Geodesic
Nonstationary axisymmetric deformation of an elastic medium with a spherical cavity under the action of volume forces
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 48-54 
V. A. Vestyak; D. V. Tarlakovskii. Nonstationary axisymmetric deformation of an elastic medium with a spherical cavity under the action of volume forces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 48-54. http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a7/
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     author = {V. A. Vestyak and D. V. Tarlakovskii},
     title = {Nonstationary axisymmetric deformation of an elastic medium with a spherical cavity under the action of volume forces},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {48--54},
     year = {2016},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A homogeneous elastic isotropic space with a spherical cavity is considered. Unsteady asymmetric volume 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.

[1] Gorshkov A.G., Tarlakovskii D.V., Nestatsionarnaya aerogidrouprugost tel sfericheskoi formy, Nauka, Gl. red. fiz.-mat. lit., M., 1990

[2] Gorshkov A.G., Medvedskii A.L., Rabinskii L.N., Tarlakovskii D.V., Volny v sploshnykh sredakh, Ucheb. pos., Fizmatlit, M., 2004

[3] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR