Analytical solution for dynamic transverse vibrations of non-uniform beams on the variable foundations
Nurakhmetov D.
1 January 2026Walter de Gruyter GmbH
Open Mathematics
2026#24Issue 1
We demonstrate an analytical solution for the dynamic transversal vibrations of non-uniform beams on variable foundations. The exact expressions of eigenvalues and eigenfunctions are derived. The proposed dynamic model of the non-uniform beam with clamped conditions reduces to the dynamic model of the uniform beam with the same boundary conditions. It is shown that this reduction is associated with the isospectral properties of a non-uniform beam with clamped-clamped ends. The analytical solution is used to study the behavior of the beam. The analytical results obtained are illustrated by numerical examples.
eigenvalue , Euler-Bernoullis theory , explicit solutions , non-uniform beam
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Pedagogical Institute, Astana International University, Astana, 01000, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Pedagogical Institute
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