Parametric Random Vibration

by Ibrahim, Raouf A.

• ISBN13: 9780486462622
• ISBN10: 0486462625
• Format: Paperback
• Copyright: 2008-01-11
• Publisher: Dover Publications

Summary

This coherent, systematic treatment examines linear and nonlinear dynamical systems subject to parametric random vibrations. It distills decades of research to formulate new stochastic stability theorems and analytical techniques for determining random response of nonlinear systems. It also resolves paradoxes related to interpretation of certain stochastic processes and analytical methods. 1985 edition.

Table of Contents

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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