TY - JOUR

T1 - Method of Asymptotic Splitting in Dynamical Problems of the Spatial Theory of Elasticity

AU - Golushko, S. K.

AU - Gorynin, G. L.

AU - Gorynin, A. G.

PY - 2025/2/26

Y1 - 2025/2/26

N2 - 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 of least squares and the finite-element method.

AB - 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 of least squares and the finite-element method.

KW - 35Q74

KW - 74H10

KW - collocation method

KW - dynamical problem

KW - finite element method

KW - free oscillations

KW - layered beam

KW - method of asymptotic splitting

KW - method of least squares

KW - spatial theory of elasticity

UR - https://www.mendeley.com/catalogue/4fb40fdf-04a6-3a3e-8435-4299f69d8b5c/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85218805068&origin=inward&txGid=b22a61ae16c3aada8c56c1adfef19e0a

U2 - 10.1007/s10958-025-07645-z

DO - 10.1007/s10958-025-07645-z

M3 - Article

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

ER -