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Kaplunov, Yu. D.

Slowly varying high-frequency stress-strain states in immersed shells. (English. Russian original) Zbl 0787.73052

J. Appl. Math. Mech. 55, No. 3, 390-396 (1991); translation from Prikl. Mat. Mekh. 55, No. 3, 478-485 (1991).
Summary: The asymptotic integration method is used to derive two-dimensional equations that describe, near the cutoff frequency, the slowly varying component of the stress-strain state of a thin elastic shell immersed in an infinite compressible liquid. The effect of the fluid on different types of high-frequency, long-wave vibrations of the shell is established. Applications of the equations to hydroacoustic problems are discussed for the case of a circular cylindrical shell.

Cited in 1 Document

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K15 Membranes
76Q05 Hydro- and aero-acoustics

Keywords:

asymptotic integration method; two-dimensional equations; infinite compressible liquid; circular cylindrical shell
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References:

[1] Kaplunov, Yu. D., The equations of the high-frequency long-wave oscillations of an elastic layer superimposed on an acoustic half-space, Dokl. Akad. Nauk SSSR, 309, 5 (1989) · Zbl 0729.73096
[2] Kaplunov, Yu. D.; Markushevich, D. G., Radiation from an elastic layer into a liquid half-space (the plane problem), Dokl. Akad. Nauk SSSR, 313, 6 (1990) · Zbl 0726.76088
[3] Kaplunov, Yu. D., Slowly varying high-frequency stress-strain state in elastic thin shells, (MTT, 5 (1990), Izv. Akad. Nauk SSSR) · Zbl 0787.73052
[4] Berdichevskii, V. L., High-frequency long-wave oscillations of plates, Dokl. Akad. Nauk SSSR, 236, 6 (1977) · Zbl 0158.46505
[5] Berdichevskii, V. L.; Le Hand Chau, High-frequency long-wave oscillations of shells, PMM, 44, 4 (1980)
[6] Kaplunov, Yu. D., Asymptotic methods in high-frequency hydroelasticity of thin shells, (Interaction of Acoustic Waves with Elastic Bodies, Proc. of Ail-Union Symp. (1989), Izd. Tallin. Univ: Izd. Tallin. Univ Tallin) · Zbl 0787.73052
[7] Veksler, N. D.; Kaplunov, Yu. D.; Korsunskii, V. M., Asymptotic formulas for resonance frequencies in the scattering of a normally incident acoustic wave by a cylindrical shell, Akust. Zh., 36, 3 (1990)
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