TY - JOUR

T1 - Optimal polynomial stability for laminated beams with Kelvin–Voigt damping

AU - Cabanillas Zannini, Victor R.

AU - Quispe Méndez, Teófanes

AU - Sánchez Vargas, Juan

N1 - Funding Information:
There are no funders to report for this submission. The authors would like to thank the anonymous referees who provided valuable and detailed comments and suggestions that helped improve the manuscript's first version. We also thank Professor Sheila Gendrau for many fruitful discussions on the subject matter of this paper and her constant encouragement. There are no funders to report for this submission.
Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.

PY - 2022/4/24

Y1 - 2022/4/24

N2 - In this manuscript, we study the asymptotic behavior of two laminated beams systems formed by two identical layers of uniform thickness, whose surfaces are held together by an adhesive layer that allows interfacial sliding. We prove that when single Kelvin–Voigt damping acts on the transverse displacement equation, the system is not exponentially stable. When the system has two frictional dampings, one working on the transverse displacement and the other on the interface, the system is exponentially stable as long as the wave propagation speeds are equal. Then, one could think that if we replace the frictional damping (weak damping), acting on the transverse displacement, with Kelvin–Voigt damping (strong damping), the system should also be exponentially stable, at least when the wave speeds are equal. However, as we show in this work, Kelvin–Voigt damping causes the loss of exponential stability of the system, even when the system's waves' propagation speeds coincide. Therefore, we are in a situation where the weak damping (frictional) is stronger than the strong damping (Kelvin–Voigt). Due to these results of lack of exponential decay, we study the polynomial stability of each of these two systems by obtaining an optimal decay rate in each case.

AB - In this manuscript, we study the asymptotic behavior of two laminated beams systems formed by two identical layers of uniform thickness, whose surfaces are held together by an adhesive layer that allows interfacial sliding. We prove that when single Kelvin–Voigt damping acts on the transverse displacement equation, the system is not exponentially stable. When the system has two frictional dampings, one working on the transverse displacement and the other on the interface, the system is exponentially stable as long as the wave propagation speeds are equal. Then, one could think that if we replace the frictional damping (weak damping), acting on the transverse displacement, with Kelvin–Voigt damping (strong damping), the system should also be exponentially stable, at least when the wave speeds are equal. However, as we show in this work, Kelvin–Voigt damping causes the loss of exponential stability of the system, even when the system's waves' propagation speeds coincide. Therefore, we are in a situation where the weak damping (frictional) is stronger than the strong damping (Kelvin–Voigt). Due to these results of lack of exponential decay, we study the polynomial stability of each of these two systems by obtaining an optimal decay rate in each case.

KW - exponential stability

KW - frictional damping

KW - Kelvin–Voigt damping

KW - laminated beams

KW - polynomial stability

UR - http://www.scopus.com/inward/record.url?scp=85128753731&partnerID=8YFLogxK

U2 - 10.1002/mma.8324

DO - 10.1002/mma.8324

M3 - Artículo (Contribución a Revista)

AN - SCOPUS:85128753731

SN - 0170-4214

VL - 45

SP - 9578

EP - 9601

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -