Analytic Determination of the Buckling Speed of Towed Slender Cylindrical Beams

Abstract

The buckling of submerged, towed slender cylindrical beams is investigated using analytic methods. The problem is formulated using the “slender body” approximation and conditions are sought for which the beam may be in equilibrium at a deflected position. The buckling modes are expressed in terms of generalized Airy functions, and determination of the critical towing speed for buckling is made by solving the resulting eigenvalve problem. The critical towing speed is obtained as a function of the bending stiffness, length-to-diameter ratio and hydrodynamic characteristics of the beam. It is concluded that a blunt tail-end with an increase in length-to-diameter ratio of the beam and externally imposed tension have a favorable effect on the buckling stability of the beam.