Non-Markovian parametrical vibration
type: Item
instance of: scholarly article
title: Non-Markovian parametrical vibration
zbMATH Open document ID: 0605.34037
DOI: 10.1016/0020-7225(86)90062-5
author: Tomasz Kapitaniak
published in: International Journal of Engineering Science
publication date: 1986-01-01T00:00:00Z
review text: The solution and its stability of Hill's equation with frequency and damping coefficient fluctuated by stochastic process modeled by Ornstein- Uhlenbeck noise is investigated. The application of Hermandez-Machado's and San Miguel's formulas allow us to calculate the mean value and the second-order moments of the solution process. The non-Markovian effect of dependence of the parametrical vibration frequency on the noise intensity is determined. The investigations of the moments of the solution give conditions for stability.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 3977463
zbMATH Keywords: stochastic parametrical vibration
zbMATH Keywords: Hill's equation
zbMATH Keywords: damping coefficient
zbMATH Keywords: stochastic process
zbMATH Keywords: Ornstein-Uhlenbeck noise
zbMATH Keywords: second-order moments
MaRDI profile type: Publication
full work available at URL: 0020-7225(86)90062-5
OpenAlex ID: W1994085904
cites work: Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980
cites work: Q5512461
cites work: On the theory of optimal control. Sufficient coordinates
cites work: Dynamical properties of non-Markovian stochastic differential equations
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description: scientific article; zbMATH DE number 3977463