The dynamics of underwater towing of #exible cylindrical structures belongs to the class of #uid}structure interaction problems commonly referred to as `cylinders in axial #owa. 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 con"gurations 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 "nite element method for the dynamics of the #exible towed cylinder with focus on the stability behaviour. The "nite element approximation is derived from a variational statement of the problem based on Hamilton's principle. The various structure-and #uid-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 "nite element and analytical results are almost exact. Using the "nite element code, the hydroelastic instability of a ship-towed array system has been analyzed. The e!ect of cable scope and shape of the downstream end on stability have been examined.
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Now in view of equations ( 1), ( 4), ( 10) and ( 13), equation ( 11) yields the governing di!erential equation [3] EI *v *x #(m#M) *v *t #M; *v *x #2M; *v *x*t !ΒΉ *v *x # 1 2 D; C D *v *t #; *v *x "0.