Stability of a String in Axial Flow

The equation of motion of a long slender beam submerged in an infinite fluid moving with constant speed is derived using Hamilton’s principle. The upstream end of the beam is pinned and the downstream end is free to move. The resulting equation of motion is then used to perform the stability analysis of a string, i.e., a beam with negligible bending stiffness. It is found that the string is stable if (a) the external tension at the free end exceeds the value of a U², where a is the “added mass” of the string and U the fluid speed; or (b) the length-over-diameter ratio exceeds the value 2C_f/π, where C_f is the frictional coefficient of the string.