RESEARCH ON FREE VIBRATION CHARACTERISTICS OF THIN PLATE STRUCTURES BASED ON IMPROVED FOURIER SERIES
Aiming at the problem of structural vibration modeling and characteristic analysis of rectangular sheets under arbitrary boundary conditions, an improved Fourier series method was proposed.Based on the Rayleigh-Ritz method, the allowable function of vibration displacement of thin plates was expresse...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | zho |
| Published: |
Editorial Office of Journal of Mechanical Strength
2025-06-01
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| Series: | Jixie qiangdu |
| Subjects: | |
| Online Access: | http://www.jxqd.net.cn/thesisDetails#10.16579/j.issn.1001.9669.2025.06.008 |
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| Summary: | Aiming at the problem of structural vibration modeling and characteristic analysis of rectangular sheets under arbitrary boundary conditions, an improved Fourier series method was proposed.Based on the Rayleigh-Ritz method, the allowable function of vibration displacement of thin plates was expressed as a linear combination of double Fourier cosine series function and auxiliary series function, which effectively avoided the possible discontinuities or singularities of the traditional Fourier series at the boundary. Firstly, the variational equation of the sheet vibration model was established by using the Hamilton energy variational principle, and the energy expressions in the equation were calculated and the displacement tolerance function was brought in. Secondly, the variational solution of the unknown Fourier coefficient was carried out to obtain the matrix equation of the model. The matrix equation was solved by numerical calculation method to obtain the free vibration frequency and eigenvector of the thin plate. Finally, the classical boundary conditions and elastic boundary conditions were used as examples to calculate and analyze. The calculation efficiency and accuracy of the proposed method were verified by comparison with the results of finite element simulation and existing literature. Additionally, the influence of the aspect ratio and constrained the spring stiffness coefficient on the vibration characteristics of the thin plate was discussed. |
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| ISSN: | 1001-9669 |