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.
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. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(7): 18-24.
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