Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (9): 1153-1166.doi: https://doi.org/10.1007/s10483-012-1612-6

• 论文 • 上一篇    下一篇

Response analysis based on smallest interval-set of parameters for structures with uncertainty

王晓军, 王磊, 邱志平   

  1. Institute of Solid Mechanics, Beihang University, Beijing 100191, P. R. China
  • 收稿日期:2011-04-29 修回日期:2012-04-12 出版日期:2012-09-10 发布日期:2012-09-10
  • 通讯作者: Xiao-jun WANG, Associate Professor, Ph.D., E-mail: xjwang@buaa.edu.cn E-mail:xjwang@buaa.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (No. 11002013), the 111 Project (No.B07009), and the Defense Industrial Technology Development Program of China (Nos.A2120110001 and B2120110011)

Response analysis based on smallest interval-set of parameters for structures with uncertainty

Xiao-jun WANG, Lei WANG, Zhi-ping QIU   

  1. Institute of Solid Mechanics, Beihang University, Beijing 100191, P. R. China
  • Received:2011-04-29 Revised:2012-04-12 Online:2012-09-10 Published:2012-09-10
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 11002013), the 111 Project (No.B07009), and the Defense Industrial Technology Development Program of China (Nos.A2120110001 and B2120110011)

摘要: An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all experimental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty propagation evaluation of the most favorable response and the least favorable response of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method (IAM) and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.

关键词: real noise, parametric excitation, co-dimension two bifurcation, detailed balance, FPK equation, singular boundary, maximal Lyapunov exponent, solvability condition

Abstract: An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all experimental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty propagation evaluation of the most favorable response and the least favorable response of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method (IAM) and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.

Key words: real noise, parametric excitation, co-dimension two bifurcation, detailed balance, FPK equation, singular boundary, maximal Lyapunov exponent, solvability condition

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