Abstract
General representations are constructed for periodic solutions of the theories of elasticity and electroelasticity for a cylinder in R3. These solutions are utilized to reduce the first boundary value problem in an unbounded isotropic medium weakened by tunnel slit cavities to a system of singular integral equations. The solvability of the characteristic part of the obtained system is proved.
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References
D. Berlincour, D. Curran, and H. Jaffe, "Piezoelectric and piezomagnetic materials and their application in transducers," in Physical Acoustics, (W. Mason, ed.) [Russian translation], Vol. 1, Part A, Moscow (1966), pp. 204–326.
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Moscow (1968).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Moscow (1962).
A. S. Kosmodamianskii and V. A. Shaldyrvan, Thick Multiconnected Plates [in Russian], Kiev (1976).
V. T. Grinchenko, Equilibrium and Steady Vibrations of Finite Elastic Bodies [in Russian], Kiev (1978).
Additional information
Sumy. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 13–20, 1990.
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Fil'shtinskii, L.A. Periodic solutions of elasticity and electroelasticity theories for a cylinder in R3 . J Math Sci 68, 636–641 (1994). https://doi.org/10.1007/BF01249395
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DOI: https://doi.org/10.1007/BF01249395