A procedure for determining nonstationary vibrations of a discretely accreted thermoelastic body in the approximation of small deformations and thermal flows is developed. A closed-form solution is constructed for a growing parallelepiped under “smoothly rigid” heat-insulated fixation conditions for the stationary faces and the growing load-free face. The temperature field on the growing face is analyzed numerically for various accretion scenarios.
This is a preview of subscription content,to check access.
Access this article
Similar content being viewed by others
N. Kh. Arutyunyan, A. V. Manzhirov, and V. E. Naumov, Contact Problems of Mechanics of Growing Bodies (Nauka, Moscow, 1991) [in Russian].
S. A. Lychev, T. N. Lycheva, and A. V. Manzhirov, “Unsteady Vibration of a Growing Circular Plate,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 199–208 (2011) [Mech. Solids (Engl. Transl.) 46 (2), 325–333 (2011)].
S. I. Kuznetsov, A. V. Manzhirov, and I. Fedotov, “Heat Conduction Problem for a Growing Ball,” Izv. Akad. Nauk.Mekh. Tverd. Tela, No. 6, 139–148 (2011) [Mech. Solids (Engl. Transl.) 46 (6), 929–936 (2011)].
A. V. Manzhirov and S. A. Lychev, “The Mathematical Theory of Growing Solids: Finite Deformations,” Dokl. Ross. Akad. Nauk 443(4), 438–441 (2012) [Dokl. Phys. (Engl. Transl.) 57 (4), 160–163 (2012)]
S. A. Lychev and Yu. E. Senitskii, “Nonsymmetric Finite Integral Transformations and Their Applications to Viscoelasticity Problems,” Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser., Special Issue, 16–38 (2002).
S. A. Lychev, “CoupledDynamic ThermoviscoelasticityProblem,” Izv. Akad.Nauk.Mekh. Tverd. Tela, No. 5, 95–113 (2008) [Mech. Solids (Engl. Transl.) 43 (5), 769–784 (2008)].
W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1975).
S. A. Lychev, A. V. Manzhirov, and S. V. Joubert, “Closed Solutions of Boundary-Value Problems of Coupled Thermoelasticity,” Izv. Akad. Nauk.Mekh. Tverd. Tela, No. 4, 138–154 (2010) [Mech. Solids (Engl. TRansl.) 45 (4), 610–623 (2010)].
P. A. Zhilin and T. P. Il’icheva, “Spectra and Oscillation Mode Shapes of a Rectangular Parallelepiped Obtained Using Three-Dimensional Theory of Elasticity and Theory of Plates,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 94–103 (1980) [Mech. Solids (Engl. Transl.)].
V. P. Mikhailov, Partial Differential Equations (Nauka, Moscow, 1976) [in Russian].
I. C. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space (Nauka, Moscow, 1965; AMS, 1969).
Online Materials Information Resource — MatWeb, URL: http://matweb.com.
Original Russian Text © A.L. Levitin, S.A. Lychev, A.V. Manzhirov, M.Yu. Shatalov, 2012, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2012, No. 6, pp. 95–109.
About this article
Cite this article
Levitin, A.L., Lychev, S.A., Manzhirov, A.V. et al. Nonstationary vibrations of a discretely accreted thermoelastic parallelepiped. Mech. Solids 47, 677–689 (2012). https://doi.org/10.3103/S0025654412060106