Journal ArticleDOI
Response of linear vibratory systems to non-stationary stochastic impulses
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In this paper, the problem of response of vibratory systems to random excitations is formulated in terms of stochastic point processes and some general methods of point processes which are applicable in a wider context are also studied through certain correlation functions known as product densities.About:
This article is published in Journal of Sound and Vibration.The article was published on 1967-09-01. It has received 24 citations till now. The article focuses on the topics: Product (mathematics) & Context (language use).read more
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Journal ArticleDOI
A Stochastic Model for Simulation and Diagnostics of Rolling Element Bearings With Localized Faults
Jérôme Antoni,Robert B. Randall +1 more
TL;DR: In this paper, a stochastic modeling of the vibration signal produced by localized faults in rolling element bearings and its use for diagnostic purposes is presented. And the analysis finally gives sound justification for squared envelope analysis and the type of spectral indicators that should be used with it.
Journal ArticleDOI
The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part II: iterative and explicit analytical solution for non-linear coupled transverse and in-plane vibrations
M. Haterbouch,R. Benamar +1 more
TL;DR: In this paper, a more realistic and complete study of the geometrically non-linear free vibrations of clamped immovable circular plates by taking into account the in-plane deformation is presented.
Journal ArticleDOI
Response distribution of non-linear systems excited by non-Gaussian impulsive noise
TL;DR: In this paper, a perturbation scheme was devised to obtain an approximate stationary probability density for the response of a non-linear oscillator subjected to an impulsive-noise process which is statistically stationary but non-Gaussian.
Journal ArticleDOI
Dynamic response of non-linear systems to poisson-distributed random impulses
R. Iwankiewicz,Søren Nielsen +1 more
TL;DR: In this article, the authors considered the dynamic response of non-linear systems to external excitations in form of a Poisson-distributed train of random impulses and obtained the equations governing its joint statistical moments by making use of a generalized Ito's differential rule, truncated with the help of a cumulant-neglect closure of different orders.
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Vibration of a non-linear single degree of freedom system due to poissonian impulse excitation
TL;DR: In this article, the behavior of a non-linear single degree of freedom system, subjected to a random excitation in the form of Poissonian impulse sequence is investigated, and the stochastic linearization technique and the generalized FPK equation are used to obtain a characteristic function and moments of system response probability distribution.
References
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Mathematical analysis of random noise
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Book
The Theory of Branching Processes
TL;DR: A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations is given in this article, followed by a systematic development of branching processes, and a brief description of some of the important applications.
Journal ArticleDOI
On the theory of brownian motion
TL;DR: In this article, it was shown that the non-Gaussian-Markoff process for Brownian motion derived on a statistical mechanical basis by Prigogine and Balescu, and Prigogueine and Philippot, is related through a transformation of variables to the Gaussian Markoff process of the conventional phenomenological theory of Brownian motions.