Page 18 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

ContEntS 15
13.6 Systems with Time-Dependent Coefficients 14.10 Power Spectral Density 14-23
(Mathieu Equation) 13-24 14.11 Wide-Band and Narrow-Band Processes 14-25
13.7 Graphical Methods 13-29 14.12 Response of a Single-Degree-of-Freedom
13.7.1 Phase-Plane Representation 13-29 System 14-28
13.7.2 Phase Velocity 13-34 14.12.1 Impulse-Response Approach 14-28
13.7.3 Method of Constructing 14.12.2 Frequency-Response Approach 14-30
Trajectories 13-34 14.12.3 Characteristics of the Response
13.7.4 Obtaining Time Solution from Phase-Plane Function 14-30
Trajectories 13-36 14.13 Response Due to Stationary Random
13.8 Stability of Equilibrium States 13-37 Excitations 14-31
13.8.1 Stability Analysis 13-37 14.13.1 Impulse-Response Approach 14-32
13.8.2 Classification of Singular Points 13-40 14.13.2 Frequency-Response Approach 14-33
13.9 Limit Cycles 13-41 14.14 Response of a Multidegree-of-Freedom
13.10 Chaos 13-43 System 14-39
13.10.1 Functions with Stable Orbits 13-45 14.15 Examples Using MATLAB 14-46
13.10.2 Functions with Unstable Orbits 13-45 Chapter Summary 14-49
13.10.3 Chaotic Behavior of Duffing’s Equation References 14-49
Without the Forcing Term 13-47 Review Questions 14-50
13.10.6 Chaotic Behavior of Duffing’s Equation Problems 14-53
with the Forcing Term 13-50 Design Project 14-61
13.11 Numerical Methods 13-52
13.12 Examples Using MATLAB 13-53 APPEnDIx A
Chapter Summary 13-62 Mathematical relations and Material Properties 1092
References 13-62
Review Questions 13-64
Problems 13-67 APPEnDIx B
Design Projects 13-75 Deflection of Beams and Plates 1095

APPEnDIx C
ChAPtEr 14 Matrices 1097
random Vibration 14-1
14.1 Introduction 14-2 APPEnDIx D
14.2 Random Variables and Random Processes 14-3 Laplace transform 1104
14.3 Probability Distribution 14-4
14.4 Mean Value and Standard Deviation 14-6
14.5 Joint Probability Distribution of Several APPEnDIx E
Random Variables 14-7 Units 1112
14.6 Correlation Functions of a Random
Process 14-9 APPEnDIx F
14.7 Stationary Random Process 14-10 Introduction to MAtLAB 1116
14.8 Gaussian Random Process 14-14
14.9 Fourier Analysis 14-16 Answers to Selected Problems 1126
14.9.1 Fourier Series 14-16
14.9.2 Fourier Integral 14-19
Index 1135