Stabilization of a viscoelastic Timoshenko beam

References

• Timoshenko , S . 1955 . Vibration Problems in Engineering , New York : Van Norstrand .
   Google Scholar
• Soufyane , A . 1999 . Stabilisation de la poutre de Timoshenko . C. R. Acad. Sci. Paris Ser. I Math. , 328 ( 8 ) : 731 – 734 .
   Google Scholar
• Soufyane , A . 2009 . Exponential stability of the linearized nonuniform Timoshenko beam . Nonl. Anal. Real World Appl. , 10 : 1016 – 1020 .
   Web of Science ®Google Scholar
• Shi , D-H and Feng , D-X . 2001 . Exponential decay of Timoshenko beam with locally distributed feedback . IMA J. Math. Control Infor. , 18 : 395 – 403 .
   Google Scholar
• Soufyane , A and Wehbe , A . 2003 . Uniform stabilization for the Timoshenko beam by a locally distributed damping . Electr. J. Diff. Eqs. , 2003 ( 29 ) : 1 – 14 .
   Google Scholar
• Xu , G-Q and Yung , S-P . 2003 . Stabilization of Timoshenko beam by means of pointwise controls . ESAIM Control Optim. Calc. Var. , 9 : 579 – 600 .
   Web of Science ®Google Scholar
• Xu , G-Q and Yung , S-P . 2004 . Exponential decay rate for a Timoshenko beam with boundary damping . J. Optim. Theoretical Appl. , 123 ( 3 ) : 669 – 693 .
   Web of Science ®Google Scholar
• Muñoz Rivera , JE and Racke , R . 2003 . Global stability for damped Timoshenko systems . Discrete Cont. Dyn. Syst. , 9 ( 6 ) : 1625 – 1639 .
   Web of Science ®Google Scholar
• Raposo , CA , Bastos , WD and Santos , ML . 2007 . A transmission problem for the Timoshenko system . Comput. Appl. Math. , 26 ( 2 ) : 215 – 234 .
   Web of Science ®Google Scholar
• Raposo , CA , Ferreira , J , Santos , ML and Castro , NNO . 2005 . Exponential stability for the Timoshenko system with two weak dampings . Appl. Math. Lett. , 18 : 535 – 541 .
   Web of Science ®Google Scholar
• Alabau-Boussouira , F . 2007 . Asymptotic behaviour for Timoshenko beams subject to a single nonlinear feedback control . Nonlinear Differ. Equ. Appl. , 14 : 643 – 669 .
   Web of Science ®Google Scholar
• Kim , JU and Renardy , Y . 1987 . Boundary control of the Timoshenko beam . SIAM J. Control Optim. , 25 ( 6 ) : 1417 – 1429 .
   Web of Science ®Google Scholar
• Morgül , Ö . 1991 . Boundary control of a Timoshenko beam attached to a rigid body . Planar Motion, Int. J. Control , 54 ( 4 ) : 763 – 791 .
   Web of Science ®Google Scholar
• Shi , D-H , Hou , SH and Feng , D-X . 1998 . Feedback stabilization of a Timoshenko beam with an end mass . Int. J. Control , 69 ( 2 ) : 285 – 300 .
   Web of Science ®Google Scholar
• Feng , D-X , Shi , D-H and Zhang , WT . 1998 . Boundary feedback stabilization of Timoshenko beam with boundary dissipation . Sci. China Sr. A , 41 ( 5 ) : 483 – 490 .
   Google Scholar
• Feng , D-X , Xu , G-Q and Yung , S-P . 2003 . Riesz basis property of Timoshenko beams with boundary control feedback . Int. J. Math. Meth. Appl. , 21 : 1807 – 1820 .
   Google Scholar
• Messaoudi , S and Mustafa , MI . 2009 . A stability result in a memory-type Timoshenko system . Dynam. Systems Appl. , 18 ( 3–4 ) : 457 – 468 .
   Web of Science ®Google Scholar
• Shoukui , S . 1999 . Boundary stabilization of nonuniform Timoshenko beam . Appl. Math. J. Chinese Univ. Ser. B , 14 ( 4 ) : 467 – 474 .
   Google Scholar
• Yan , Q-X , Hou , SH and Feng , SH . 2002 . Asymptotic behaviour of Timoshenko beam with dissipative boundary feedback . J. Math. Anal. Appl. , 269 : 556 – 577 .
   Web of Science ®Google Scholar
• Xu , G-Q , Feng , D-X and Yung , S-P . 2004 . Riesz basis property of generalized eigenvector system of a Timoshenko beam . IMA J. Math. Control Infor. , 21 : 65 – 83 .
   Google Scholar
• Xu , GQ . 2005 . Boundary feedback exponential stabilization of a Timoshenko beam with both ends free . Int. J. Control , 78 ( 4 ) : 286 – 297 .
   Web of Science ®Google Scholar
• Zhang , C-G . 2007 . Boundary feedback stabilization of the undamped Timoshenko beam with both ends free . J. Math. Anal. Appl. , 326 : 488 – 499 .
   Web of Science ®Google Scholar
• Fernandez Sare , HD and Racke , R . 2009 . On the stability of damped Timoshenko systems: Cattaneo versus Fourier law . Arch. Ration. Mech. Anal. , 194 ( 1 ) : 221 – 251 .
   Web of Science ®Google Scholar
• Muñoz Rivera , JE and Racke , R . 2008 . Timoshenko systems with indefinite damping . J. Math. Anal. Appl. , 341 : 1068 – 1083 .
   Web of Science ®Google Scholar
• Santos , ML . 2002 . Decay rates for solutions of a Timoshenko beam system with a memory condition at the boundary . Abstr. Appl. Anal. , 7 ( 10 ) : 531 – 546 .
   Google Scholar
• Djebabla , A and Tatar , N-e . 2010 . Exponential stabilization of the Timoshenko system by a thermo-viscoelastic damping . J. Dynam. Control Syst. , 16 ( 2 ) : 189 – 210 .
   Web of Science ®Google Scholar
• Djebabla , A and Tatar , N-e . 2010 . Stabilization of the Timoshenko beam with thermal effect, . Mediterranean J. Math. , 7 : 373 – 385 .
   Web of Science ®Google Scholar
• Ammar-Khodja , F , Benabdallah , A and Muñoz Rivera , JE . 2003 . Energy decay for Timoshenko system of memory type . J. Diff. Eqs , 194 ( 1 ) : 82 – 115 .
   Web of Science ®Google Scholar
• Guesmia , A and Messaoudi , S . 2009 . General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping . Math. Meth. Appl. Sci. , 32 ( 16 ) : 2102 – 2122 .
   Web of Science ®Google Scholar
• Giorgi , C and Vegni , FM . 2004 . Uniform energy estimates for a semilinear evolution equation of the Mindlin–Timoshenko beam with memory . Math. Comput. Model. , 39 ( 9–10 ) : 1005 – 1021 .
   Web of Science ®Google Scholar
• Muñoz Rivera , JE and Fernandez Sare , HD . 2008 . Stability of Timoshenko systems with past history . J. Math. Anal. Appl. , 339 ( 1 ) : 482 – 502 .
   Web of Science ®Google Scholar
• Messaoudi , S and Said-Houari , B . 2009 . Uniform decay in a Timoshenko-type system with past history . J. Math. Anal. Appl. , 360 : 459 – 475 .
   Web of Science ®Google Scholar