Numerical approximation of the dissipativity of energy and spectrum for a damped Euler-Bernoulli beam with variable coefficients

Volume 16, Issue 3, pp 123--144 http://dx.doi.org/10.22436/jnsa.016.03.01

Publication Date: August 18, 2023 Submission Date: April 20, 2023 Revision Date: June 26, 2023 Accteptance Date: July 28, 2023

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Authors

B. G. Jean-Marc - Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees. Y. S. A. Joresse - Universite Nangui Abrogoua d’Abobo-Adjame and UFR Sciences Fondamentales et Appliquees, Cote d’Ivoire. T. K. Augustin - Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, Cote d’Ivoire.

Abstract

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.

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Keywords

• Beam equation
• viscous damping
• Galerkin approximation
• finite elements
• error estimates

MSC

•  35A15
•  35B35
•  35B45
•  37N30
•  35L20
•  65N30
•  74S05

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