解释自由端含集中质量悬臂输流管固有频率计算悖论

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (7) : 18-24.

论文

赵桂欣，孟帅，车驰东,陈俐

作者信息 +

Explanation for paradox in natural frequency calculation of cantilever fluid-conveying pipe system with an end-mass

ZHAO Guixin, MENG Shuai, CHE Chidong, CHEN Li

Author information +

文章历史 +

摘要

深海钻井系统一旦发生紧急脱离，钻井液需下泄入海防止悬挂立管系统固有频率与波浪频率接近而发生共振破坏，同时海水必须注入管内以防止立管挤毁。此时悬臂立管机构为一典型低端含集中质量（低端总成）悬臂输流管系统。该系统采用伽辽金法计算固有频率时通常采用两种方法：（1）将集中质量作为边界条件；（2）利用狄拉克函数将集中质量嵌入输流管模型。内流速度为零时两种方法计算结果一致。但当内流速度不为零时两种方法计算结果差别较大，Paidoussis 指出此时第一种方法错误，但并未给出合理解释。重新推导集中质量作为边界条件时悬臂梁系统固有模态正交条件，提出改进方法进行重新计算，与第二种方法及文献结果比较完成验证。并对比自由端含集中质量悬臂输流管系统内流效应试验结果，发现基于改进方法可正确预测临界内流速度及失稳振动频率。可解释自由端含集中质量悬臂输流管系统固有频率计算悖论，同时为不同边界条件下输流管系统动力学分析提供参考。

Abstract

Once emergency disconnection occurs for a deep-water drilling system, drilling mud should be released to avoid undesired axial loading from resonance while seawater must be refilled in case of riser collapse. The riser system following an emergency disconnection is a typical flow-conveying pipe system attached with an end-mass (Low Marine Riser Package). There are typically two methods utilized to calculate the natural frequencies of the pipe system via Galerkin method: (1) the end-mass is accounted for in the boundary conditions; (2) the end-mass is included in the equation of motion via a Dirac delta function. Although Paidoussis have pointed out that the first method is incorrect when the internal flow velocity is nonzero, a reasonable explanation has not been given. The orthogonality relations of a beam accounting for the end-mass in the boundary conditions is re-derived. Then the natural frequencies of the aforementioned pipe system is calculated employing first method and verified by comparing with the results adopting the second method. Then an experiment employing a cantilevered fluid-conveying pipe under gravity is introduced. The refined method can predict the critical internal flow velocity and the vibration frequency when the pipe loses stability. This new finding can not only explain the paradox in natural frequency calculation of the pipe system under consideration, but also provide as a workbench for dynamic analysis of fluid-conveying pipe systems with various boundary conditions.

导出引用

赵桂欣，孟帅，车驰东,陈俐. 解释自由端含集中质量悬臂输流管固有频率计算悖论[J]. 振动与冲击, 2023, 42(7): 18-24

ZHAO Guixin, MENG Shuai, CHE Chidong, CHEN Li. Explanation for paradox in natural frequency calculation of cantilever fluid-conveying pipe system with an end-mass[J]. Journal of Vibration and Shock, 2023, 42(7): 18-24

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