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Bulletin of the Abai KazNPU, the 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
Zh Kaiyrbek+− G. Auzerkhan+− L.K Zhapsarbaeva+−
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.

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Keywords
Cantilever Euler beam swelling pressure beam equation self-adjoint operator eigenvalues eigenfunctions two-sided estimates
How to Cite

[1]
Қайырбек, Ж., Аузерхан, Г. and Жапсарбаева, Л. 2020. ESTIMATES OF THE EIGENVALUES AND EIGENFUNCTIONS OF OPERATOR ARISING IN SWELLING PRESSURE MODEL. Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences". 71, 3 (Sep. 2020), 59–66. DOI:https://doi.org/10.51889/2020-3.1728-7901.08.