Optimal stability for laminated beams with Kelvin–Voigt damping and Fourier’s law

Article type: Research Article

Authors: Cabanillas Zannini, Victor^{a; b; *} | Quispe Méndez, Teófanes^b | Ramos, A.J.A.^c

Affiliations: [a] Universidad de Lima, Programa de Estudios Generales, Lima, Perú | [b] Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas, Lima, Perú | [c] Faculty of Mathematics, Federal University of Pará, Salinópolis–PA, Brazil

Correspondence: [*] Corresponding author. E-mail: vcabanil@ulima.edu.pe.

Abstract: This article deals with the asymptotic behavior of a mathematical model for laminated beams with Kelvin–Voigt dissipation acting on the equations of transverse displacement and dimensionless slip. We prove that the evolution semigroup is exponentially stable if the damping is effective in the two equations of the model. Otherwise, we prove that the semigroup is polynomially stable and find the optimal decay rate when damping is effective only in the slip equation. Our stability approach is based on the Gearhart–Prüss–Huang Theorem, which characterizes exponential stability, while the polynomial decay rate is obtained using the Borichev and Tomilov Theorem.

Keywords: Laminated beam, Kelvin–Voigt damping, exponential stability, polynomial stability

DOI: 10.3233/ASY-231883

Journal: Asymptotic Analysis, vol. 137, no. 1-2, pp. 123-151, 2024