Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2007-1pp.72-84

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 42, Issue 1 / 2007 | Next article >>
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
1.  A. A. Abramov, "On the Transfer of Boundary Conditions for Systems of Linear Ordinary Differential Equations (a Version of the Thomas Method)," Zh. Vychisl. Mat. i Mat. Fiz. 1 (3), 542-545 (1961) [U.S.S.R. Comput. Math. and Math. Phys.].
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.)].
6.  S. A. Ambartsumyan, General Theory of Anisotropic Shells (Nauka, Moscow, 1974) [in Russian].
7.  F. Riesz and B. Sz.-Nagy, Lectures in Functional Analysis (Mir, Moscow, 1979) [in Russian].
8.  J.-L. Lions and E. Magenes, Inhomogeneous Boundary Value Problems and Their Applications (Mir, Moscow, 1971) [Russian translation].
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.].
14.  G. M. Fikhtengol'ts, Course of Differential and Integral Calculus, Vol. 3 (Fizmatgiz, Moscow, 1963) [in Russian].
15.  L. V. Kontorovich and V. I. Krylov, Approximate Methods of Higher-Order Analysis (Gostekhizdat, Moscow-Leningrad, 1952) [in Russian].
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
Link to Fulltext
<< Previous article | Volume 42, Issue 1 / 2007 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100