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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences
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Vol. 71 No. 3 (2020)

ESTIMATES OF THE EIGENVALUES AND EIGENFUNCTIONS OF OPERATOR ARISING IN SWELLING PRESSURE MODEL

Published September 2020

131

131

Zh Kaiyrbek+−
Al Farabi Kazakh National University, Almaty
G. Auzerkhan+−
Al Farabi Kazakh National University, Almaty,
L.K Zhapsarbaeva+−
Al Farabi Kazakh National University, Almaty,
Al Farabi Kazakh National University, Almaty
Al Farabi Kazakh National University, Almaty,
Al Farabi Kazakh National University, Almaty,
DOI: 10.51889/2020-3.1728-7901.08
Abstract

Swelling forces from materials confined by structures can cause structural deformations and instability. Due to the
complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining
structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic initial/boundary value
problem based on the Euler-elastic beam theory and some swelling force model. In this paper, we study a nonlinear
problem for the equation of a beam. The self-adjointness of the operator corresponding to the nonlinear problem for the
Euler equations is proved. Two-sided estimates of the eigenvalues of the operator in question are established. Two-sided
estimates of the eigenfunctions of the operator of the initial-boundary value problem for the beam equation are also
obtained.

.pdf (Қазақ)
Keywords
Cantilever Euler beam swelling pressure beam equation self-adjoint operator eigenvalues eigenfunctions two-sided estimates
Language

Қазақ

How to Cite

[1]
Kaiyrbek Ж., Auzerkhan Г. and Zhapsarbaeva Л. 2020. ESTIMATES OF THE EIGENVALUES AND EIGENFUNCTIONS OF OPERATOR ARISING IN SWELLING PRESSURE MODEL. Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 71, 3 (Sep. 2020), 59–66. DOI:https://doi.org/10.51889/2020-3.1728-7901.08.