[1] Timoshenko S. Vibration Problems in Engineering. New York: Van Norstrand, 1955
[2] Alabau-Boussouira F. Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control. Nonlinear Differ Equ Appl, 2007, 14: 643–669
[3] Ammar-Khodja F, Benabdallah A, Mu˜noz Rivera J E, Racke R. Energy decay for Timoshenko system of memory type. J Diff Eqs, 2003, 194(1): 82–115
[4] Guesmia A, Messaoudi S. General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math Meth Appl Sci, 2009, 32(16): 2102–2122
[5] Messaoudi S, Said-Houari B. Uniform decay in a Timoshenko-type system with past history. J Math Anal Appl, 2009, 360: 459–475
[6] Messaoudi S, Mustafa M I. A stability result in a memory-type Timoshenko system. Dynam Syst Appl, 2009, 18(3/4): 457–468
[7] Soufyane A. Stabilisation de la poutre de Timoshenko. C R Acad Sci Paris Series I Math, 1999, 328(8): 731–734
[8] Soufyane A. Exponential stability of the linearized nonuniform Timoshenko beam. Nonl Anal Real World Appl, 2009, 10: 1016–1020
[9] Shi D H, Feng D X. Exponential decay of Timoshenko beam with locally distributed feedback. IMA J Math Contr Infor, 2001,18: 395–403
[10] Soufyane A, Wehbe A. Uniform stabilization for the Timoshenko beam by a locally distributed damping. Electr J Diff Eqs, 2003, 2003(29): 1–14
[11] Xu G Q, Yung S P. Stabilization of Timoshenko beam by means of pointwise controls. ESAIM Control Optim Calc Var, 2003, 9: 579–600
[12] Xu G Q, Yung S P. Exponential decay rate for a Timoshenko beam with boundary damping. J Optim Th Appl, 2004, 123(3): 669–693
[13] Mu˜noz Rivera J E, Racke R. Global stability for damped Timoshenko systems. Discrete Cont Dyn Syst, 2003, 9(6): 1625–1639
[14] Raposo C A, Bastos W D, Santos M L. A transmission problem for the Timoshenko system. Comput Appl Math, 2007, 26(2): 215–234
[15] Raposo C A, Ferreira J, Santos M L, Castro N N O. Exponential stability for the Timoshenko system with two weak dampings. Appl Math Letters, 2005, 18: 535–541
[16] Kim J U, Renardy Y. Boundary control of the Timoshenko beam. SIAM J Control Optim, 1987, 25(6): 1417–1429
[17] Morg¨ul ¨O. Boundary control of a Timoshenko beam attached to a rigid body. Planar Motion Int J Control, 1991, 54(4): 763–791
[18] Shi D H, Hou S H, Feng D X. Feedback stabilization of a Timoshenko beam with an end mass. Int J Control, 1998, 69(2): 285–300
[19] Feng D X, Shi D H, Zhang W T. Boundary feedback stabilization of Timoshenko beam with boundary dissipation. Science in China Sr. A, 1998, 41(5): 483–490
[20] Feng D X, Xu G Q, Yung S P. Riesz basis property of Timoshenko beams with boundary control feedback. Int J Math Meth Appl, 2003, 21: 1807–1820
[21] Shoukui S. Boundary stabilization of nonuniform Timoshenko beam. Appl Math J Chinese Univ Ser B, 1999, 14(4): 467–474
[22] Yan Q X, Hou S H, Feng D X. Asymptotic behavior of Timoshenko beam with dissipative boundary feedback. J Math Anal Appl, 2002, 269: 556–577
[23] Xu G Q, Feng D X, Yung S P. Riesz basis property of generalized eigenvector system of a Timoshenko beam. IMA J Math Control Infor, 2004, 21: 65–83
[24] Xu G Q. Boundary feedback exponential stabilization of a Timoshenko beam with both ends free. Int J Control, 2005, 78(4): 286–297
[25] Zhang C G. Boundary feedback stabilization of the undamped Timoshenko beam with both ends free. J Math Anal Appl, 2007, 326: 488–499
[26] Han Z J, Xu G Q. Dynamical behavior of an hybrid system of nonhomogeneous Timoshenko beam with partial non-collocated inputs. J Dynamical Contr Syst, 2011, 17(1): 77–121
[27] Han Z J, Xu G Q. Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks. ESAIM: Control Optim Calc Var, 2011, 17(2): 552–574
[28] Fernandez Sare H D, Racke R. On the stability of damped Timoshenko systems: Cattaneo versus Fourier law. Arch Ration Mech Anal, 2009, 194(1): 221–251
[29] Mu˜noz Rivera J E, Racke R. Timoshenko systems with indefinite damping. J Math Anal Appl, 2008, 341: 1068-1083
[30] Santos M L. Decay rates for solutions of a Timoshenko beam system with a memory condition at the boundary. Abstr Appl Anal, 2002, 7(10): 531–546
[31] Djebabla A, Tatar N-e. Exponential stabilization of the Timoshenko system by a thermo-viscoelastic damping. J Dynamical Control Syst, 2010, 16(2): 189–210
[32] Djebabla A, Tatar N-e. Stabilization of the Timoshenko beam with thermal effect. Mediterranean J Math, 2010, 7: 373–385
[33] Giorgi C, Vegni F M. Uniform energy estimates for a semilinear evolution equation of the Mindlin-Timoshenko beam with memory. Math Comput Modelling, 2004, 39(9/10): 1005–1021
[34] Mu˜noz Rivera J E, Fernandez Sare H D. Stability of Timoshenko systems with past history. J Math Anal Appl, 2008, 339(1): 482–502
[35] Pata V. Exponential stability in linear viscoelasticity. Quarterly Appl Math, 2006, 64(3): 499–513
[36] Pata V. Exponential stability in linear viscoelasticity with almost flat memory kernels. Comm Pure Appl Anal, 2010, 9: 721–730 |