Aslanjan, A. G.; Lidskii, V. B. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 74K25 Shells 74H99 Dynamical problems in solid mechanics 47E05 General theory of ordinary differential operators 70J10 Modal analysis in linear vibration theory PDFBibTeX XMLCite \textit{A. G. Aslanjan} and \textit{V. B. Lidskii}, J. Appl. Math. Mech. 35, 648--664 (1971; Zbl 0268.73048); translation from Prikl. Mat. Mekh. 35, 701--717 (1971) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.