffing’s Equation
Without the Forcing Term 13-47
13.10.6 Chaotic Behavior of Duffing’s Equation
with the Forcing Term 13-50
13.11 Numerical Methods 13-52
13.12 Examples Using MATLAB 13-53
Chapter Summary 13-62
References 13-62
Review Questions 13-64
Problems 13-67
Design Projects 13-75
ChAPtEr 14
random Vibration 14-1
14.1 Introduction 14-2
14.2 Random Variables and Random Processes 14-3
14.3 Probability Distribution 14-4
14.4 Mean Value and Standard Deviation 14-6
14.5 Joint Probability Distribution of Several
Random Variables 14-7
14.6 Correlation Functions of a Random
Process 14-9
14.7 Stationary Random Process 14-10
14.8 Gaussian Random Process 14-14
14.9 Fourier Analysis 14-16
14.9.1 Fourier Series 14-16
14.9.2 Fourier Integral 14-19
14.10 Power Spectral Density 14-23
14.11 Wide-Band and Narrow-Band Processes 14-25
14.12 Response of a Single-Degree-of-Freedom
System 14-28
14.12.1 Impulse-Response Approach 14-28
14.12.2 Frequency-Response Approach 14-30
14.12.3 Characteristics of the Response
Function 14-30
14.13 Response Due to Stationary Random
Excitations 14-31
14.13.1 Impulse-Response Approach 14-32
14.13.2 Frequency-Response Approach 14-33
14.14 Response of a Multidegree-of-Freedom
System 14-39
14.15 Examples Using MATLAB 14-46
Chapter Summary 14-49
References 14-49
Review Questions 14-50
Problems 14-53
Design Project 14-61
APPEnDIx A
Mathematical relations and Material Properties 1092
APPEnDIx B
Deflection of Beams and Plates 1095
APPEnDIx C
Matrices 1097
APPEnDIx D
Laplace transform 1104
APPEnDIx E
Units 1112
APPEnDIx F
Introduction to MAtLAB 1116
Answers to Selected Problems 1126
Index 1135


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