Approximation of the Problem on Eigenvibrations of a String with Attached Load.

Autor: Korosteleva, D. M., Koronova, L. N., Samsonov, A. A., Solov'ev, S. I.
Zdroj: Lobachevskii Journal of Mathematics; Apr2022, Vol. 43 Issue 4, p996-1005, 10p
Abstrakt: The second-order ordinary differential eigenvalue problem governing eigenvibrations of a string with fixed ends and rigidly attached load at interior point is investigated. This problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a complete orthonormal system of eigenfunctions. We introduce limit differential eigenvalue problems and derive the convergence of the eigenvalues and eigenfunctions of the initial problem to the corresponding eigenvalues and eigenfunctions of the limit problems as a load mass tending to infinity. The original differential eigenvalue problem is approximated by the finite element method on a non-uniform mesh. Error estimates for approximate eigenvalues and eigenfunctions are established. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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