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This paper establishes the governing equations of the nonlinear vibration of a functionally graded shell with a crack，based on the extended isogeometric analysis （XIGA） and the first-order shear deformation theory. The study investigates the effects of the crack on the nonlinear vibrational frequency ratio of the model，taking into account large amplitude vibrations. Enriched functions，which represent displacement changes，are used to describe the position and length of the crack. This approach enhances calculation accuracy and avoids mesh refinement at the crack. The nonlinear governing equation is solved using the direct iteration method，and its correctness is validated by comparing the results with existing literature. The study further explores the effects of the pre-twisted angle，crack location，crack length and material variation parameters on the nonlinear vibration characteristics of the pre-twisted shells with cracks.
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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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