Stability analysis of laminated beams with Kelvin–Voigt damping and strong time delay

Article type: Research Article

Authors: Nonato, C.A.^a | Raposo, C.A.^a | Feng, B.^{b; *} | Ramos, A.J.A.^c

Affiliations: [a] Department of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil | [b] Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China | [c] Facult of Mathematics, Federal University of Pará, Salinópolis, Pará, Brazil

Correspondence: [*] Corresponding author. E-mail: bwfeng@swufe.edu.cn.

Abstract: In this paper we consider a model of laminated beams combining viscoelastic damping and strong time-delayed damping. The global well-posedness is proved by using the theory of semigroups of linear operators. We prove the lack of exponential stability when the speed wave propagations are not equal. In fact, we show in this situation, that the system goes to zero polynomially with rate t−1/2. On the other hand, by constructing some suitable multipliers, we establish that the energy decays exponentially provided the equal-speed wave propagations hold.

Keywords: Laminated beams, Kelvin–Voigt damping, strong delay, exponential decay, polynomial decay

DOI: 10.3233/ASY-221802

Journal: Asymptotic Analysis, vol. 132, no. 3-4, pp. 549-574, 2023