Relative perturbation theory for matrix eigenproblems in free vibration analysis

Abstract

This article aims to introduce a relative perturbation theory for eigenvalues of the standard and generalized eigenproblems in free vibration analysis. This theory shows that the results of the standard eigenproblems can be applied to find a similar bounds for the eigenvalues of the generalized eigenproblems when the perturbation happens in either the mass matrix or in the stiffness matrix. Numerical examples are given to illustrate the effect of the perturbation in these bounds.

^†On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

Keywords:

• Generalized eigenproblems
• Relative perturbation

Notes

^†On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.