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Vasil’ev, D. G.; Levitin, M. R.; Lidskij, V. B.

Forced vibrations of a shell immersed in a viscous compressible fluid. (English. Russian original) Zbl 0756.73067

Funct. Anal. Appl. 25, No. 4, 309-311 (1991); translation from Funkts. Anal. Prilozh. 25, No. 4, 93-95 (1991).
Forced vibrations of a shell immersed in a viscous compressible liquid are investigated, This problem is called as “external problem” in the present paper. The aim of the work is to demonstrate the existence and uniqueness of the solution for the governing system, consisting of three linear differential equations, under the “radiation” and “contact” conditions. Two necessary conditions for solving this problem are demonstrated.
Reviewer: G.V.Vasiliev (Bucureşti)

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
74K15 Membranes

Keywords:

Hankel’s spherical functions; Fourier series; existence; uniqueness; linear differential equations
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\textit{D. G. Vasil'ev} et al., Funct. Anal. Appl. 25, No. 4, 309--311 (1991; Zbl 0756.73067); translation from Funkts. Anal. Prilozh. 25, No. 4, 93--95 (1991)
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References:

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[14] A. G. Aslanyan and V. B. Lidskii, Distribution of Proper Frequencies of Thin Elastic Shells [in Russian], Nauka, Moscow (1974).
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