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Stationary response of multi-degree-of-freedom strongly nonlinear systems to fractional Gaussian noise

[+] Author and Article Information
Qiangfeng Lü

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
qflv@zju.edu.cn

Mao Lin Deng

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
mldeng@zju.edu.cn

Weiqiu Zhu

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
wqzhu@zju.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037409 History: Received April 22, 2017; Revised July 25, 2017

Abstract

The stationary response of multi-degree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (fGn) (of Hurst index 1/2<H<1) is studied. First, the system is modeled as fGn excited and dissipated Hamiltonian system. Based on the integrability and resonance of the associated Hamiltonian system, the system is divided into five classes: partially integrable and resonant, partially integrable and non-resonant, completely integrable and resonant, completely integrable and non-resonant, and non-integrable. Then the averaged fractional stochastic differential equations (SDEs) for five classes of quasi Hamiltonian systems with lower dimension and involving only slowly varying processes are derived. Finally, the approximate stationary probability densities and other statistics of two example systems are obtained by numerical simulation of the averaged fractional SDEs to illustrate the application and compared with those from original systems to show the advantages of the proposed procedure.

Copyright (c) 2017 by ASME
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