Drag on an Oscillating Rod with Longitudinal and Torsional Motion

An analytical expression for the viscous drag on a smooth circular cylindrical rodlike cable oscillating with longitudinal and torsional motion is obtained. Based on a linear damping law, an approximate value for the drag coefficient is also presented. The analysis and con- clusions are useful when dealing with many ocean engineering problems of practical importance. the analysis of many practical problems related to the sea-state excitation of long rods and cable-body systems for salvage, buoy, oil drilling, and towing operations, an expression for the viscous drag force acting on the longi- tudinal rod or cable is required. It has been shown that the inclusion of this term can have a pronounced effect on the tension in the rod or cable and subsequent response of the system. For example, the propagation and attenuation of internal stress waves and snap loads through the cable in a cable lifting system are affected by the external viscous damping.1 The problem is also of considerable interest in offshore oil drilling problems since a similar analysis is usually performed.2 It is a common practice to postulate a linear relationship between the external damping force and the surface velocity of the rod when investigating the longitudinal vibrations based on the wave equation. The solution of this damped wave equation with an arbitrary damping coefficient can show the qualitative effects of external damping. However, the magnitude and frequency dependence of the damping coefficient can significantly alter the nature of the solution. The purpose of this investigation is to formulate an analyti- cal expression for the viscous drag on a smooth circular cylindrical rodlike cable oscillating with longitudinal and torsional motion. An examination of the hypothesis of the linear damping law will be made and the damping coefficient estimated.