| 韩振南
1 ，随岁寒 1，2 ，刘金建 2*.局部支承功能梯度板的自由振动分析[J].海南师范大学学报自科版,2022,35(2):186-193 |
| 局部支承功能梯度板的自由振动分析 |
| Free Vibration Analysis on Locally SupportedFunctionally Graded Plates |
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| DOI：10.12051/j.issn.1674-4942.2022.02.014 |
| 中文关键词: 局部支承 功能梯度板 自由振动 有限元法 |
| 英文关键词: local support functionally gradient plate free vibration finite element method |
| 基金项目:国家自然科学基金项目（11972240）；商丘工学院校级科研项目（2022KYXM21） |
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| 中文摘要: |
| 基于Mindlin板理论和有限元法研究了局部支承功能梯度板的自由振动问题。假设材
料由陶瓷和金属组成，且材料参数沿板厚度方向按照幂指数形式连续变化，利用虚功原理推导功
能梯度板横向自由振动的有限元方程，分别在100%、50%和25%等3种支承条件下研究系统自由
振动特性。算例部分首先求解了纯金属板和纯陶瓷板的前三阶固有频率，同时给出了ANSYS软件
计算得到的前三阶频率及其模态，两者对比证实了本文方法的准确性；随后重点探讨了支承范围
和梯度指数与前三阶固有频率的关系。结果显示：支承范围对模态有重要影响，可通过调整支承
来控制振动；支承范围与固有频率正相关，梯度指数与固有频率负相关；为实现同等精度，支撑范
围越小需要的单元数越多。 |
| 英文摘要: |
| Based on Mindlin plate theory and finite element method, the free vibration of functionally graded plates with lo⁃
cal supports was studied. It is assumed that the material is composed of ceramic and metal, and the material parameters
change continuously along the direction of plate thickness in a power exponential form. The finite element equation of trans⁃
verse free vibration of functionally graded thin plate was derived based on the principle of virtual work, and the free vibra⁃
tion characteristics of the system were studied under 100%, 50% and 25% support conditions respectively. In the example
part, the first three order natural frequencies of pure metal plate and pure ceramic plate were solved, and the first three or⁃
der frequencies and their modes were calculated by ANSYS software. The comparison between the two verifies the accuracy
of the method in this paper. Then the relationship between support range and the gradient index and the first three natural
frequencies was discussed. The results showed that the supporting range has an important effect on the mode, and the mode
can be controlled by adjusting the support. The range of support is positively correlated with the natural frequency, while
the gradient index is negatively correlated with the natural frequency. In order to achieve the same accuracy, the smaller the
support range, the more elements are needed. |
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