Abstract
We consider self-excited vibrations of strongly nonlinear mechanical systems obeying the hereditary theory of viscoelasticity. using the Bubnov-Galerkin method, the problem is reduced to a system of ordinary nonlinear integrodifferential equations. The normal modes of vibration of nonlinear conservative elastic systems are chosen as the unperturbed solutions. Self-vibrating solutions are found by iteration to any degree of accuracy. The process converges for certain restrictions on the unperturbed functions and on the small parameter of the problem.
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E. M. Dmitrenko, Yu. V. Mikhlin, and B. I. Morgunov, “Iterative calculation of resonant quasinormal vibrations in strongly nonlinear viscoelastic mechanical systems,” in: Differential Equations and Their Applications [in Russian], Dnepropetrovsk Univ., (1984), pp. 55–61.
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R. M. Rosenberg and C. S. Hsu, “On the geometrization of normal vibrations of nonlinear systems with many degrees of freedom,” in: Trans. Int. Symp. on Nonlinear Vibrations [in Russian], Academy of Sciences of the Ukrainian SSR, Kiev (1973), Vol. 1, pp. 380–416.
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Translated from Dinamicheskie Sistemy, No. 5, pp. 86–90, 1986.
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Dmitrenko, E.M., Mikhlin, Y.V. & Morgunov, B.I. Iterative calculation of strongly nonlinear self-vibrating viscoelastic mechanical systems. J Math Sci 65, 1455–1458 (1993). https://doi.org/10.1007/BF01105296
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DOI: https://doi.org/10.1007/BF01105296