The stationary response of multidegree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (FGN) with 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 nonresonant, completely integrable and resonant, completely integrable and nonresonant, and nonintegrable. 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.
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October 2017
Research-Article
Stationary Response of Multidegree-of-Freedom Strongly Nonlinear Systems to Fractional Gaussian Noise
Qiang Feng Lü,
Qiang Feng Lü
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Search for other works by this author on:
Mao Lin Deng,
Mao Lin Deng
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Search for other works by this author on:
Wei Qiu Zhu
Wei Qiu Zhu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Search for other works by this author on:
Qiang Feng Lü
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Mao Lin Deng
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
Wei Qiu Zhu
Department of Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power and
Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China
e-mail: wqzhu@zju.edu.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 22, 2017; final manuscript received July 25, 2017; published online August 18, 2017. Editor: Yonggang Huang.
J. Appl. Mech. Oct 2017, 84(10): 101001 (14 pages)
Published Online: August 18, 2017
Article history
Received:
April 22, 2017
Revised:
July 25, 2017
Citation
Lü, Q. F., Deng, M. L., and Zhu, W. Q. (August 18, 2017). "Stationary Response of Multidegree-of-Freedom Strongly Nonlinear Systems to Fractional Gaussian Noise." ASME. J. Appl. Mech. October 2017; 84(10): 101001. https://doi.org/10.1115/1.4037409
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