Errata List | p. ix |
Parametric Vibrations | |
Introduction | p. 1 |
Mechanics of Deterministic Problems | p. 1 |
Chaotic Motion | p. 10 |
Pseudo-Random Excitation | p. 12 |
Crypto-Deterministic Systems | p. 13 |
Random Parametric Vibration | p. 14 |
Random Variables and Stochastic Processes | |
Introduction | p. 19 |
Random Variables | p. 19 |
Random Processes | p. 24 |
Stochastic Calculus Operations | |
Introduction | p. 53 |
Basic Notations of Advanced Calculus | p. 53 |
Modes of Stochastic Convergence | p. 54 |
Stochastic Limit Theorems | p. 56 |
Mean Square Derivative | p. 57 |
Riemann and Riemann-Stieltjes Integrals | p. 58 |
Lebesgue Integral | p. 61 |
Calculus of Stochastic Processes | |
Introduction | p. 63 |
The Brownian Motion Process | p. 63 |
The White Noise | p. 66 |
The Narrow Band Process | p. 69 |
Markov Processes | p. 72 |
The Fokker-Planck-Kolmogorov (FPK) Equation | p. 74 |
Stochastic Calculus Rules | p. 75 |
Generation of Response Statistics | |
Introduction | p. 91 |
The Fokker-Planck-Kolmogorov Equation Approach | p. 91 |
The Ito Formula Approach | p. 100 |
The Infinite Hierarchy Problem | p. 104 |
Stochastic Averaging Methods | |
Introduction | p. 107 |
Basic Concept | p. 108 |
Standard Form of Stochastic Averaging | p. 109 |
Papanicolaou and Kohler Asymptotic Theorem | p. 112 |
Weidenhammer Method | p. 114 |
Stochastic Averaging of the Response Energy Envelope | p. 115 |
Stochastic Behavior of Linear Systems | p. 120 |
Stochastic Behavior of Non-Linear Systems | p. 142 |
Second Order Averaging | p. 149 |
Parametric Stochastic Stability | |
Introduction and Historical Review | p. 163 |
Basic Definitions | p. 172 |
Stability of the Moments | p. 177 |
Almost Sure Stability Theorems | p. 193 |
Parametric Random Response | |
Introduction and Historical Review | p. 209 |
Linear Time-Variant Systems Under Random External Excitation | p. 215 |
The Moment Equation Method | p. 221 |
Random Response of Helicopter Rotor Blades | p. 229 |
Random Forced Response Near Combination Parametric Resonance | p. 250 |
Response of Non-Linear Systems | p. 252 |
Experimental Results | |
Introduction | p. 281 |
Random Behavior of Liquid Free Surface | p. 282 |
Random Behavior of Elastic Columns | p. 285 |
Systems with Autoparametric Interaction | p. 288 |
References | p. 293 |
Unreferenced Literature | p. 323 |
Principal Notations | p. 335 |
Index | p. 339 |
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