| 陈康康,随岁寒.含缺薄板固有振动的流动特性分析[J].井冈山大学自然版,2025,46(4):88-96 |
| 含缺薄板固有振动的流动特性分析 |
| FLOWING CHARACTERISTICS ANALYSIS ON NATURAL VIBRATION OF THIN PLATES WITH DEFECTS |
| 投稿时间：2025-02-03 修订日期：2025-04-20 |
| DOI：10.3969/j.issn.1674-8085.2025.04.011 |
| 中文关键词: 流动效应 含缺板 固有频率 模态跃变 有限差分法 二维节点编号 |
| 英文关键词: flowing effects plate with defects natural frequency mode jump finite difference method two-dimensional node numbering |
| 基金项目:河南省高等学校重点科研项目(26B130002)；河南省科技攻关项目(222102210147)；商丘工学院校级科研项目(2025KYXM01) |
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| 中文摘要: |
| 针对流动含缺板的固有振动，研究了其固有频率和模态的流动特性。应用Hamilton原理推导了流动板的自由振动控制方程，对求解域进行二维节点划分和编号，据此给出各阶偏导的差分表达式，从而导出系统广义复特征方程。进一步转化为标准特征值方程并求解特征值，对特征函数拟合得到模态。通过与ANSYS软件所得固有频率和模态对比，验证了算法的准确性，随后重点分析了前四阶固有频率和前两阶模态的流速效应。结果表明，随着流速增大，含缺板的固有频率加速降低，第一阶模态略微收缩。进入再稳定区后第一阶模态跃变，该模态对速度变化更加敏感。第二阶模态受到速度变化的影响更大。 |
| 英文摘要: |
| The natural frequency and modal flow characteristics of the natural vibration of the flow plate with defects are studied. Hamilton principle is applied to derive the free vibration governing equation of the flowing plate, and the solution domain is divided into two dimensional nodes and number. The difference expressions of each order deflection are given accordingly, and the generalized complex characteristic equation of the system is derived. It is further transformed into the standard eigenvalue equation, and the eigenvalues are solved, and the modes are obtained by fitting the eigenfunction. Compared with the natural frequencies and modes obtained by ANSYS software, the accuracy of the proposed algorithm is verified. Then, the velocity effects of the first four natural frequencies and the first two modes are analyzed. The results show that with the increase of flow velocity, the natural frequency of the plate with defects decreases and the first mode shrinks slightly. After entering the re-stabilization zone, the first mode jumps, which is more sensitive to velocity changes. The second mode is more significantly affected by the velocity change. |
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