Abstract
Averaging [2, 3] is used to examine the free transverse oscillations of a viscoelastic beam supported at the ends, the rheological properties being described by a certain cubic integral relationship. The forced principal and fractional resonant oscillations are considered for n=1, these being excited by a transverse periodic force; the limiting oscillations are determined that correspond to the principal resonance.
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Literature cited
T. Kadyrbekov, Mekhan. Polim., No. 4, 752 (1971).
A. N. Filatov, in: Researches on Analytical Mechanics [in Russian], Tashkent (1955), p. 135.
A. N. Filatov, Averaging in Systems of Differential, Integrodifferential, and Integral Equations [in Russian], Tashkent (1967).
A. N. Filatov, Averaging Methods in Differential and Integrodifferential Equations [in Russian], Tashkent (1971).
I. G. Malkin, Some Topics in the Theory of Nonlinear Oscillations [in Russian], Moscow (1956).
Additional information
M. T. Urazbaev Institute of Building Mechanics and Seismic Stability, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 5, pp. 939–943, September–October, 1973.
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Kadyrbekov, T. Nonlinear vibrations of a viscoelastic beam. Polymer Mechanics 9, 832–835 (1973). https://doi.org/10.1007/BF00856290
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DOI: https://doi.org/10.1007/BF00856290