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St. Petersburg Mathematical Journal

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On the problem of time-harmonic water waves in the presence of a freely floating structure


Author: N. Kuznetsov
Original publication: Algebra i Analiz, tom 22 (2010), nomer 6.
Journal: St. Petersburg Math. J. 22 (2011), 985-995
MSC (2010): Primary 76B15, 76B03; Secondary 35Q35, 35P05
DOI: https://doi.org/10.1090/S1061-0022-2011-01179-3
Published electronically: August 19, 2011
MathSciNet review: 2760090
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Abstract: The two-dimensional problem of time-harmonic water waves in the presence of a freely floating structure (it consists of a finite number of infinitely long surface-piercing cylinders connected above the water surface) is considered. The coupled spectral boundary value problem modeling the small-amplitude motion of this mechanical system involves the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations governing the structure's motion. It is proved that any value of the frequency turns out to be an eigenvalue of the problem for a particular structure obtained with the help of the so-called inverse procedure.


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Additional Information

N. Kuznetsov
Affiliation: Institute of Mechanical Engineering Problems, Russian Academy of Sciences, Bol′shoĭ Pr. 61, St. Petersburg 199178, Russia
Email: nikolay.g.kuznetsov@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2011-01179-3
Keywords: Coupled spectral problem, time-harmonic water waves, freely floating structure, trapped mode
Received by editor(s): April 5, 2010
Published electronically: August 19, 2011
Additional Notes: The author is indebted to Dr. O. Motygin for stimulating discussions and to Professor S. Nazarov for his comments on the first version of the paper
Dedicated: To V. M. Babich on the occasion of his 80th birthday
Article copyright: © Copyright 2011 American Mathematical Society