Seyyed Abbas Mohammadi, Heinrich Voss
On the distribution of real eigenvalues in linear viscoelastic oscillators

Type           : PREPRINT

MSC : 35P30 Nonlinear eigenvalue problems, nonlinear spectral theory for PDO 49R05 Variational approach to eigenvalues
Language : ENGLISH

Format : application/pdf

Upload : 10/01/2017
Abstract:
In this paper a linear viscoelastic system is considered where the viscoelastic force depends on the past history of motion via convolution integral over exponentially decaying kernel function. The free-motion equation of this nonviscous system yields a nonlinear eigenvalue problem where it has a certain number of real eigenvalues corresponding to the non-oscillatory nature. The quality of the current numerical methods for deriving those eigenvalues is directly related with damping properties of the viscoelastic system. The main contribution of this paper is to explore the structure of the set of nonviscous eigenvalues of the system while the damping coefficient matrices are rank deficient and the damping level is changing.

Keywords:
Viscoelastic oscillators, nonviscous eigenvalues, damping properties, variational characterization, nonlinear eigenvalue problems