Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

Hongfei Cao, Xi Peng, Bin Xu, Fengjiang Qin () and Qiuwei Yang ()
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Hongfei Cao: School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China
Xi Peng: School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China
Bin Xu: Ningbo Roaby Technology Industrial Group Co., Ltd., Ningbo 315800, China
Fengjiang Qin: Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education, School of Civil Engineering, Chongqing University, Chongqing 400045, China
Qiuwei Yang: School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China

Mathematics, 2024, vol. 12, issue 22, 1-23

Abstract: In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Keywords: modal random analysis; subspace iteration; stochastic finite element; flexibility disassembly perturbation; Krylov subspace (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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