NUMERICAL STUDY OF SPECTRUM FOR NON UNIFORM EULER-BERNOULLI BEAM WITH INDEFINITE DAMPING UNDER A FORCE CONTROL IN POSITION AND VELOCITY
Keywords:
beam equation, semigroup theory, asymptotic analysis, Riesz basis, exponential stability, finite difference methodDOI:
https://doi.org/10.17654/0975045224010Abstract
In this paper, we use asymptotic techniques and the finite difference method to study the spectrum of differential operator arising in exponential stabilization of non-uniform Euler-Bernoulli beam with indefinite damping that is clamped at one end and is free at the other. We build a numerical scheme and investigate the eigenvalues locus as a function of the positive feedback parameters $\alpha$, $\beta$ and the damping coefficient $\gamma$.
Received: May 3, 2024
Revised: June 13, 2024
Accepted: June 26, 2024
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