NUMERICAL APPROXIMATION OF SPECTRUM FOR
VARIABLE COEFFICIENTS EULER-BERNOULLI BEAMS
UNDER A FORCE CONTROL IN POSITION AND VELOCITY
Kouassi Ayo Ayébié Hermith1, Coulibaly Adama2,
Touré Kidjégbo Augustin3
1Université Félix Houphouët Boigny
Yamoussoukro, BP 2444, CÔTE D'IVOIRE
2Université Félix Houphouët Boigny
BP 582, Abidjan 22, CÔTE D'IVOIRE
3Institut National Polytechnique Houphouët-Boigny
Yamoussoukro, BP 2444, CÔTE D'IVOIRE

Abstract

In this paper, we use asymptotic techniques and the finite differences method to study the spectrum of differential operator arising in exponential stabilization of Euler-Bernoulli beam with nonuniform thickness or density that is clamped at one end and is free at the other. To stabilize the system, we apply at the free end, the following shear force feedback control:

\begin{displaymath} \left( EI\left( \cdot\right) u_{xx}\left( \cdot,t\right) \r... ...a u\left( 1,t\right) +\beta u_{t}\left( 1,t\right) ,\ \ t>0. \end{displaymath}

We build a numerical scheme and investigate the eigenvalues locus as a function of the positive feedback parameters $\alpha$ and $\beta$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 3
Year: 2017

DOI: 10.12732/ijam.v30i3.1

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