分布轴向力作用下隔水管横向自由振动分析

隔水管固有频率的精确计算对保证隔水管的安全使用和防止共振的发生有着极为重要的意义.在分析中,考虑了分布轴向力和顶张力的共同作用,建立了隔水管横向振动力学模型;基于牛顿定律和纵横弯曲梁理论,对微单元受力分析,得到隔水管横向自由振动的四阶偏微分方程;利用分离变量法将四阶偏微分方程简化为四阶变系数常微分方程;采用积分法求解四阶变系数常微分方程,得到隔水管横向自由振动固有频率的解析解.结果表明:(1)分布轴向力作用下隔水管横向自由振动的固有频率和振型,与将分布轴向力简化为集中力作用下隔水管的固有频率和振型有很大差别;(2)顶张力一定时,随着分布轴向力减小,隔水管固有频率增大;分布轴向力一定时,随着顶张力增大,隔水管固有频率增大;(3)采用积分法求解隔水管横向振动特性时,计算精度高,为隔水管的优化设计提供了可靠的理论依据.

ANALYSIS OF TRANSVERSE FREE VIBRATION OF RISER EFFECTED BY DISTRIBUTION OF AXIAL FORCE

It is very important to accurately calculate a riser's natural frequency for ensuring a safe use of the riser and preventing the occurrence of resonance. Considering the influence of the uniform distribution of axial force and the top tense, a transverse vibration mechanics model of the riser is established.Based on Newton's law and the vertical and horizontal bending beam theory and the stress analysis of micro unit,transverse free vibration of fourth order linear partial differential equation of the riser is achieved. Using the method of separation of variables, we simplify it to a fourth order ordinary differential equation with variable coefficients. To get the analytic solution for transverse free vibration natural frequency, the integral method is used. With examples, we show the following results. First, the uniform distribution of axial force has great effect on natural frequency and vibration mode. Secondly, when the top tension is unchanged and the distribution of axial force is reduced, riser's natural frequency increases; meanwhile when distribution of axial force is constant and the top tension increases, riser natural frequency increases. Thirdly, with high calculation accuracy and speed, the integral method is capable to solve the fourth order ordinary differential equation with variable coefficients, and provides reliable theoretical basis for optimal design of the riser.