Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator

Abstract

For the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The problem was approximated by the mesh scheme of the finite element method with Hermite finite elements. Theoretical error estimates for the approximate solutions were proved. The theoretical findings were verified by the results of numerical experiments.

Keywords

• eigenvibration
• shallow shell
• oscillator
• eigenvalue
• eigenvector
• eigenvalue problem
• finite element method
• hermite finite element