带腐蚀Euler-Bernoulli海洋管道模型在海波激励下的振动分析

研究了考虑腐蚀和海生物附着作用的海洋管道在海波激励下的动力学响应．采用欧拉-伯努利梁模型建立细长海洋管道动力学模型，利用格林函数法得到了该受迫振动问题的稳态响应．首先，推导了未腐蚀且考虑海生物附着的海洋管道在海波激励作用下的动力学响应．其次在考虑腐蚀、海生物附着情况下，利用前面未腐蚀模型的解得到腐蚀管道的动力学响应解析解．最后进行了数值讨论，分析了不同腐蚀深度、不同生物质量对管道固有频率的影响．研究了三种输流截面面积相同的环（圆、矩形、三角）模型在同一海波激励作用下的稳态位移响应．分析了不同海波高度、不同海波数目、不同海洋深度及腐蚀深度对管道模型位移的影响；对比了未腐蚀和有腐蚀深度时，某点随时间变化的位移效果．研究结果对海波激励下的管道响应分析和保护具有重要意义．

Vibration Analysis of Marine Pipelines with Corrosion Euler-Bernoulli Model under the Excitation of the Waves

The dynamic response of marine pipelines under sea wave excitation considering corrosion and adhesion of marine organisms is studied. The Euler-Bernoulli beam model is used to establish the dynamic model of slender offshore pipeline, and the steady-state response of the forced vibration problem is obtained by using Green's function method. Firstly, the dynamic response of marine pipelines without corrosion and considering the attachment of marine organisms under sea wave excitation is deduced. Secondly, considering corrosion and marine organism attachment, the analytical solution of the dynamic response of corroded pipeline is obtained by using the solution of the previous non-corroded model. Finally, the analytical solutions are discussed numerically, and the effects of different corrosion depths and biomass on the natural frequencies of pipelines are analyzed. The steady-state displacement responses of three rings (circle, rectangle and triangle) with the same conveying area under the same sea wave excitation are studied. The effects of different sea wave heights, numbers, depths and corrosion depths on the displacement of pipeline models were analyzed. The displacement effects of a certain point varying with time in the cases of non-corrosion depth and corrosion depth were compared.