海洋立管悬挂状态的固有频率和振型  

Natural frequencies and mode shapes of free-hanging risers

作　　者：雷松[1,2] 郑向远[1] 张文首[2] 林家浩[2] 岳前进[2] 

机构地区：[1]清华大学深圳研究生院海洋学部,广东深圳518055 [2]大连理工大学运载工程与力学学部工程力学系,辽宁大连116023

出　　处：《船舶力学》2015年第10期1267-1274,共8页Journal of Ship Mechanics

基　　金：中国博士后科学基金(2015M571043);国家创新研究群体科学基金(5092100)

摘　　要：文章把悬挂状态的立管简化为一端固定一端自由的梁模型,考虑截面性质和有效张力及质量的变化,其控制方程为变系数的四阶偏微分方程,运用微分变换方法推导了固有频率和振型的数值计算方法。通过数值算例验证了文中方法的有效性,考察了收敛速度的变化情况,讨论了立管末端的悬挂器具对固有频率和振型的影响,并结合工程实际,给出了若干海况下立管悬挂状态时在飞溅区的共振区域。Free-hanging risers are simulated as Euler-Bernoulli beams with fixed-free boundary conditions. Considering varying flexural rigidities, effective tensions and mass density, free vibration of the riser is expressed in form of fourth order partial differential equation with variable coefficient whose analytic solution is not straightforward. The natural frequencies and mode shapes are obtained by using differential transfor- mation method. The efficiency of this method and its good convergence rate are validated by numerical examples. Furthermore, the influence of a lumped mass at riser tip is discussed. Resonance zones, which are important during the installation of risers at the wave splash zone, are illustrated.

关 键 词：微分变换 有效张力 固有频率 振型 

分 类 号：O175.2[理学—数学]