skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Response of MDOF strongly nonlinear systems to fractional Gaussian noises

Abstract

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Authors:
;  [1]
  1. Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)
Publication Date:
OSTI Identifier:
22596479
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; DEGREES OF FREEDOM; DIFFERENTIAL EQUATIONS; HAMILTONIANS; INTEGRAL CALCULUS; NOISE; NONLINEAR PROBLEMS; SIMULATION; STOCHASTIC PROCESSES

Citation Formats

Deng, Mao-Lin, and Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn. Response of MDOF strongly nonlinear systems to fractional Gaussian noises. United States: N. p., 2016. Web. doi:10.1063/1.4960817.
Deng, Mao-Lin, & Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn. Response of MDOF strongly nonlinear systems to fractional Gaussian noises. United States. doi:10.1063/1.4960817.
Deng, Mao-Lin, and Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn. 2016. "Response of MDOF strongly nonlinear systems to fractional Gaussian noises". United States. doi:10.1063/1.4960817.
@article{osti_22596479,
title = {Response of MDOF strongly nonlinear systems to fractional Gaussian noises},
author = {Deng, Mao-Lin and Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn},
abstractNote = {In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.},
doi = {10.1063/1.4960817},
journal = {Chaos (Woodbury, N. Y.)},
number = 8,
volume = 26,
place = {United States},
year = 2016,
month = 8
}
  • A new stochastic analysis is developed to estimate the response of multiple supported multi-degree-of-freedom (mdof) secondary systems to dynamic loading. In the proposed stochastic analysis, the effect of the dynamic interaction between the secondary and primary systems is included. An outline for the theoretical formulation of the proposed stochastic analysis is presented. The assumptions adopted in the formulation are discussed. The dynamic interaction is shown to comprise two effects: the effect of the interaction forces arising at the attachment points, and the effect of the changes in the primary system properties resulting from the attachment of the secondary system. Inmore » addition, numerical examples are provided to demonstrate the validity of the proposed analysis.« less
  • We have studied Laguerre-Gaussian spatial solitary waves in strongly nonlocal nonlinear media analytically and numerically. An exact analytical solution of two-dimensional self-similar waves is obtained. Furthermore, a family of different spatial solitary waves has been found. It is interesting that the spatial soliton profile and its width remain unchanged with increasing propagation distance. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity.
  • Within the framework of non-Markovian stochastic Schroedinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.
  • The authors derive a number of new results for correlated nearest neighbor site percolation on Z/sup d/. They show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance - ..delta.., has a nontrivial percolation behavior, sites on which S/sub x/ greater than or equal to h percolate if and only if h < h/sub c/ with O less than or equal to h/sub c/ < infinity. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.
  • The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractionalmore » order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.« less