Abstract
The perturbation method is used to reduce a coupled three-dimensional problem of stationary vibrations of thermoelasticity to a number of three-dimensional vibration problems of the theory of thermal stresses. We develop an algorthm for constructing the solution in the zeroth approximation on the basis of the method of homogeneous solutions.
Similar content being viewed by others
Literature Cited
W. Nowacki,Dynamic Problems of Thermoelasticity, Noordhoof, Leyden (1976).
L. D. Landau and E. M. Lifshits,Mechanics of Solid Media [in Russian], Moscow (1954).
A. D. Kovalenko,Foundations of Thermoelasticity [in Russian], Moscow (1970).
V. A. Ditkin and A. P. Prudnikov,Operational Calculus in two Variables and its Applications, Pergamon Press, New York, (1962).
A. S. Kosmodamianskii, Yu. V. Mysovskii, and R. M. Mysovskaya, “Steady-state vibrations of thick multiconnected plates,” in:Proceedings of the Tenth All-Union Conference on the Theory of Plates and Shells [in Russian], Tbilisi (1975), Vol. 2, pp. 218–225.
G. Arfken,Mathematical Methods for Physicists, 3rd ed., Academic Press, Orlando (1985).
A. S. Kosmodamianskii, V. N. Lozhkin, Yu. V. Mysovskii, and V. A. Shaldyrvan, eds.,The Stress State of Plates with Holes in Three-Dimensional Formation [in Russian], Donetsk (1970).
W. Nowacki,Theory of Elasticity [Russian translation], Moscow (1975).
U. Nigul, “On the roots of the Lamb equation for the deformation of a plate that is antisymmetric with respect to the middle surface,”Izv. Akad. Nauk EstSSR,12, No. 3, 25–30 (1963).
Additional information
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 119–127.
Rights and permissions
About this article
Cite this article
Mysovskii, Y.V. The thermoelastic problem for steady-state vibrations of a plante in three-dimensional formulation. J Math Sci 76, 2435–2440 (1995). https://doi.org/10.1007/BF02362916
Issue Date:
DOI: https://doi.org/10.1007/BF02362916