Abstract
The vibrational problem is considered for a long hollow viscoelastic cylinder with a variable internal boundary, this being enclosed in an elastic shell. An asymptotic method based on averaging is used to find the resonant vibrations in response to a small uniformly distributed internal pressure that varies periodically with time. The calculation is carried through to quadrature working formulas.
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Literature cited
A. A. Il'yushin and B. E. Pobedrya, Principles of Mathematical Theory of Thermoviscoelasticity [in Russian], Moscow (1970).
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V. M. Volosov and B. I. Morgunov, The Averaging Method in the Theory of Nonlinear Vibrational Systems [in Russian], Moscow (1971).
Additional information
Moscow Institute of Electric Machine Construction. Translated from Mekhanika Polimerov, No. 5, pp. 935–939, September–October, 1973.
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Morgunov, B.I. An asymptotic calculation of the vibrations of a viscoelastic cylinder with a slowly varying internal boundary. Polymer Mechanics 9, 828–831 (1973). https://doi.org/10.1007/BF00856289
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DOI: https://doi.org/10.1007/BF00856289