THE FINITE ELEMENT METHOD FOR HYDROELASTIC INSTABILITY OF UNDERWATER TOWED CYLINDRICAL STRUCTURES

The dynamics of underwater towing of flexible cylindrical structures belongs to the class of fluid–structure interaction problems commonly referred to as “cylinders in axial flow”. The serious concern in such towing operations is the various types of hydroelastic instabilities exhibited by the structure at certain critical tow speeds. In practice, reliable prediction of tow configurations and stability characteristics of such towed systems can lead to optimum deployment of cable scope and control of tow speed. The present investigation is concerned with the development of a comprehensive linear finite element method for the dynamics of the flexible towed cylinder with focus on the stability behaviour. The finite element approximation is derived from a variational statement of the problem based on Hamiltonʹs principle. The various structure- and fluid-related matrices as well as matrices resulting from boundary terms have been derived, resulting in a complex unsymmetric eigenvalue problem. Exhaustive validation and convergence studies show that the comparisons between finite element and analytical results are almost exact. Using the finite element code, the hydroelastic instability of a ship-towed array system has been analyzed. The effect of cable scope and shape of the downstream end on stability have been examined.