Geodesic
Numerical approximation of the dissipativity of energy and spectrum for a damped Euler-Bernoulli beam with variable coefficients
Jean-Marc, B. G. 1 ; Joresse, Y. S. A. 2 ; Augustin, T. K.3
1 Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees
2 Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees, Cote d’Ivoire
3 Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, Cote d’Ivoire
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 3, p. 123-144.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This article concerns the numerical study of the behaviour of a flexible beam of Euler-Bernoulli to which one adds to its internal composition a damping of the viscous type. This damping naturally exerts a dissipative force (or viscous damping force) on the beam and opposes any deformation, in proportion to the rate of deformation. We are therefore interested in the impact of the damper on the exponential stability of the beam. We develop here a numerical method which faithfully reproduces the theoretical results obtained by several authors. Simulations are provided to illustrate our results.
DOI : 10.22436/jnsa.016.03.01
Classification : 35A15, 35B35, 35B45, 37N30, 35L20, 65N30, 74S05
Keywords: Beam equation, viscous damping, Galerkin approximation, finite elements, error estimates

Jean-Marc, B. G.  1 ; Joresse, Y. S. A.  2 ; Augustin, T. K. 3

1 Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees
2 Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees, Cote d’Ivoire
3 Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, Cote d’Ivoire 
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     title = {Numerical approximation of the dissipativity of energy and spectrum for a damped {Euler-Bernoulli} beam with variable coefficients},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {123-144},
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Jean-Marc, B. G. ; Joresse, Y. S. A. ; Augustin, T. K. Numerical approximation of the dissipativity of energy and spectrum for a damped Euler-Bernoulli beam with variable coefficients. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 3, p. 123-144. doi : 10.22436/jnsa.016.03.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.03.01/

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