Abstract
Wave processes in an isotropic hollow cylinder located in an inhomogeneous prestress field are studied. The dispersion equation of the problem is investigated, and some features of the structure of the dispersion curves in relation to the type of prestressed state are identified. Formulas describing the behavior of the dispersion curves in the neighborhood of radial resonances are derived using the perturbation method.
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References
L. Pochhammer, “Über die Fortpflanzungsgeschwindigkeiten Kleiner Schwingungen in Einem Unbegrenzten Isotropen Kreiscylinder,” J. Reine angew. Math. 81, 324–336 (1876).
C. Chree, “Longitudinal Vibrations of a Circular Bar,” J. Quart. Pure Appl. Math. 21, 287–298 (1886).
A. N. Guz’, Elastic Waves in Bodies with Initial Stresse, Vol. 2 Propagation Patterns (Naukova Dumka, Kiev, 1986) [in Russian].
A. N. Guz’, F. G. Makhort, and O. I. Gushcha, Introduction to Acoustoelasticity (Naukova Dumka, Kiev, 1977) [in Russian].
A. I. Lur’e, Elastic Theory (Nauka, Moscow, 1970) [in Russian].
A. L. Uglov, V. I. Erofeev, and A. N. Smirnov, Acoustic Control of Equipment in Manufacture and Operation (Nauka, Moscow, 2009) [in Russian].
V. V. Kalinchuk and T. I. Belyankova, Dynamics of the Surface of Inhomogeneous Media (Fizmatlit, Moscow, 2009) [in Russian].
E. Trefftz, “Zur Theorie der Stabilität des Elastischen Gleichgewichts,” Z. Angew. Math. Mech. 12 (2), 160–165 (1933).
Z. P. Bazant, “A Correlation Study of Formulations of Incremental Deformation and Stability of Continuous Bodies,” J. Appl. Mech. 38, 919–928 (1971).
A. O. Vatul’yan and R. D. Nedin, “Models of Prestressed State and Principles of Its Identification,” in The Results of Science. South of Russia: Mathematical Forum, Vol. 8, Part 2: Research on Differential Equations, Mathematical Modeling, and Problems of Mathematical Education (South Mathematical Institute of the Vladikavkaz Scientific Center of RAS and the Government of the Republic of North Ossetia–Alania, Vladikavkaz, 2014), pp. 32–52.
I. I. Vorovich and V. A. Babeshko, Dynamic Mixed Elastic Problems for Nonclassical Regions (Nauka, Moscow, 1979) [in Russian].
V. T. Grinchenko and V. V. Meleshko, Harmonic Perturbations and Waves in Elastic Solids (Naukova Dumka, Kiev 1981) [in Russian].
A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 4, pp. 182–191, July–August, 2016.
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Vatul’yan, A.O., Yurov, V.O. Wave processes in a hollow cylinder in an inhomogeneous prestress field. J Appl Mech Tech Phy 57, 731–739 (2016). https://doi.org/10.1134/S0021894416040180
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DOI: https://doi.org/10.1134/S0021894416040180