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The dynamics of towed flexible cylinders Part 2. Negatively buoyant elements

Published online by Cambridge University Press:  21 April 2006

A. P. Dowling
A. P. Dowling
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
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Abstract

A ship, towing a heavier-than-water cable with a neutrally buoyant slender cylinder attached to the downstream end of the cable, is considered. The neutrally buoyant element contains a sonar array. Linear changes in the ship's velocity cause perturbations of both the cable and cylinder. The form of transverse vibrations of the neutrally buoyant cylinder was determined in Part 1. The propagation of disturbances along the cable is investigated in this paper. In particular, the effectiveness of the cable at isolating the sonar array from forcing due to unsteady ship motion is examined.

The cable and cylinder are found to be stable under constant towing conditions. It is therefore appropriate to investigate their response to forcing. Meanderings in the ship's track produce transverse displacements of both the cable and the cylinder. These transverse oscillations entirely decouple from any in-plane motion. The propagation of disturbances of frequency ω along the cable depends strongly on the value of the non-dimensional frequency ωlC/U, where lC is the cable length and U is the towing speed, and only weakly on the other cable parameters. The cable acts as an effective low-pass filter to transverse oscillations, the amplitude of disturbances with non-dimensional frequency greater than 10 being reduced by at least 90% as they propagate along the cable.

Unsteadiness in the ship's speed can result in in-plane deflections of the cable, and vertical oscillations of the cylinder containing the sonar array. In contrast to the transverse oscillations a significant proportion of the in-plane disturbances at the ship travels to the sonar array at all values of the frequency. Low- and high-frequency analytical forms are derived to explain why this occurs. Perturbations in the ship's position are most effectively transformed into vertical oscillations of the array at a frequency of 2.8U/lC. The effect of cable properties on transmission along the cable is investigated. The transmission again depends on the value of the non-dimensional frequency ωlC/U. Parameter changes, which increase the cable critical angle, increase the proportion of the disturbance at the towing point that is transformed into vertical array motion, for a fixed value of ωlC/U. This is explained by reference to the low- and high-frequency analytical solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 533 - 571
Copyright
© 1988 Cambridge University Press

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References

Cannon, T. C. & Genin, J. 1972a Dynamical behaviour of a materially damped flexible towed cable. Aero. Q. 23, 109–120.Google Scholar
Cannon, T. C. & Genin, J. 1972b Three-dimensional dynamical behaviour of a flexible towed cable. Aero. Q. 23, 201–210.Google Scholar
Dowling, A. P. 1988 The dynamics of towed flexible cylinders. Part 1. Neutrally buoyant elements. J. Fluid Mech. 187, 507–532.Google Scholar
Huffman, R. R. & Genin, J. 1971 The dynamical behaviour of a flexible cylinder in a uniform flow field. Aero. Q. 22, 183–195.Google Scholar
Kennedy, R. M. & Strahan, E. S. 1981 A linear theory of transverse cable dynamics at low frequencies. NUSC Tech. Rep. 6463, Naval Underwater Systems Center, Newport, Rhode Island/New London, Connecticut.
Ketchman, J. 1981 Vibration induced in towed linear underwater array cables. IEEE J. Oceanic Engng, OE-6, 77–87.Google Scholar
Lyon, R. H. 1962 The transmission of vibration by towed cables. Bolt, Beranek and Newman Rep. 934.
Païdoussis, M. P. 1966 Dynamics of flexible slender cylinders in axial flow: Part 1. Theory. J. Fluid Mech. 26, 717–736.Google Scholar
Païdoussis, M. P. 1968 Stability of towed, totally submerged flexible cylinders. J. Fluid Mech. 34, 273–297.Google Scholar
Païdoussis, M. P. 1973 Dynamics of cylindrical structures subjected to axial flow. J. Sound Vib. 29, 365–385.Google Scholar
Phillips, W. H. 1949 Theoretical analysis of oscillations of a towed cable. NACA Tech. Note 1796.
Schram, J. W. & Reyle, S. P. 1968 A three-dimensional dynamic analysis of a towed system. J. Hydron. 2, 213–220.Google Scholar
Taylor, G. I. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. 14, 158–183.Google Scholar
Zajac, E. E. 1957 Dynamics and kinematics of the laying and recovery of submarine cable. Bell Syst. Tech. J. 1129–1207.Google Scholar