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Random vibration and statistical linearization
J.B. Roberts,Pol D. Spanos +1 more
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TLDR
In this paper, a comprehensive account of statistical linearization with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems is given, and the principal value of these methods is that they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.Abstract:
Interest in the study of random vibration problems using the concepts of stochastic process theory has grown rapidly due to the need to design structures and machinery which can operate reliably when subjected to random loads, for example winds and earthquakes. This is the first comprehensive account of statistical linearization - powerful and versatile methods with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems. The principal value of these methods is that unlike other analytical methods, they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.read more
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Journal ArticleDOI
Conjugate unscented transformation–based uncertainty analysis of energy harvesters
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Time Dependent Gaussian Equivalent Linearization of Duffing Oscillator Using Continuous Wavelet Transform
TL;DR: In this article, the evolution response analysis of a Duffing oscillator using Gaussian equivalent linearization in wavelet based time-frequency frame work is presented, where the instantaneous parameters of the ELTVS (equivalent linear time varying system) are evaluated by minimizing the error between the displacements of non-linear and equivalent linear systems in the wavelet domain.
Journal ArticleDOI
Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
TL;DR: In this article, the authors developed a time-domain technique for linear tracking controller design based on two loci: the saturating root locus (to account for dynamics) and the tracking error locus to account for statics.
Proceedings ArticleDOI
Path integral method for first-passage probability determination of nonlinear systems under levy white noise
TL;DR: In this paper, the problem of first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed, and the determination of reliability functions and firstpassage time probability density functions is handled step-by-step through a modification of the path integral technique.
Book ChapterDOI
Useful Definitions and Facts of Probability Theory for Further Reading
TL;DR: In this paper, the authors present supplementary facts of probability theory which can be useful in studying error analysis problems, such as statistical linearization, multidimensional regression, limit theorems of probability theories, and elements of mathematical statistics such as: estimators, testing statistical hypotheses or confidence intervals.