RIESZ BASIS PROPERTY AND EXPONENTIAL STABILITY FOR A DAMPED SYSTEM AND CONTROLLED DYNAMICALLY
Keywords:
Euler-Bernoulli beam, variable coefficients, internal damping, Riesz basis, exponential stability.DOI:
https://doi.org/10.17654/0975045222005Abstract
This paper deals with exponential stability of a flexible Euler-Bernoulli beam with variable coefficients and internal damping. We begin by providing the well-posedness of problem in the sense of $C_0$ -semi-groups of contractions. Then, by making use of Naimark [7] and Wang et al. [11, 12] ideas, the spectral properties of the studied problem are established. This leads to the construction of a Riesz basis for the energy space and allows to show the exponential stability of the system. We conclude by showing that even when the internal damping is not of constant sign, the exponential stability of the system remains.
Received: August 4, 2022
Accepted: September 26, 2022
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