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[1] Zhu Lei, Zhang Jianxun, Sun Hailin, et al. Numerical solution method for fundamental frequency and mode shape of Euler-Bernoulli beam based on Monte Carlo method [J]. Journal of Southeast University (English Edition), 2024, 40 (2): 203-209. [doi:10.3969/j.issn.1003-7985.2024.02.011]
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Numerical solution method for fundamental frequency and mode shape of Euler-Bernoulli beam based on Monte Carlo method()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
40
Issue:
2024 2
Page:
203-209
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2024-06-13

Info

Title:
Numerical solution method for fundamental frequency and mode shape of Euler-Bernoulli beam based on Monte Carlo method
Author(s):
Zhu Lei1;  2;  Zhang Jianxun1;  2;  Sun Hailin3
1Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
2School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
3China Architecture Design and Research Group, Beijing 100044, China
Keywords:
Euler-Bernoulli beam;  fundamental frequency;  Monte Carlo method;  numerical solution
PACS:
O302
DOI:
10.3969/j.issn.1003-7985.2024.02.011
Abstract:
To address the challenge of solving free vibration problems in beams with uniform cross-sections, beams with variable cross-sections, and Euler-Bernoulli beams with concentrated masses, an innovative method combining the Rayleigh method and the Monte Carlo method is introduced. This dual-method strategy offers a novel solution by first discretizing the continuous beam structure model, followed by employing the Monte Carlo method to determine the vibration modes of the beam structure. Subsequently, these identified vibration modes are integrated into the Rayleigh method to calculate the fundamental frequency and vibration modes. The process involves a meticulous comparison with the minimum value obtained during calculations to ensure the satisfaction of the convergence condition. The results show that this combined method achieves a maximum error of 10% or less in predicting the fundamental frequency across different calculation models. This accuracy level is well within acceptable engineering requirements. The control parameters for accuracy and time can be easily adjusted to meet various needs. The method, which is simple in theory and widely applicable, enables the quick and precise determination of fundamental frequencies and vibration modes for diverse beam structures.

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Memo

Memo:
Biography: Zhu Lei(1980—), male, doctor, professor, zhulei@bucea.edu.cn.
Foundation item: The National Natural Science Foundation of China(No.51778035).
Citation: Zhu Lei, Zhang Jianxun, Sun Hailin.Numerical solution method for fundamental frequency and mode shape of Euler-Bernoulli beam based on Monte Carlo method[J].Journal of Southeast University(English Edition), 2024, 40(2):203-209.DOI:10.3969/j.issn.1003-7985.2024.02.011.
Last Update: 2024-06-20