Exponential stability of a laminated beam system with thermoelasticity of type III and distributed delay

References

• M.S. Alves and R.N. Monteiro, Exponential stability of laminated Timoshenko beams with boundary/internal controls, J. Math. Anal. Appl. 482(1) (2020), 123516. doi: 10.1016/j.jmaa.2019.123516
   Web of Science ®Google Scholar
• T. Apalara, Exponential stability of laminated beams with interfacial slip, Mechanics of Solids 56(1) (2021), 131–137. doi: 10.3103/S0025654421010039
   Web of Science ®Google Scholar
• T. Apalara, Uniform stability of a laminated beam with structural damping and second sound, Z. Angew. Math. Phys. 68(2) (2017), 41. doi: 10.1007/s00033-017-0784-x
   Web of Science ®Google Scholar
• T. Apalara, On the stability of a thermoelastic laminated beam, Acta Math. Sci. 39(6) (2019), 1517–1524. doi: 10.1007/s10473-019-0604-9
   Web of Science ®Google Scholar
• T.A. Apalara, A.O. Ige, C.D. Enyi, and M.E. Omaba, Uniform stability result of laminated beams with thermoelasticity of type III, AIMS Mathematics 8(1) (2023), 1090–1101. doi: 10.3934/math.2023054
   Web of Science ®Google Scholar
• T.A. Apalara, A.M. Nass, and H. Al Sulaimani, On a laminated Timoshenko beam with nonlinear structural damping, Math. Comput. Appl. 25(2) (2020), 35.
   Web of Science ®Google Scholar
• T.A. Apalara, C.A. Raposo, and C.A. Nonato, Exponential stability for laminated beams with a frictional damping, Arch. Math. (Basel) 114(4) (2020), 471–480. doi: 10.1007/s00013-019-01427-1
   Web of Science ®Google Scholar
• Z. Chen, W. Liu, and D. Chen, General decay rates for a laminated beam with memory, Taiwan. J. Math. 23(5) (2019), 1227–1252. doi: 10.11650/tjm/181109
   Web of Science ®Google Scholar
• A. Choucha, D. Ouchenane, and S. Boulaaras, Well posedness and stability result for a thermoelastic laminated timoshenko beam with distributed delay term, Math. Methods Appl. Sci. 43(17) (2020), 9983–10004. doi: 10.1002/mma.6673
   Web of Science ®Google Scholar
• D. Fayssal and T.A. Apalara, General decay for laminated beams with structural memory and modified thermoelasticity of type III, Ann. Univ. Ferrara Sez. VII Sci. Mat. (2022), 1–20. doi: 10.1007/s11565-022-00451-4
   Google Scholar
• B. Feng, Well-posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks, Math. Methods Appl. Sci. 41(3) (2018), 1162–1174. doi: 10.1002/mma.4655
   Web of Science ®Google Scholar
• B. Feng, On a thermoelastic laminated Timoshenko beam: Well posedness and stability, Complexity 2020 (2020), Art. 5139419. doi: 10.1155/2020/5139419
   Web of Science ®Google Scholar
• A.E. Green and P.M. Naghdi, A re-examination of the basic postulates of thermomechanics, Proc. R. Soc. Lond. Ser. A 432(1885) (1991), 171–194. doi: 10.1098/rspa.1991.0012
   Web of Science ®Google Scholar
• A.E. Green and P.M. Naghdi, On undamped heat waves in an elastic solid, J. Therm. Stresses 15(2) (1992), 253–264. doi: 10.1080/01495739208946136
   Web of Science ®Google Scholar
• A.E. Green and P.M. Naghdi, Thermoelasticity without energy dissipation, J. Elasticity 31(3) (1993), 189–208. doi: 10.1007/BF00044969
   Web of Science ®Google Scholar
• S.W. Hansen and R.D. Spies, Structural damping in laminated beams due to interfacial slip. J. Sound Vib. 204(2) (1997), 183–202. doi: 10.1006/jsvi.1996.0913
   Web of Science ®Google Scholar
• M. Kafini, S.A. Messaoudi, and M.I. Mustafa, Energy decay result in a Timoshenko-type system of thermoelasticity of type III with distributive delay, J. Math. Phys. 54(10) (2013), 101503. doi: 10.1063/1.4826102
   Web of Science ®Google Scholar
• G. Li, X. Kong, and W. Liu, General decay for a laminated beam with structural damping and memory: The case of non-equal wave speeds, J. Integral Equ. Appl. 30(1) (2018), 95–116. doi: 10.1216/JIE-2018-30-1-95
   Web of Science ®Google Scholar
• W. Liu, X. Kong, and G. Li, Asymptotic stability for a laminated beam with structural damping and infinite memory, Math. Mech. Solids 25(10) (2020), 1979–2004. doi: 10.1177/1081286520917440
   Web of Science ®Google Scholar
• W. Liu, Y. Luan, Y. Liu, and G. Li, Well-posedness and asymptotic stability to a laminated beam in thermoelasticity of type III, Math. Meth. Appl. Sci. 43(6) (2020), 3148–3166. doi: 10.1002/mma.6108
   Web of Science ®Google Scholar
• W. Liu and W. Zhao, Stabilization of a thermoelastic laminated beam with past history, Appl. Math. Optim. 80(1) (2019), 103–133. doi: 10.1007/s00245-017-9460-y
   Web of Science ®Google Scholar
• A. Lo and N.E. Tatar, Stabilization of laminated beams with interfacial slip, Electron. J. Diff. Equ. 2015(129) (2015), 1–14.
