Abstract
A homogeneous elastic isotropic space with a spherical cavity is considered. Unsteady axisymmetric body forces are exerted on this space. Disturbances are absent at the boundary of the cavity. Series expansions in Legendre polynomials and their derivatives as well as the Laplace time transform are used. The solution is represented in an integral form with kernels in the form of Green’s functions. The structure of these kernels is determined and their originals are found. Numerical results are discussed.
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References
A. G. Gorshkov and D. V. Tarlakovskiy, Unsteady Aeroelasticity of Bodies of Spherical Shape (Nauka, Moscow, 1990) [in Russian].
A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continuous Media (Fizmatlit, Moscow, 2004) [in Russian].
M. Abramowitz and I. A. Stegun (Eds.), Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972; Nauka, Moscow, 1979).
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Original Russian Text © V.A. Vestyak, D.V. Tarlakovskii, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 4, pp. 48–54.
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Vestyak, V.A., Tarlakovskii, D.V. Unsteady axisymmetric deformation of an elastic space with a spherical cavity under the action of body forces. Moscow Univ. Mech. Bull. 71, 87–92 (2016). https://doi.org/10.3103/S0027133016040038
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DOI: https://doi.org/10.3103/S0027133016040038