ABSTRACT:

Two efficient techniques are presented for analyzing cables under zero- or low-tension. First, an explicit finite-difference algorithm is presented. The method proves stable if artificial dissipation is added to the scheme. Secondly, an implicit finite-difference algorithm, which incorporates the effects of bending stiffness, is discussed. The importance of bending stiffness is shown for low-tension problems and the method proves stable, regardless of the cable tension magnitude. Therefore, the implicit method provides an efficient means with which to study a wider class of cable problems in a more physically accurate way.

INTRODUCTION

Understanding the dynamics of submerged cables is of great importance for many underwater operations, such as cable deployment and towed or moored acoustic arrays. Therefore, it is not surprising that a substantial amount of research has been conducted in this area. The specific topics addressed within this investigation are the dynamics of low-tension cables and cables under zero initial tension. The term "low-tension" is used to refer to problems in which the cable static tension is significantly lower than the dynamic tension. This phenomena can be restricted to finite regions, for example near the free-end of a towed cable, or may occur along the entire cable length. In low-tension problems, the basic mechanisms that serve to propagate energy are altered. To understand why this occurs, consider that transverse disturbances of taut cables are propagated at a speed proportional to the square-root of the tension (Rao, 1986). Therefore, as the tension becomes low, very little energy is transferred in this fashion. An additional mechanism that gains importance in such cases is determined by considering a beam in bending. In this situation, as the tension vanishes, transverse disturbances are propagated by bending stiffness, at speeds independent of the cable tension (Rao, 1986).

This content is only available via PDF.
You can access this article if you purchase or spend a download.