Random Vibration and Statistical Linearization

ISBN-10: 0486432408

ISBN-13: 9780486432403

Edition: 2003

Authors: J. B. Roberts, P. D. Spanos

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Coherent and self-contained, this volume explains the general method of statistical, or equivalent, linearization and its use in solving random vibration problems. Numerous examples offer advanced undergraduate and graduate engineering students a comprehensive view of the method's practical applications. Subjects include general equations of motion and the representation of non-linearities, probability theory and stochastic processes, elements of linear random vibration theory, statistical linearization for simple systems with stationary response, statistical linearization of multi-degree of freedom systems with stationary response, and non-stationary problems. 1990 edition. 122 figures. 16 tables.
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Book details

List price: $26.95
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 12/9/2003
Binding: Paperback
Pages: 446
Size: 5.50" wide x 8.75" long x 1.00" tall
Weight: 1.078
Language: English

Preface to the Dover Edition
Random vibration
Importance of non-linearities
Non-linear random vibration problems
Methods of solution
Statistical linearization
Moment closure
Equivalent non-linear equations
Perturbation and functional series
Markov methods
Monte Carlo simulation
Role of statistical linearization
Scope of book
Plan of book
General equations of motion and the representation of non-linearities
The general equations of motion
Small vibrations
Large vibrations
Non-linear conservative forces
Motion in a gravitational field
Restoring moments for floating bodies
Elastic restoring forces
Non-linear elasticity
Geometric non-linearities
Non-linear dissipative forces
Internal damping in materials
Mathematical representation of hysteresis loops
Interface damping
Flow induced forces
Probability theory and stochastic processes
Random events and probability
Random variables
Probability distributions
Transformation of random variables
Expectation of random variables
The Gaussian distribution
Properties of Gaussian random variables
Expansions of the Gaussian distribution
The concept of a stochastic process
The complete probabilistic specification
The Gaussian process
Stationary processes
Differentiation of stochastic processes
Integration of stochastic processes
Spectral decomposition
Specification of joint processes
Elements of linear random vibration theory
General input-output relationships
Stochastic input-output relationships
Analysis of lumped parameter systems
Response prediction
Free undamped motion
Classical modal analysis
State variable formulation
Complex modal analysis
Stochastic response of linear systems
Single degree of freedom systems
Two degree of freedom systems
Multi-degree of freedom systems
State variable analysis
Analysis using complex modes
Statistical linearization for simple systems with stationary response
Non-linear elements without memory
Statistical linearization procedure
Optimum linearization
Oscillators with non-linear stiffness
The statistical linearization approximation
Standard deviation of the response
The case of small non-linearity
Power spectrum of the response
Inputs with non-zero means
Asymmetric non-linearities
Systems with a softening restoring characteristic
Systems with multiple static equilibrium positions
Response to narrow-band excitation
Oscillators with non-linear stiffness and damping
Standard deviation of the response
The case of small non-linearity
Power spectrum of the response
Input and output with non-zero means
Higher order linearization
Friction controlled slip of a structure on a foundation
Ship roll motion in irregular waves
Flow induced vibration of cylindrical structures
Statistical linearization of multi-degree of freedom systems with stationary response
The non-linear system
The equivalent linear system
Minimization procedure
Equations for the equivalent linear system parameters
Examination of the minimum
Existence and uniqueness of the equivalent linear system
Mechanization of the method
Determination of the elements of the equivalent linear system
Gaussian approximation
Chain-like systems
Treatment of asymmetric non-linearities
Solution procedures
General remarks
Spectral matrix solution procedure
Modal analysis
State variable solution procedure
Complex modal analysis
Mode-by-mode linearization
Non-stationary problems
General theory
White noise excitation
Friction controlled slip of a structure on a foundation
Oscillator with asymmetric non-linearity
Non-white excitation
Decomposition method
Use of pre-filters
An example
Systems with hysteretic non-linearity
Averaging method
An alternative approach
Evaluation of the expectations
Application to non-hysteretic oscillators
Inputs with non-zero means
The bilinear oscillator
Allowance for drift motion
Use of differential models of hysteresis
Oscillators with hysteresis
The bilinear oscillator
The curvilinear model
Inputs with non-zero means
Biaxial hysteretic restoring forces
Multi-degree of freedom systems
Non-stationary problems
Degrading systems
Non-stationary excitation
Relaxation of the Gaussian response assumption
Statistical linearization and Gaussian closure
An example
Non-Gaussian closure
Moment equations
Closure techniques
An example
Method of equivalent non-linear equations (ENLE)
Exact solution
Equivalent non-linear equations
Oscillators with linear stiffness and non-linear damping
Oscillators with quadratic damping
Oscillators with linear-plus-cubic damping
An alternative approach
Reliability estimation
First passage probability
Fatigue life
An example
Parametric identification
Direct optimization
State variable filters
An example
Accuracy of statistical linearization
Exact solutions
Linear damping
Chain-like systems
First-order systems
Comparison with exact solutions
First-order systems
Oscillators with power-law springs
Duffing oscillators
Oscillators with tangent-law springs
Oscillators with non-linear damping
Comparison with Monte Carlo simulation results
Simulation technique
Oscillators with non-linear damping
Oscillators with non-linear springs
Oscillators with hysteresis
Multi-degree of freedom systems with hysteresis
Non-stationary response
Concluding remarks
Evaluation of expectations
A useful integral for random vibration analyses
Addendum to Appendix B
Additional References
Author index
Subject index
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