| 随岁寒1,2
，韩振南1,3*.轴向运动圆板自由振动的DQM解[J].海南师范大学学报自科版,2025,38(3):274-280 |
| 轴向运动圆板自由振动的DQM解 |
| DQM Solutions for Natural Vibration of Axially Moving Circular Plates |
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| DOI：10.12051/j.issn.1674-4942.2025.03.003 |
| 中文关键词: 轴向运动 圆板 自由振动 坐标映射 微分求积法 |
| 英文关键词: axially moving circular plate free vibration coordinate mapping DQM |
| 基金项目:国家自然科学基金项目（11972240）；河南省高等学校重点科研项目（23B130002）；商丘市科技发展指导性计划
项目（SK202325）；商丘工学院校级科研项目（2025KYXM01） |
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| 中文摘要: |
| 应用微分求积法（DQM）揭示了轴向运动圆板的固有振动特性。在笛卡尔坐标系中，采
用Kirchhoff薄板理论和虚功原理建立轴向运动圆板的动力学微分控制方程。利用坐标映射技术，
将笛卡尔坐标系中的圆板映射到自然坐标系中的方形板，在自然坐标系中采用微分求积法将微分
控制方程转化为代数方程组，求解可得在特定速度和预应力条件下的固有频率。结果显示，轴向
运动圆板失稳前速度与固有频率反相关，在速度增大过程中会出现不稳定、稳定和耦合颤振等现
象。预应力对固有频率的影响具有模态相关性。 |
| 英文摘要: |
| Differential quadrature method(DQM) was used to reveal the natural vibration characteristics of axially
moving circular plates. In Cartesian coordinate system, the dynamic differential governing equations of axially moving
circular plates were established by using the third order shear deformation plate theory and virtual work principle. A
circular plate in Cartesian coordinate system was mapped to a square plate in natural coordinate system by using
the coordinate mapping technique. In the natural coordinate system, the differential quadrature method was used to
transform the differential governing equations into algebraic equations, and the natural frequencies under certain ve⁃
locities and pre-stress conditions can be obtained. The results showed that when the velocity of axially moving circu⁃
lar plate was lower than critical velocity, the velocity was inversely correlated with the natural frequency, and instabili⁃
ty, stable and coupled chatter would occur during the process of velocity increasing. The influence of pre-stress on
natural frequency was modal dependent. |
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