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

Wu Qin (State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, China; State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China and School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China)
Hui Yin (State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, China; State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China and School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China)
D.J. Yu (Department of Mechanical Engineering, Hunan University, Changsha, China)
Wen-Bin Shangguan (State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, China and School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 29 May 2020

Issue publication date: 28 October 2020

96

Abstract

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.

Keywords

Acknowledgements

The paper is supported by the financial support of Foundation of State Key Laboratory of Automotive Simulation and Control (Project No. 20160110), the National Natural Science Foundation of China (No. 51605167, No. 11472107), the Science and Technology Program of Guangzhou (No. 201804010092), the China Postdoctoral Science Foundation (2019M652880), the Fundamental Research Funds for the Central Universities, SCUT (2019MS064) and the Open Funds for the State Key Laboratory of Advanced Design and Manufacture of Automobile Body of Hunan University (No. 31915002).

Citation

Qin, W., Yin, H., Yu, D.J. and Shangguan, W.-B. (2020), "A Chebyshev convex method for mid-frequency analysis of built-up structures with large convex uncertainties", Engineering Computations, Vol. 37 No. 9, pp. 3431-3453. https://doi.org/10.1108/EC-08-2019-0379

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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