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Spectrum of the system describing oscillations of a shell of revolution. (English. Russian original) Zbl 0268.73048

J. Appl. Math. Mech. 35, 648-664 (1971); translation from Prikl. Mat. Mekh. 35, 701-717 (1971).

MSC:

74K25 Shells
74H99 Dynamical problems in solid mechanics
47E05 General theory of ordinary differential operators
70J10 Modal analysis in linear vibration theory
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References:

[1] Gol’denveizer, A. L., Some mathematical problems of the linear theory of thin shells, Usp. Matem. Nauk, Vol. 15, No. 5 (1960)
[2] Gol’denveizer, A. L., Asymptotic integration of linear partial differential equations with a small principal part, PMM, Vol. 23, No. 1 (1959)
[3] Gol’denveizer, A. L., Qualitative analysis of free vibrations of an elastic thin shell, PMM, Vol. 30, No. 1 (1966)
[4] Alumaa, N. A., On the fundamental system of integrals of the equation for small axisymmetric steady-state vibrations of an elastic conical shell of revolution, (Ser.Tekhn. ifiz.-matem. nauk., Vol. 9 (1960), Izv. Akad. Nauk EstSSR), No.1
[5] Tovstik, P. E., Integrals of the system of equations for nonaxisymmetiic vibrations of shells of revolution, (In a Collection.-Investigations on Elasticity and Plasticity (1966), Izd. LGU, (Leningrad State University)), 45-55, No. 5 · Zbl 0705.73082
[6] Lidskii, V. B.; Khar’kova, N. V., Spectrum of a system of membrane equations in the case of axisymmetric vibrations of shells of revolution, Dokl. Akad. Nauk. SSSR, Vol. 194, No. 4 (1970) · Zbl 0223.73067
[7] Dunford, N.; Schwartz, J. T., Linear Operators (1958), Interscience Publishers: Interscience Publishers New York
[8] Vishik, M. I.; Liusternik, L. A., Regular degeneracy and boundary layer for linear differential equations with a small parameter, J. Usp. Matem. Nauk, Vol. 12, No. 5 (1957), (77)
[9] Khar’kova, N. V., On the lower portion of the spectrum of natural axisymmetric vibrations of a thin elastic shell of revolution, PMM, Vol. 35, No. 3 (1971) · Zbl 0255.73101
[10] Gokhberg, I. Ts.; Krein, M. G., Fundamental statements on defective numbers, radical numbers and indices of linear operators, J. Usp. Matem. Nauk, Vol. 12, No. 2 (1957), (74) · Zbl 0088.32101
[11] Riesz, F.; Sz. -Nagy, B., Functional Analysis (1955), Frederick Ungar: Frederick Ungar New York
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