Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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S.A. Lychev, T.N. Lycheva, and A.V. Manzhirov, "Unsteady Vibration of a Growing Circular Plate," Mech. Solids. 46 (2), 325-333 (2011)
Year 2011 Volume 46 Number 2 Pages 325-333
DOI 10.3103/S002565441102021X
Title Unsteady Vibration of a Growing Circular Plate
Author(s) S.A. Lychev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia,
T.N. Lycheva (Moscow State University of Instrument Engineering and Computer Science, Stromynka 20, Moscow, 107996 Russia)
A.V. Manzhirov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia,
Abstract Forced vibration of a thickening circular plate is studied within the framework of the small deformation theory. The plate material is assumed to be elastic and isotropic and the plate thickness to be continually increasing due to influx of material from outside. It is also assumed that the plate thickness varies with time but is independent of the space coordinates. Moreover, in the process of growth, the midsurface position does not change, which suggests that the plate grows symmetrically on both its surfaces.
Keywords growing plate, small deformations, forced vibration, analytical solutions, spectral expansions
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2.  N. Kh. Arutyunyan and A. V. Manzhirov, Contact Problems of Creep Theory (Inst. Mekh. NAN, Erevan, 1999).
3.  N. Kh. Arutyunyan, A. V. Manzhirov, and V. E. Naumov, Contact Problems of Mechanics of Growing Bodies (Nauka, Moscow, 1991) [in Russian].
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5.  L. Collatz, Eigenvalue Problems with Technical Applications (Chelsea, New York, 1948; Nauka, Moscow, 1968).
6.  V. F. Zaitsev and A. D. Polyanin, Handbook of Ordinary Differential Equations (Fiz.-Mat. Lit., Moscow, 2001) [in Russian].
7.  Material Property Data, MatWeb, URL:
Received 16 December 2010
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