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Inverting mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation

  • Jin Cheng , Zhiwei Yang EMAIL logo and Xiangcheng Zheng
Published/Copyright: January 30, 2024

Abstract

We propose an inverse problem of determining the mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation. For this goal, we develop a fully-discrete Hermite finite element scheme for this model and analyze the corresponding error estimates. The Levenberg–Marquardt method is then applied to determine the multiple parameters. Extensive numerical experiments are performed under practical settings to demonstrate the behavior of the proposed model and the efficiency of the algorithm.

MSC 2020: 35A20; 35R11; 35R30

Award Identifier / Grant number: 11971121

Award Identifier / Grant number: 12241103

Award Identifier / Grant number: 12301555

Funding statement: This work was supported by the National Natural Science Foundation of China (Nos. 11971121, 12241103, 12301555), the Sino-German Mobility Programme (M-0187) by Sino-German Center for Research Promotion, the Taishan Scholars Program of Shandong Province (No. tsqn202306083), the National Key R&D Program of China (No. 2023YFA1008903), and the China Postdoctoral Science Foundation under Grants 2022M720809 and 2023T160109

Acknowledgements

The authors would like to express their sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.

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Received: 2023-11-08
Revised: 2024-01-16
Accepted: 2024-01-17
Published Online: 2024-01-30
Published in Print: 2024-04-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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