Geodesic
Spectral decompositions in dynamic linear viscoelasticity problems for piecewise homogeneous bodies
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 51-59

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The nonstationary dynamic viscoelasticity problem for a piecewise homogeneous body is considered. It is known that, under certain conditions, the construction of a solution to such a problem can be reduced to finding the eigenvalues of the free oscillation problem. The properties of a spectral set are considered and a method for searching for its elements is proposed. The theoretical considerations are used to study the unsteady dynamics of a piecewise homogeneous viscoelastic plane-parallel layer. For some specific parameters of this layer, the elements of the spectrum are found and, then, the transition wave process is studied. 
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     author = {S. G. Pshenichnov},
     title = {Spectral decompositions in dynamic linear viscoelasticity problems for piecewise homogeneous bodies},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {51--59},
     publisher = {mathdoc},
     number = {2},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2025_2_a7/}
}
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S. G. Pshenichnov. Spectral decompositions in dynamic linear viscoelasticity problems for piecewise homogeneous bodies. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 51-59. http://geodesic.mathdoc.fr/item/VMUMM_2025_2_a7/