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IssuesArchive of Issues2007-1pp.72-84

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G. R. Gulgazaryan, "Vibrations of a cantilever nonclosed orthotropic cylindrical membrane shell of variable curvature," Mech. Solids. 42 (1), 72-84 (2007)
Year 2007 Volume 42 Number 1 Pages 72-84
Title Vibrations of a cantilever nonclosed orthotropic cylindrical membrane shell of variable curvature
Author(s) G. R. Gulgazaryan (Abovyan Armenian State Pedagogical University, pr-t Tigran Metsi 17, Yerevan, 0010, Republic of Armenia, lusina@mail.ru)
Abstract We study natural vibrations of a cantilever nonclosed orthotropic cylindrical shell with an arbitrary plane directrix. We assume that the shell is hinged on two generators and its bending rigidity is zero (a membrane shell). We find the dispersion and characteristic equations for the characteristics of natural frequencies and damping ratios of the corresponding modal vibrations. Specific computations are performed for shells with directrix being a parabola and with various values of the curvature and length of the generator.
References
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2.  Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar', Free Vibrations of Members of Shell Structures (Naukova Dumka, Kiev, 1986) [in Russian].
3.  V. P. Kostromin and V. I. Myachenkov, "Vibrations of Nonclosed Cylindrical Shells of Variable Curvature," Prikl. Mekh. 8 (8), 113-116 (1972) [Sov. Appl. Mech.].
4.  G. R. Gulgazaryan, "Formula for the Distribution of Frequencies of a Cylindrical Shell with an Arbitrary Directrix," Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 161-163 (1979) [Mech. Solids (Engl. Transl.)].
5.  G. R. Gulgazaryan and V. B. Lidskii, "Density of Free Vibration Frequencies of a Thin Anisotropic Shell Composed of Anisotropic Layers," Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 171-174 (1982) [Mech. Solids (Engl. Transl.)].
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9.  V. A. Solonnikov, "About General Boundary Value Problems for Systems Elliptic in the Sense of A. Douglis and L. Nirenberg," Izv. Akad. Nauk SSSR. Ser. Mat. 28 (3), 665-706 (1964) [Math. USSR-Izv.].
10.  V. A. Solonnikov, "On Green's Matrices for Elliptic Boundary Value Problems," Trudy Mat. Inst. Steklov 110 (6), 107-145 (1970) [Proc. Steklov Inst. Math.].
11.  A. L. Gol'denveizer, V. B. Lidskii, and P. E. Tovstik, Free Vibrations of Thin Elastic Shells (Nauka, Moscow, 1979) [in Russian].
12.  G. R. Gulgazaryan, V. B. Lidskii, and G. I. Eskin, "Spectrum of a Membrane System in the Case of a Thin Shell of an Arbitrary Contour," Sibirsk. Mat. Zh. 4 (5), 978-986 (1973) [Siberian Math. J.].
13.  Ya. B. Lopatinskii, "On a Method for Reducing the Boundary-Value Problems for a System of Differential Equations of Elliptic Type to Regular Integral Equations," Ukrain. Mat. Zh. 5 (2), 123-151 (1953) [Ukrainian Math. J.].
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16.  T. M. Grigoryan and G. R. Gulgazaryan, "Vibrations Localized near the Free Edge of a Half-Infinite Orthotropic Nonclosed Cylindrical Membrane Shell," in Proceedings of Kh. Abovyan Armenian Pedagogical Institute (2002), Vol. 1, pp. 43-52.
17.  G. R. Gulgazaryan and L. G. Gulgazaryan, 'Vibrations Localized near the Free Edge of a Half-Infinite Nonclosed Membrane Cylindrical Shell," Akust. Visn. NAN Ukraini 2 (4), 42-48 (1999).
Received 07 April 2004
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