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Frequencies of free vibrations of a thin shell interacting with a liquid. (English) Zbl 0576.73039
Translation from Funkts. Anal. Prilozh. 15, No.3, 1-9 (Russian) (1981; Zbl 0477.73052).

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K15 Membranes
74K25 Shells
74H45 Vibrations in dynamical problems in solid mechanics
47Gxx Integral, integro-differential, and pseudodifferential operators
76D05 Navier-Stokes equations for incompressible viscous fluids
47A10 Spectrum, resolvent
47B38 Linear operators on function spaces (general)
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References:
[1] V. N. Buivol, Oscillations and Stability of Deformable Systems in a Liquid [in Russian], Naukova Dumka, Kiev (1975).
[2] L. I. Balabukh, ”Interaction of shells with liquid and gas,” in: Proceedings of the Sixth All-Union Conference on the Theory of Shells and Membranes [in Russian], Nauka, Moscow (1966). · Zbl 0153.11601
[3] A. L. Gol’denveizer, V. B. Lidskii, and P. E. Tovstik, Free Vibrations of Thin Elastic Shells [in Russian], Nauka, Moscow (1979).
[4] A. G. Aslanyan and V. B. Lidskii, Distribution of the Natural Frequencies of Thin Elastic Shells [in Russian], Nauka, Moscow (1974).
[5] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag (1972).
[6] I. M. Glazman, Direct Methods of the Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963). · Zbl 0143.36505
[7] D. G. Vasil’ev, ”Asymptotic of the distribution function of the spectra of pseudodifferential operators with parameters,” Funkts. Anal. Prilozhen.,14, No. 3, 65-66 (1980).
[8] L. H?rmander, ”The spectral function of an elliptic operator,” Acta Math.,121, Nos. 3-4, 193-218 (1968). · Zbl 0164.13201 · doi:10.1007/BF02391913
[9] M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978). · Zbl 0451.47064
[10] A. G. Aslanyan, D. G. Vasil’ev, and V. B. Lidskii, ”The frequencies of free vibrations of shells interacting with liquid,” in: Proceedings of the Twelfth All-Union Conference on the Theory of Shells and Membranes [in Russian], Erevan State Univ. (1980), pp. 86-92.
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