Approaching an Overdamped System as a Quadratic Eigenvalue Problem

Authors

Maria Antonia Forjaz, Centro de Matema´tica (CMAT), Universidade do Minho. Departamento de Matema´tica e Aplicac¸o?es, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. Braga, Portugal.Follow
Antonio Mario Almeida, Centro de F´ısica (CFUM), Universidade do Minho. Departamento de F´ısica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. Braga, Portugal.Follow
Luıs M. Fernandes, Instituto Polite´cnico de Tomar e Instituto de Telecomunicac¸o?es, Coimbra, PortugalFollow
Jorge Pamplona, Instituto de Cieˆncias da Terra (ICT) Po´lo da Universidade do Minho. Departamento de Cieˆncias da Terra, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal.Follow
T. de Lacerda–Aroso, Centro de F´ısica (CFUM), Universidade do Minho. Departamento de F´ısica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. Braga, Portugal.Follow

Author Country (or Countries)

Portugal.

Abstract

In viscous material systems, time and stress dependent instabilities often occur. The evolution of visco-elastic systems under external stress has already been modeled by applying a matricial dynamics equation comprehending elasticity and viscosity matrices. In this study we report a novel formulation for such kind of systems in an overdamped regime as a nonlinear quadratic eigenvalue problem. The results presented were obtained after solving the eigenvalue equation of several sets of discrete damped mass-spring systems.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110402

Recommended Citation

Antonia Forjaz, Maria; Mario Almeida, Antonio; M. Fernandes, Luıs; Pamplona, Jorge; and de Lacerda–Aroso, T. (2017) "Approaching an Overdamped System as a Quadratic Eigenvalue Problem," Applied Mathematics & Information Sciences: Vol. 11: Iss. 4, Article 2.
DOI: http://dx.doi.org/10.18576/amis/110402
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss4/2