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The added mass of two-dimensional cylinders heaving in water of finite depth

Published online by Cambridge University Press:  12 April 2006

Kwang June Bai
Kwang June Bai
Affiliation:
David W. Taylor Naval Ship Research and Development Center, Bethesda, Maryland 20084
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Abstract

This paper presents numerical results for the added-mass and damping coefficients of semi-submerged two-dimensional heaving cylinders in water of finite depth. A simple proof is given which shows that the added mass is bounded for all frequencies in water of finite depth. The limits of the added-mass and damping coefficients are studied as the frequency tends to zero and to infinity. A new formulation valid in the low-frequency limit is constructed by using a perturbation expansion in the wavenumber parameter. For the limiting cases, dual extremum principles are used, which consist of two variational principles: a minimum principle for a functional and a maximum principle for a different but related functional. These two functionals are used to obtain lower and upper bounds on the added mass in the limiting cases. However, the functionals constructed (Bai & Yeung 1974) for the general frequency range (excluding the limiting cases) have neither a minimum nor a maximum. In this case, the approximate solution cannot be proved to be bounded either below or above by the true solution. To illustrate these methods, the added-mass and damping coefficients are computed for a circular cylinder oscillating in water of several different depths. Results are also presented for rectangular cylinders with three different beamdraft ratios at several water depths.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 1 , 9 June 1977 , pp. 85 - 105
Copyright
© 1977 Cambridge University Press

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