   Google Scholar
• K. Mpungu and T.A. Apalara, Exponential stability of laminated beam with constant delay feedback, Math. Model. Anal. 26(4) (2021), 566–581. doi: 10.3846/mma.2021.13759
   Web of Science ®Google Scholar
• K. Mpungu and T.A. Apalara, Stability result of laminated beam with internal distributed delay, J. Math. Inequal. 15(3) (2021), 1075–1091. doi: 10.7153/jmi-2021-15-73
   Web of Science ®Google Scholar
• K. Mpungu and T.A. Apalara, Exponential stability of laminated beam with neutral delay, Afr. Mat. 33(2) (2022), 1–12. doi: 10.1007/s13370-022-00965-2
   Web of Science ®Google Scholar
• K. Mpungu, T.A. Apalara, and M. Muminov, On the stabilization of laminated beams with delay, Appl. Math. 66(5) (2021), 789–812. doi: 10.21136/AM.2021.0056-20
   Web of Science ®Google Scholar
• S.E. Mukiawa, T.A. Apalara, and S.A. Messaoudi, A stability result for a memory-type Laminated-thermoelastic system with Maxwell–Cattaneo heat conduction, J. Therm. Stresses 43(11) (2020), 1437–1466. doi: 10.1080/01495739.2020.1785979
   Web of Science ®Google Scholar
• S.E. Mukiawa, T.A. Apalara, and S.A. Messaoudi, Stability rate of a thermoelastic laminated beam: case of equalwave speed and nonequal-wave speed of propagation, AIMS Math. 6(1) (2021), 333–361. doi: 10.3934/math.2021021
   Web of Science ®Google Scholar
• M.I. Mustafa, Boundary control of laminated beams with interfacial slip, J. Math. Phys. 59(5) (2018), 051508. doi: 10.1063/1.5017923
   Web of Science ®Google Scholar
• M.I. Mustafa, Laminated Timoshenko beams with viscoelastic damping, J. Math. Anal. Appl. 466(1) (2018), 619–641. doi: 10.1016/j.jmaa.2018.06.016
   Web of Science ®Google Scholar
• S. Nicaise and 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(5) (2006), 1561–1585. doi: 10.1137/060648891
   Web of Science ®Google Scholar
• J.G. Nie and C.S. Cai, Steel–concrete composite beams considering shear slip effects, J. Struct. Eng. 129(4) (2003), 495–506. doi: 10.1061/(ASCE)0733-9445(2003)129:4(495)
   Web of Science ®Google Scholar
• C.A. Raposo, Exponential stability for a structure with interfacial slip and frictional damping, Appl. Math. Lett. 53 (2016), 85–91. doi: 10.1016/j.aml.2015.10.005
   Web of Science ®Google Scholar
• A.S. Ribeiro, A.M. de Jesus, A.M. Lima, and J.L. Lousada, Study of strengthening solutions for glued-laminated wood beams of maritime pine wood, Constr Build Mater. 23(8) (2009), 2738–2745. doi: 10.1016/j.conbuildmat.2009.02.042
   Web of Science ®Google Scholar
• S.H. Schulze, M. Pander, K. Naumenko, and H. Altenbach, Analysis of laminated glass beams for photovoltaic applications, Int. J. Solids Struct. 49(15–16) (2012), 2027–2036. doi: 10.1016/j.ijsolstr.2012.03.028
   Web of Science ®Google Scholar
• L. Seghour, N.E. Tatar, and A. Berkani, Stability of a thermoelastic laminated system subject to a neutral delay, Math. Methods Appl. Sci. 43(1) (2020), 281–304. doi: 10.1002/mma.5878
   Web of Science ®Google Scholar
• H. Suh and Z. Bien, Use of time-delay actions in the controller design, IEEE Trans. Autom. Control 25(3) (1980), 600–603. doi: 10.1109/TAC.1980.1102347
   Web of Science ®Google Scholar
• N.E. Tatar, Stabilization of a laminated beam with interfacial slip by boundary controls, Bound. Value Probl. 2015(1) (2015), 169. doi: 10.1186/s13661-015-0432-3
   Google Scholar
• J.M. Wang, G.Q. Xu, and S.P. Yung, Exponential stabilization of laminated beams with structural damping and boundary feedback controls, SIAM J. Control Optim. 44(5) (2005), 1575–1597. doi: 10.1137/040610003
   Web of Science ®Google Scholar
• P. Wu, D. Zhou, and W. Liu, 2-d elasticity solution of layered composite beams with viscoelastic interlayers, Mech. Time-Depend. Mat. 20(1) (2016), 65–84. doi: 10.1007/s11043-015-9284-6
   Web of Science ®Google Scholar
• C. Zener, Internal friction in solids II. General theory of thermoelastic internal friction, Phys. Rev. 53(1) (1938), 90. doi: 10.1103/PhysRev.53.90
   Google Scholar