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.