On the Kramers-Kronig relations for ship motions¹

Article type: Research Article

Authors: Kotik, Jack | Mangulis, Visvaldis

Affiliations: TRG, Inc., Syosset, New York

Note: [1] Work at TRG, Inc. supported in part by Nonr-2692(00).

Abstract: It is shown, for the case of forced simple harmonic heave, that if the damping parameter is known for all frequencies then the virtual mass parameter (minus its value at infinite frequency) is readily determined for all frequencies, and vice versa, by an integral transform (equations (3) and (4) ). These relations are called the Kramers-Kronig relations. It follows that any approximate method for computing damping gives rise to an approximate method for computing added mass, and vice versa. Also, the response (for all time) to an impulse in acceleration can be calculated if either the damping or added-mass parameters are known for all frequencies (equation (A-5)). Some approximate added-mass parameters obtained in this way are presented and compared with exact results. Some asymptotic consequences of the Kramers-Kronig relations are also presented. It is expected that these relations can be derived for any motion, with forward speed, and can therefore play a very useful role in ship motion theory.

DOI: 10.3233/ISP-1962-99701

Journal: International Shipbuilding Progress, vol. 9, no. 97, pp. 361-368, 1962