Mathematical modeling of the eigenvibrations for the loaded shallow shell

Abstract

The eigenvalue problems modeling of the eigenvibrations of the loaded shallow shell are studied. The asymptotic properties of the eigenvalues and eigenvectors are investigated in dependence on the load parameters. The original problem is approximated by the finite element method with Bogner-Fox-Schmit finite elements in the square domain. The new efficient algorithms for solving finite element eigenvalue problems are developed and investigated. A classification of resonance curves for one-dimensional and two-dimensional loaded mechanical systems is given. The results of numerical experiments are presented.

Keywords

• shallow shell
• eigenvibration
• load
• eigenvalue
• eigenvector
• eigenvalue problem
• finite element method
• bogner-fox-schmit finite element