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Research Papers

A Partition Expansion Method for Nonlinear Response Analysis of Stochastic Dynamic Systems With Local Nonlinearity

[+] Author and Article Information
Changqing Bai

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China e-mail: baichq@mail.xjtu.edu.cn

Hongyan Zhang

School of Science, Chang'an University, Xi'an 710064, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Design Engineering Division. Manuscript received July 21, 2011; final manuscript received November 26, 2012; published online January 7, 2013. Assoc. Editor: Henryk Flashner.

J. Comput. Nonlinear Dynam 8(3), 031009 (Jan 07, 2013) (7 pages) Paper No: CND-11-1114; doi: 10.1115/1.4023163 History: Received July 21, 2011; Revised November 26, 2012

This paper focuses on the problem of nonlinear dynamic response variability resulting from stochastic system properties and random loads. An efficient and accurate method, which can be employed to analyze the dynamic responses of random finite element systems with local nonlinearity, is presented in this paper. This method, dubbed as the partition expansion method, is based on the partitioned time integration algorithm in conjunction with the Neumann expansion technique within the framework of the Monte Carlo simulation. Two numerical examples involving structural and mechanical stochastic vibration problems are employed to illustrate the advantage of the proposed method with respect to accuracy and efficiency. By comparing the results obtained by the direct Monte Carlo simulation, the dynamic response statistics can be accurately determined using the proposed method with four order expansion while the computational efforts are significantly reduced. The comparison of computing time indicates that the proposed method is efficient and practical for analyzing the statistical quantities of stochastic dynamic systems with local nonlinearity.

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Figures

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Fig. 1

Angled beam subjected to impact loads

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Fig. 2

Mean value of nonlinear angular displacement of angled beam

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Fig. 3

Standard deviation of nonlinear angular displacement of angled beam

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Fig. 4

Standard deviation error of angular displacement as a function of sample size

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Fig. 5

Turbopump rotor-seal system

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Fig. 6

Mean value of nonlinear displacement response of rotor-seal system

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Fig. 7

Standard deviation of nonlinear displacement response of rotor-seal system

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Fig. 8

Standard deviation error of displacement response as a function of sample size

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