J Shanghai Jiaotong Univ Sci

Journal of shanghai Jiaotong University (Science) ›› 2014, Vol. 19 ›› Issue (1): 123-128.doi: 10.1007/s12204-014-1480-z

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Equivalent Stochastic Linearization for Nonlinear Uncertain Structure Under Stationary Gaussian Stochastic Excitation

Equivalent Stochastic Linearization for Nonlinear Uncertain Structure Under Stationary Gaussian Stochastic Excitation

LIU Yong* (刘 勇), CHEN Lu-yun (陈炉云), YI Hong (易 宏)   

  1. (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China)
  2. (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China)
  • Online:2014-01-15 Published:2014-01-15
  • Contact: LIU Yong (刘 勇) E-mail: flydark@126.com

Abstract: Equivalent stochastic linearization (ESL) for nonlinear uncertain structure under stationary stochastic excitation is presented. There are two parts of difference between the original system and equivalent system: one is caused by the difference between the means of original and equivalent stochastic structure; and another is caused by the difference between the original and equivalent stochastic structure which has the relation with stochastic variables. Statistical characteristics of equivalent stochastic structure can be obtained in accordance with mean square criterion, so nonlinear stochastic structure is transformed into linear stochastic structure. In order to attain that objective, the compound response spectrum of linear stochastic structure under stationary random excitation which is used in the solution is derived in the case of the mutual independence between stochastic excitation and stochastic structure. Finally, the example shows the accuracy and validity of the proposed method.

Key words: equivalent stochastic linearization| nonlinear stochastic structure| pseudo excitation method

摘要： Equivalent stochastic linearization (ESL) for nonlinear uncertain structure under stationary stochastic excitation is presented. There are two parts of difference between the original system and equivalent system: one is caused by the difference between the means of original and equivalent stochastic structure; and another is caused by the difference between the original and equivalent stochastic structure which has the relation with stochastic variables. Statistical characteristics of equivalent stochastic structure can be obtained in accordance with mean square criterion, so nonlinear stochastic structure is transformed into linear stochastic structure. In order to attain that objective, the compound response spectrum of linear stochastic structure under stationary random excitation which is used in the solution is derived in the case of the mutual independence between stochastic excitation and stochastic structure. Finally, the example shows the accuracy and validity of the proposed method.

关键词: equivalent stochastic linearization| nonlinear stochastic structure| pseudo excitation method

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