In viscous materials systems, time and stress dependent instabilities often occur. The evolution of visco-elastic systems under external stress has already been modeled by applying matricial dynamic equations comprehending elasticity and viscosity matrices. In this study we report a novel formulation for such kind of systems as a nonlinear quadratic eigenvalue problem evolving from an already defined adjacency matrix. A four mass-spring damped system is presented as case study.
REFERENCES
1.
F.
Tisseur
and K.
Meerbergen
. The quadratic eigenvalue problem
. SIAM Review
, Vol. 43
, No. 2
, pp. 235
–286
, 2001
.2.
M. A.
Forjaz
, A.M.
Almeida
, T.
de Lacerda-Arôso
and J.
Pamplona
, Complementary Eigenvalue Problem in systems with frictional contact: the Stiffness Matrix for the contact nodes between different materials
, in Proceeding of the 14th International Conference on Computational Science and Its Applications (ICCSA 2014
), edited by A. M.
Rocha
. J. G.
Rocha
and M. I.
Falcão
(IEEE Computer Society, Guimarães
, Portugal
, 2014
), pp. 268
–271
.3.
Computer code MATLAB, v. 8.2.0.701 (R2013b)
. The MathWorks Inc
., Natick, Massachusetts
(2013
).4.
M. A.
Forjaz
, A.M.
Almeida
, T.
de Lacerda-Arôso
and J.
Pamplona
, Special matrices for visco-elastic systems
, In AIP Conference Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 (ICNAAM-2015
). Edited by Theodore E.
Simos
and Charalambos
Tsitouras.
5.
A. Pinto
da Costa
, I.
Figueiredo
, J. J.
Júdice
and J.
Martins
, A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact, in Complementarity: Applications, Algorithms and Extensions
, edited by M.C.
Ferris
, O.L.
Mangasarian
and J.S.
Pang
(Kluwer Academic Publishers
, Dordrecht
, 2001
), pp. 67
–83
.6.
Fernandes
, L.M.
, Júdice
, J.
, Sherali
, H.
, Fukushima
, Alfredo
Iusen
, On the symmetric quadractic eigenvalues complementarity problems
, Optimization Methods and Software
29
(2014
) 751
–770
.
This content is only available via PDF.
© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.