リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「LAMINATED BEAMS WITH TIME-VARYING DELAY」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

LAMINATED BEAMS WITH TIME-VARYING DELAY

Raposo, Carlos A. 大阪大学 DOI:10.18910/84958

2021.10

概要

This manuscript is concerned with long-time dynamics for a laminated beam which consists of two identical layers of uniform thickness, taking into account that an adhesive of small thickness is bonding the two surfaces thereby producing an interfacial slip. Using the variable norm technique of Kato, we prove the global well-posedness of solutions. For asymptotic behavior, we apply the Energy Method. Assuming the control through a time-varying delay just on the transverse displacement of the beam, we establish the exponential decay of energy to the system by using an appropriate Lyapunov functional.

参考文献

[1] F. Alabau-Boussouira: Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control, NoDEA Nonlinear Differential Equations Appl. 14 (2007), 643–669.

[2] F. Amar-Khodja, A. Benabdallah, J.E. Munoz Rivera and R. Racke: ˜ Energy decay for Timoshenko systems of memory type, J. Differential Equations 194 (2003), 82–115.

[3] T.A. Apalara: Uniform decay in weakly dissipative Timoshenko system with internal distributed delay feedbacks, Acta Math. Sci. 36 (2016), 815–830.

[4] T.A. Apalara, C.A. Raposo and C.A.S. Nonato: Exponential stability for laminated beams with a frictional damping, Arch. Math. (Basel) 114 (2020), 471–480.

[5] V. Barros, C. Nonato and C. Raposo: Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights, Electron. Res. Arch. 28 (2020), 205–220.

[6] X,G. Cao, D.Y. Liu and G.Q. Xu: Easy test for stability of laminated beams with structural damping and boundary feedback controls, J. Dyn. Control Syst. 13 (2007), 313–336.

[7] R. Datko, J. Lagnese and M.P. Polis: An example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim. 24 (1986), 152–156.

[8] B. Feng: Well-posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks, Math. Methods Appl. Sci. 41 (2018), 1162–1174.

[9] D.X. Feng, D.H. Shi and W. Zhang: Boundary feedback stabilization of Timoshenko beam with boundary dissipation, Sci. China Ser. A-Math. 41 (1998), 483–490.

[10] A. Guesmia and S.A. Messaoudi: General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping, Math. Methods Appl. Sci. 32 (2009), 2102–2122.

[11] A. Guesmia: Some well-posedness and general stability results in Timoshenko systems with infinite memory and distributed time delay, J. Math. Phys. 55 (2014), 081503, 40pp.

[12] S.W. Hansen: A model for a two-layered plate with interfacial slip; in Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena, International Series of Numerical Analysis 118, Birkhauser ¨ Cerlag, Basel, 1994, 143–170.

[13] S.W. Hansen and R. Spies: Structural damping in a laminated beams due to interfacial slip, J. Sound Vibration 204 (1997), 183–202.

[14] Z.J. Han and G.Q. Xu: Exponential stability of timoshenko beam system with delay terms in boundary feedbacks, ESAIM Control Optim. Calc. Var. 17 (2011), 552–574.

[15] T. Kato: Linear and quasilinear equations of evolution of hyperbolic type; in Hyperbolisity, C.I.M.E. Summer Schools, 72, Springer, Berlin-Heidelberg, 2011, 125–191.

[16] M. Kirane, B. Said-Houari and M.N. Anwar: Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks, Commun. Pure Appl. Anal. 10 (2011), 667–686.

[17] V. Komornik: Exact Controllability and Stabilization, The Multiplier Method, Masson-John Wiley, Paris, 1994.

[18] J.U. Kim and Y. Renardy: Boundary control of the Timoshenko beam, SIAM J. Control Optim. 25 (1987), 1417–1429.

[19] Y. Laskri and B. Said-Houari: A stability result of a Timoshenko system with a delay term in the internal feedback, Appl. Math. Comput. 217 (2010), 2857–2869.

