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
Published electronically:
August 19, 2011
MathSciNet review:2760090 Full-text PDF
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.
8.
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L. Euler, Principia motus fluidorum, Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae. T. VI, 1761, pp. 271-311. English translation available at http://www.math.dartmouth.edu/ ~euler/docs/translations/E258.pdf
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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