Geodesic
Mechanical oscillators with dampers defined by implicit constitutive relations
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 51-61.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples to the uniqueness when these conditions are not met.
DOI : 10.14712/1213-7243.2015.143
Classification : 34A09, 34K32, 70F40
Keywords: lumped parameter systems; differential-algebraic equations; Coulomb's friction; uniqueness of solutions 
@article{10_14712_1213_7243_2015_143,
     author = {Pra\v{z}\'ak, Dalibor and Rajagopal, Kumbakonam R.},
     title = {Mechanical oscillators with dampers defined by implicit constitutive relations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {51--61},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2016},
     doi = {10.14712/1213-7243.2015.143},
     mrnumber = {3478338},
     zbl = {06562195},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.143/}
}
TY  - JOUR
AU  - Pražák, Dalibor
AU  - Rajagopal, Kumbakonam R.
TI  - Mechanical oscillators with dampers defined by implicit constitutive relations
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2016
SP  - 51
EP  - 61
VL  - 57
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.143/
DO  - 10.14712/1213-7243.2015.143
LA  - en
ID  - 10_14712_1213_7243_2015_143
ER  - 
%0 Journal Article
%A Pražák, Dalibor
%A Rajagopal, Kumbakonam R.
%T Mechanical oscillators with dampers defined by implicit constitutive relations
%J Commentationes Mathematicae Universitatis Carolinae
%D 2016
%P 51-61
%V 57
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.143/
%R 10.14712/1213-7243.2015.143
%G en
%F 10_14712_1213_7243_2015_143
Pražák, Dalibor; Rajagopal, Kumbakonam R. Mechanical oscillators with dampers defined by implicit constitutive relations. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 51-61. doi : 10.14712/1213-7243.2015.143. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.143/

Cité par Sources :