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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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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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