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In view of the fact that it is difficult to obtain analytical solutions for vibration problems of combined shells and it is hard to solve strongly coupled acoustic and vibration control equations, a Ritz-Legendre spectral element method was proposed to discuss the vibration characteristics of underwater conical-cylindrical-spherical shells. Based on Reissner shell theory, virtual spring technology and the displacement angle relationship of adjacent subshells, the theoretical structural model of the combined shells was established. The Legendre spectral element method was introduced to avoid the problem of discontinuity of normal derivative and discretize the Kirchhoff-Helmholtz boundary integral equation, then the theoretical model of underwater external sound field was constructed. Based on Fourier transform and coupled surface Euler equation, the coupled vibration control equation of underwater combined shells was obtained. Compared with FEM simulation results, the convergence, reliability and correctness of this method were verified. This method can provide theoretical reference for engineering application in the design stage.
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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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