Аннотация
Abstract 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.