TY - JOUR
T1 - Laminated beams with thermoelasticity acting on the shear force
AU - Cabanillas Zannini, Victor R.
AU - Quispe Méndez, Teófanes
AU - Ramos, Anderson J.A.
N1 - Funding Information:
The third author was funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant No 310729/2019‐0). Funding information
Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.
PY - 2022/7/26
Y1 - 2022/7/26
N2 - In this paper, we study the stabilization of a laminated beam system under the action of a new thermal coupling. Motivated by the work of Almeida Júnior et al. in the context of the Timoshenko system, we consider a thermoelastic coupling acting on the shear force. The present work constitutes a generalization of Almeida Júnior's paper because our study model considers an interfacial slip. More precisely, if we make the parameter (Formula presented.) of our system go to infinity, we obtain the Timoshenko beam system studied by the authors. We show that the weakly dissipative system of our manuscript is exponentially stable if, and only if, the wave propagation speeds are equal. Otherwise, we show that the system is polynomially stable and that the associated semigroup decays with rate (Formula presented.). Furthermore, we show that this decay rate is optimal.
AB - In this paper, we study the stabilization of a laminated beam system under the action of a new thermal coupling. Motivated by the work of Almeida Júnior et al. in the context of the Timoshenko system, we consider a thermoelastic coupling acting on the shear force. The present work constitutes a generalization of Almeida Júnior's paper because our study model considers an interfacial slip. More precisely, if we make the parameter (Formula presented.) of our system go to infinity, we obtain the Timoshenko beam system studied by the authors. We show that the weakly dissipative system of our manuscript is exponentially stable if, and only if, the wave propagation speeds are equal. Otherwise, we show that the system is polynomially stable and that the associated semigroup decays with rate (Formula presented.). Furthermore, we show that this decay rate is optimal.
KW - exponential stability
KW - laminated beams
KW - linear thermoelasticity
KW - optimal decay
KW - polynomial stability
UR - https://hdl.handle.net/20.500.12724/17931
UR - http://www.scopus.com/inward/record.url?scp=85134766458&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/c63e76c4-54ad-3c97-90ec-9dcdb9d2931a/
U2 - 10.1002/mma.8584
DO - 10.1002/mma.8584
M3 - Artículo (Contribución a Revista)
AN - SCOPUS:85134766458
SN - 0170-4214
VL - 46
SP - 1352
EP - 1374
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 1
ER -