A Chebyshev convex method for mid-frequency analysis of built-up structures with large convex uncertainties

Purpose This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties. Design/methodology/approach Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite e...

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Bibliographic Details
Published in:Engineering computations 2020-10, Vol.37 (9), p.3431-3453
Main Authors: Qin, Wu, Yin, Hui, Yu, D.J, Shangguan, Wen-Bin
Format: Article
Language:English
Subjects:
Acoustics
Algorithms
Approximation
Chebyshev approximation
Construction
Design optimization
Finite element method
Frequency analysis
Lagrange multiplier
Mathematical programming
Numerical methods
Parameter uncertainty
Polynomials
Response functions
Statistical energy analysis
Systems analysis
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Summary:Purpose This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties. Design/methodology/approach Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM. Findings CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method. Originality/value The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.
ISSN:0264-4401
1758-7077
DOI:10.1108/EC-08-2019-0379