On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

Fatima Siham Djeradi; Fares Yazid; Svetlin G. Georgiev; Zayd Hajjej; Khaled Zennir; Fatima Siham Djeradi; Fares Yazid; Svetlin G. Georgiev; Zayd Hajjej; Khaled Zennir

doi:10.3934/math.20231330

AIMS Mathematics

2023, Volume 8, Issue 11: 26096-26114. doi: 10.3934/math.20231330

Previous Article Next Article

Research article Special Issues

On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

1.
Laboratory of Pure and Applied Mathematics, Amar Teledji University, Laghouat 03000, Algeria
2.
Department of Mathematics, Sorbonne University, Paris, France
3.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
4.
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401 Guelma 24000, Algeria

Received: 17 May 2023 Revised: 13 August 2023 Accepted: 20 August 2023 Published: 11 September 2023
MSC : 35B40, 35L56, 74F05, 93D15, 93D20

This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms.
- laminated beam,
- nonlinear damping,
- microtemperature effects,
- general decay,
- nonlinear weight,
- time-varying delay
Citation: Fatima Siham Djeradi, Fares Yazid, Svetlin G. Georgiev, Zayd Hajjej, Khaled Zennir. On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay[J]. AIMS Mathematics, 2023, 8(11): 26096-26114. doi: 10.3934/math.20231330

Related Papers:

Abstract

This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms.

References

[1]	H. Suh, Z. Bien, Use of time-delay actions in the controller design, IEEE Trans. Automat. Contr., 25 (1980), 600–603. https://doi.org/10.1109/TAC.1980.1102347 doi: 10.1109/TAC.1980.1102347
[2]	S. E. Mukiawa, C. D. Enyi, S. A. Messaoudi, Stability of thermoelastic Timoshenko beam with suspenders and time-varying feedback, Adv. Contin. Discret. Models, 2023 (2023), 7. https://doi.org/10.1186/s13662-023-03752-w doi: 10.1186/s13662-023-03752-w
[3]	J. M. Wang, G. Q. Xu, S. P. Yung, Exponential stabilization of laminated beams with structural damping and boundary feedback controls, SIAM J. Control Optim., 44 (2005), 1575–1597. https://doi.org/10.1137/040610003 doi: 10.1137/040610003
[4]	N. E. Tatar, Stabilization of a laminated beam with interfacial slip by boundary controls, Bound. Value Probl., 2015 (2015), 169. https://doi.org/10.1186/s13661-015-0432-3 doi: 10.1186/s13661-015-0432-3
[5]	H. E. Khochemane, Exponential stability for a thermoelastic porous system with microtemperature effects, Acta Appl. Math., 173 (2021), 8. https://doi.org/10.1007/s10440-021-00418-1 doi: 10.1007/s10440-021-00418-1
[6]	D. Fayssal, Well posedness and stability result for a thermoelastic laminated beam with structural damping, Ric. Mat., 2022.
[7]	A. Benaissa, A. Benaissa, S. A. Messaoudi, Global existence and energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks, J. Math. Phys., 53 (2012), 123514. https://doi.org/10.1063/1.4765046 doi: 10.1063/1.4765046
[8]	L. Djilali, A. Benaissa, A. Benaissa, Global existence and energy decay of solutions to a viscoelastic Timoshenko beam system with a nonlinear delay term, Appl. Anal., 95 (2016), 2637–2660. https://doi.org/10.1080/00036811.2015.1105961 doi: 10.1080/00036811.2015.1105961
[9]	K. Mpungu, T. A. Apalara, Asymptotic behavior of a laminated beam with nonlinear delay and nonlinear structural damping, Hacet. J. Math. Stat., 51 (2022), 1517–1534. https://doi.org/10.15672/hujms.947131 doi: 10.15672/hujms.947131
[10]	I. Lasiecka, D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Diff. Integ. Equ., 6 (1993), 507–533.
[11]	S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim., 45 (2006), 1561–1585. https://doi.org/10.1137/060648891 doi: 10.1137/060648891
[12]	T. A. Apalara, A. Soufyane, Energy decay for a weakly nonlinear damped porous system with a nonlinear delay, Appl. Anal., 101 (2022), 6113–6135. https://doi.org/10.1080/00036811.2021.1919642 doi: 10.1080/00036811.2021.1919642
[13]	V. I. Arnol'd, Mathematical methods of classical mechanics, New York: Springer, 1989.
[14]	A. Benaissa, M. Bahlil, Global existence and energy decay of solutions to a nonlinear Timoshenko beam system with a delay term, Taiwanese J. Math., 18 (2014), 1411–1437. https://doi.org/10.11650/tjm.18.2014.3586 doi: 10.11650/tjm.18.2014.3586
[15]	C. S. Zhu, X. Q. Fang, J. X. Liu, H. Y. Li, Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells, Eur. J. Mech. A-Solid., 66 (2017), 423–432. https://doi.org/10.1016/j.euromechsol.2017.08.001 doi: 10.1016/j.euromechsol.2017.08.001
[16]	J. Xie, Z. Zhang, The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients, Comput. Math. Appl., 75 (2018), 3558–3570. https://doi.org/10.1016/j.camwa.2018.02.017 doi: 10.1016/j.camwa.2018.02.017
[17]	J. Xie, X. Yan, M. Aamir Ali, Z. Hammouch, A linear decoupled physical-property-preserving difference method for fractional-order generalized Zakharov system, J. Comput. Appl. Math., 426 (2023), 115044. https://doi.org/10.1016/j.cam.2022.115044 doi: 10.1016/j.cam.2022.115044
[18]	X. Q. Fang, H. W. Ma, C. S. Zhu, Non-local multi-fields coupling response of a piezoelectric semiconductor nanofiber under shear force, Mech. Adv. Mater. Struc., 2023. https://doi.org/10.1080/15376494.2022.2158503 doi: 10.1080/15376494.2022.2158503

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)