[20] A, Lo and N.E. Tatar: Stabilization of laminated beams with interfacial slip, Electron. J. Differential Equations 2015, No. 129, 14pp.

[21] A. Lo and N.E. Tatar: Exponential stabilization of a structure with interfacial slip, Discrete Contin. Dyn. Syst. 36 (2016), 6285–6306.

[22] G. Li, D. Wang and B. Zhu: Well-posedness and decay of solutions for a transmission problem with history and delay, Electron. J. Differential Equations 2016, No. 23, 21pp.

[23] S.A. Messaoudi and M.I. Mustafa: On the stabilization of the Timoshenko system by a weak nonlinear dissipation, Math. Methods Appl. Sci. 32 (2009), 454–469.

[24] J.E. Munoz Rivera and R. Racke: ˜ Global stability for damped Timoshenko systems, Discrete Contin. Dyn. Syst. 9 (2003), 1625–1639.

[25] J.E. Munoz Rivera and H.D.F. Sare: ˜ Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (2008), 482–502.

[26] S. Nicaise, C. Pignotti and J. Valein: Exponential stability of the wave equation with boundary time-varying delay, Discrete Contin. Dyn. Syst. Ser. S 4 (2011), 693–722.

[27] S. Nicaise and C. Pignotti: Stabilization of the wave equation with boundary or internal distributed delay, Differential Integral Equations 21 (2008), 935–958.

[28] S. Nicaise, J. Valein and E. Fridman: Stability of the heat and of the wave equations with boundary timevarying delays, Discrete Contin. Dyn. Syst. Ser. S 2 (2009), 559–581.

[29] C.A. Raposo, H. Nguyen, J.O. Ribeiro and V. Barros: Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition, Electron. J. Differential Equations 2017, No. 279, 11pp.

[30] C.A. Raposo: Exponential stability for a structure with interfacial slip and frictional damping, Appl. Math. Lett. 53 (2016), 85–91.

[31] C.A. Raposo, A.L. Araujo and M.S. Alves: A Timoshenko-Cattaneo system with viscoelastic Kelvin-Voigt damping and time delay, Far East J. Appl. Math. 93 (2015), 153–178.

[32] C.A. Raposo, J. Ferreira, M.L. Santos and N.N. Castro: Exponential stabilization for the Timoshenko system with two weak dampings, Appl. Math. Lett. 18 (2005), 535–541.

[33] C.A. Raposo, D.A.Z. Villanueva, S.D.M. Borjas and D.C. Pereira: Exponential stability for a structure with interfacial slip and memory, Poincare J. Anal. Appl. (2016), 39–48.

[34] B. Said-Houari and A. Kasimov: Decay property of Timoshenko system in thermoelasticity, Math. Methods Appl. Sci. 35 (2012), 314–333.

[35] H.D.F. Sare and R. Racke: On the stability of damped Timoshenko systems: Cattaneo versus Fourier law, Arch. Ration. Mech. Anal. 194 (2009), 221–251.

[36] A. Soufyane and A. Wehbe: Uniform stabilization for the Timoshenko beam by a locally distributed damping, Electron. J. Differential Equations, 2003, No. 29, 14pp.

[37] F.G. Shinskey: Process Control Systems, McGraw-Hill Book Company, New York, 1967.

[38] I.H. Suh and Z. Bien: Use of time delay action in the controller design, IEEE Trans. Automat. Control 25 (1980), 600–603.

[39] N.E. Tatar: Stabilization of a laminated beam with interfacial slip by boundary controls, Bound. Value Probl. 169 (2015), 1–14.

[40] S.P. Timoshenko: On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Lond. Edinb. Dubl. Phil. Mag. (6) 41 (1921), 744–746.

[41] S.P. Timoshenko and J.M. Gere: Mechanics of Materials. D. Van Nostrand Company, Inc, New York, 1972.

[42] Z. Tian and G.Q. Xu: Exponential Stability analysis of Timoshenko beam system with boundary delays, Appl. Anal. 95 (2016), 1–29.

[43] 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 (2005), 1575–1597.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る