EBOOK - Vibrations (Balakumar Balachandran & Edward B. Magrab) | Cộng đồng Kỹ thuật cơ điện Việt Nam EBOOKBKMT

EBOOK - Rung động (Balakumar Balachandran & Edward B. Magrab) - 793 Trang.

1 Introduction 1
1.1 Introduction 1
1.2 Preliminaries from Dynamics 4
1.3 Summary 19
Exercises 19
2 Modeling of Vibratory Systems 23
2.1 Introduction 23
2.2 Inertia Elements 24
2.3 Stiffness Elements 28
2.4 Dissipation Elements 49
2.5 Model Construction 54
2.6 Design for Vibration 60
2.7 Summary 61
Exercises 61
3 Single Degree-Of-Freedom Systems: Governing Equations 69
3.1 Introduction 69
3.2 Force-Balance and Moment-Balance Methods 70
3.3 Natural Frequency and Damping Factor 79
3.4 Governing Equations for Different Types of Damping 88
3.5 Governing Equations for Different Types of Applied Forces 89
3.6 Lagrange’s Equations 93
3.7 Summary 116
Exercises 117

4 Single Degree-of-Freedom System: Free-Response Characteristics 127
4.1 Introduction 127
4.2 Free Responses of Undamped and Damped Systems 129
4.3 Stability of a Single Degree-of-Freedom System 161
4.4 Machine Tool Chatter 165
4.5 Single Degree-of-Freedom Systems with Nonlinear Elements 168
4.6 Summary 174
Exercises 174
5 Single Degree-of-Freedom Systems Subjected to Periodic Excitations 181
5.1 Introduction 181
5.2 Response to Harmonic Excitation 183
5.3 Frequency-Response Function 204
5.4 System with Rotating Unbalanced Mass 218
5.5 System with Base Excitation 225
5.6 Acceleration Measurement: Accelerometer 235
5.7 Vibration Isolation 238
5.8 Energy Dissipation and Equivalent Damping 244
5.9 Response to Excitation with Harmonic
Components 255
5.10 Influence of Nonlinear Stiffness on
Forced Response 269
5.11 Summary 277
Exercises 277
6 Single Degree-of-Freedom Systems Subjected to Transient Excitations 285
6.1 Introduction 285
6.2 Response to Impulse Excitation 287
6.3 Response to Step Input 300
6.4 Response to Ramp Input 310
6.5 Spectral Energy of the Response 316
6.6 Response to Rectangular Pulse Excitation 317
6.7 Response to Half-Sine Wave Pulse 322
6.8 Impact Testing 332
6.8 Summary 333
Exercises 333
7 Multiple Degree-of-Freedom Systems: Governing Equations, Natural Frequencies, and Mode Shapes 337
7.1 Introduction 337
7.2 Governing Equations 338
7.3 Free Response Characteristics 369
7.4 Rotating Shafts On Flexible Supports 409
7.5 Stability 419
7.6 Summary 422
Exercises 422
8 Multiple Degree-of-Freedom Systems: General Solution for Response and Forced Oscillations 435
8.1 Introduction 435
8.2 Normal-Mode Approach 438
8.3 State-Space Formulation 458
8.4 Laplace Transform Approach 471
8.5 Transfer Functions and Frequency-Response
Functions 481
8.6 Vibration Absorbers 495
8.7 Vibration Isolation: Transmissibility Ratio 525
8.8 Systems with Moving Base 530
8.9 Summary 534
Exercises 535
9Vibrations of Beams 541
9.1 Introduction 541
9.2 Governing Equations of Motion 543
9.3 Free Oscillations: Natural Frequencies and
Mode Shapes 562
9.4 Forced Oscillations 632
9.5 Summary 648
Glossary 649
Appendix
A Laplace Transform Pairs 653
B Fourier Series 660
C Decibel Scale 661
D Solutions to Ordinary Differential Equations 663
vi Contents
E Matrices 675
F Complex Numbers and Variables 679
G Natural Frequencies and Mode Shapes of Bars,
Shafts, and Strings 683
Answers to Selected Exercises 693

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