Abstract
The method of averaging is used to investigate the damping of the vibrations of a one-dimensional, physically and geometrically linear viscoelastic system with one degree of freedom. The motion of this system under an external load is studied at resonance. The averaging principle is justified on both finite and infinite time intervals for nonlinear multidimensional systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. A. Il'yushin and P. M. Igibalov, Mekhan. Polim., No. 3, 33 (1965).
A. N. Filatov, in: Studies in Analytical Mechanics [in Russian], Tashkent (1965), p. 135.
A. N. Filatov, Averaging in Differential and Integro-Differential Equations [in Russian], Tashkent (1967).
A. N. Filatov, Dokl. Akad. Nauk SSSR,165, No. 3, 490 (1965).
C. Banfi, Boll. Unione mat. ital., No. 22 (1967).
Ya. A. Bykov, Some Problems in the Theory of Integro-Differential Equations [in Russian], Frunze (1957).
Additional information
Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 5, pp. 806–813, September–October, 1969.
Rights and permissions
About this article
Cite this article
Larionov, G.S. Investigation of the vibrations of relaxing systems by the averaging method. Polymer Mechanics 5, 714–720 (1969). https://doi.org/10.1007/BF00855542
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00855542