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This paper focuses on analyzing the circumferential free vibration of the functionally graded joined conical-cylindrical shell to enhance the vibration performance and stability of the structure, particularly in the aerospace field. First, the properties of the functionally graded materials (FGMs) are described using the Voigt model and the four-parameter power function volume fraction. The energy expressions for the conical shell and cylindrical shell are derived based on the previously obtained displacement-strain relationships formulated utilizing the Donnell thin shell theory. Then, artificial springs are introduced to simulate the continuity conditions and boundary conditions. The displacement function is constructed using Chebyshev polynomials to enable a more accurate analysis of the structural response and performance. The modal frequencies of the functionally graded joined conical-cylindrical shell are calculated employing the Rayleigh-Ritz method with this displacement function. Hence, the influence of gradient exponent, boundary conditions, and geometric parameters on the modal frequencies is analyzed to reveal the vibration characteristics of the structure. The main results indicate that increasing the volume fraction of ceramics effectively enhances the modal frequencies of the structure, while higher gradient exponents lead to a decrease in the modal frequencies. Stronger boundary constraints result in higher modal frequencies for the functionally graded joined conical-cylindrical shell. With an increase in the circumferential wave number, the influence of boundary conditions on the structural modal frequencies diminishes. The effect of boundary constraints is more pronounced on the cylindrical shell compared to the conical shell. Additionally, the axial spring stiffness has a more significant impact on the modal frequencies of the structure compared to the circumferential and radial spring stiffnesses. When the circumferential wave number is greater than 3, the modal frequency of the structure exhibits a linear increase with increasing shell thickness, whereas increasing the conical and cylindrical shell length ratio leads to a decrease in modal frequency. Finally, when the length ratio of the conical and cylindrical shell is fixed, increasing the cone angle initially results in an increase in the modal frequencies of the structure until it reaches a peak value, after which it starts to decrease.
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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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