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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.
MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
74K15 Membranes
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[1] D. G. Vasil’ev and A. L. Gol’denveizer, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela,4, 184-193 (1983).
[2] D. G. Vasil’ev and V. B. Lidskii, Funkts. Anal. Prilozhen.,20, No. 4, 17-28 (1986). · Zbl 0629.58017
[3] D. G. Vasil’ev, A. L. Gol’denveizer, and E. V. Nol’de, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela,5, 158-168 (1989).
[4] D. G. Markushevich, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela,5, 124-131 (1989).
[5] D. G. Vasil’ev and V. B. Lidskii, in: Mathematical Methods of the Mechanics of a Deformable Solid Body [in Russian], Nauka, Moscow (1986), pp. 30-36.
[6] A. G. Aslanyan, D. G. Vasil’ev, and V. B. Lidskii, in: Proceedings of the 12th All-Union Conference on the Theory of Plates and Shells [in Russian], Vol. 1 (1980), pp. 86-92.
[7] A. N. Guz?, V. D. Kubenko, and A. E. Babaev, Hydroelasticity of Shell Systems [in Russian], Vishcha Shkola, Kiev (1984).
[8] A. N. Guz? and V. D. Kubenko, Theory of Nonstationary Aeroelasticity [in Russian], Naukova Dumka, Kiev (1982). · Zbl 0549.73058
[9] M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978). · Zbl 0451.47064
[10] D. G. Vasil’ev, Distribution of Proper Frequencies of a Thin Shell Interacting with a Fluid [in Russian], Candidate Dissertation, Moscow Physico-Technological Institute (1981).
[11] M. R. Levitin, Dokl. Akad. Nauk SSSR,259, No. 6, 1355-1358 (1987).
[12] D. G. Vasil’ev, M. R. Levitin, and V. B. Lidskii, Dokl. Akad. Nauk SSSR,305, No. 2, 329-332 (1989).
[13] M. R. Levitin, Vibrations of a Thin Elastic Shell Filled by a Viscous Compressible Fluid (Asymptotic Analysis) [in Russian], Candidate Dissertation, Moscow Physico-Technological Institute (1981).
[14] A. G. Aslanyan and V. B. Lidskii, Distribution of Proper Frequencies of Thin Elastic Shells [in Russian], Nauka, Moscow (1974).
[15] A. L. Gol’denveizer, V. B. Lidskii, and P. E. Tovstik, Free Vibrations of Thin Elastic Shells [in Russian], Nauka, Moscow (1979).
[16] Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 2, McGraw-Hill, New York (1953). · Zbl 0051.40603
[17] J. Meixner, Math. Nachr.,3, No. 1, 9-13 (1949). · Zbl 0036.17701
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