Page 12 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

Contents

Preface 16 1.7.4 Combination of Springs 60
1.7.5 Spring Constant Associated with the
Acknowledgments 21 Restoring Force due to Gravity 68
1.8 Mass or Inertia Elements 69
List of Symbols 23 1.8.1 Combination of Masses 70
1.9 Damping Elements 74
1.9.1 Construction of Viscous Dampers 75
ChAPtEr 1 1.9.2 Linearization of a Nonlinear Damper 81
Fundamentals of Vibration 29 1.9.3 Combination of Dampers 81
1.1 Preliminary Remarks 30 1.10 Harmonic Motion 83
1.2 Brief History of the Study of Vibration 31 1.10.1 Vectorial Representation of
1.2.1 Origins of the Study of Vibration 31 Harmonic Motion 85
1.2.2 From Galileo to Rayleigh 33 1.10.2 Complex-Number Representation
1.2.3 Recent Contributions 36 of Harmonic Motion 86
1.3 Importance of the Study of Vibration 38 1.10.3 Complex Algebra 87
1.3.1 Conversion of Vibrations to 1.10.4 Operations on Harmonic Functions 87
Sound by the Human Ear 40 1.10.5 Definitions and Terminology 90
1.4 Basic Concepts of Vibration 43 1.11 Harmonic Analysis 93
1.4.1 Vibration 43 1.11.1 Fourier Series Expansion 93
1.4.2 Elementary Parts of 1.11.2 Complex Fourier Series 95
Vibrating Systems 43 1.11.3 Frequency Spectrum 96
1.4.3 Number of Degrees of Freedom 44 1.11.4 Time- and Frequency-Domain
1.4.4 Discrete and Continuous Systems 46 Representations 97
1.5 Classification of Vibration 46 1.11.5 Even and Odd Functions 98
1.5.1 Free and Forced Vibration 46 1.11.6 Half-Range Expansions 100
1.5.2 Undamped and Damped Vibration 47 1.11.7 Numerical Computation
1.5.3 Linear and Nonlinear Vibration 47 of Coefficients 101
1.5.4 Deterministic and 1.12 Examples Using MATLAB 105
Random Vibration 47 1.13 Vibration Literature 109
1.6 Vibration Analysis Procedure 48 Chapter Summary 110
1.7 Spring Elements 52 References 110
1.7.1 Nonlinear Springs 53 Review Questions 112
1.7.2 Linearization of a Nonlinear Spring 55 Problems 116
1.7.3 Spring Constants of Elastic Elements 57 Design Projects 149
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