Geodesic
Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 43-53.

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In this paper, we apply the method of asymptotic splitting to dynamical problems of the spatial theory of elasticity, whose equations contain a small parameter, and obtain asymptotic solutions. Two-dimensional and one-dimensional boundary-value problems arising in the process of asymptotic splitting allow obtaining analytical solutions in some special cases. In the general case, they can be solved numerically by the collocation method, the method of least squares, and the finite-element method.
Keywords: spatial theory of elasticity, dynamical problem, method of asymptotic splitting, collocation method, method of least squares, finite element method, layered beam, free oscillations. 
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S. K. Golushko; G. L. Gorynin; A. G. Gorynin. Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 43-53. http://geodesic.mathdoc.fr/item/INTO_2020_188_a3/

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