Abstract
A plate reinforced by ribs and placed in an absorbing acoustic medium is considered. The uniqueness of the solution of the stationary acoustic problem for this system is established. The connection of the uniqueness problem with the optical theorem is discussed.
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Literature cited
D. P. Kouzov, “The energy principle for uniqueness of boundary-value problems of acoustics,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,89, 124–133 (1979).
B. P. Belinskii, V. A. Veshev, I. I. Klyukin, and D. P. Kouzov, “On the effect of ribs on the propagation of flexure waves in a plate of finite width,” Mekh. Tverd. Tela, No. 5, 166–170 (1977).
S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Moscow (1957).
B. P. Belinskii and D. P. Kouzov, “The optical theorem for a plate – fluid system,” Akust. Zh.,26, No. 1, 13–19 (1980).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 14–19, 1981.
The author is grateful to D. P. Kouzov for posing the problem and for valuable discussions.
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Belinskii, B.P. Uniqueness of the solution of stationary acoustic problems for reinforced plates. J Math Sci 20, 1754–1757 (1982). https://doi.org/10.1007/BF01119355
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DOI: https://doi.org/10.1007/BF01119355