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Anisotropic materials find widespread applications across various engineering domains. The investigation on vibrational properties of anisotropic materials holds significance for structural vibration mitigation and safety design. This paper introduces a novel approach, the peridynamic operator method (PDOM), to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates. The model incorporates the unique feature of PDOM, which transforms local differentials and their products into non-local integrals, thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory. Additionally, the paper employs a variational principle and introduces the free vibration equation to develop a PDOM solution for anisotropic free vibration problems. Three numerical examples are provided, including the free vibrations of a thin anisotropic rectangular plate, an anisotropic rectangular plate with cracks, and an anisotropic rectangular plate with holes. The results are compared with finite element results, showcasing the model's convergence, stability, and high computational accuracy in dealing with free vibrations of anisotropic plates with defects and discontinuities.
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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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