Dynamic boundary stabilization of a Reissner-Mindlin plate with Timoshenko beam

Mathematical Methods in the Applied Sciences

Volumn 27, Issue 11, 2004, Pages 1301-1315

  Grobbelaar Van Dalsen, Marié ^a  

^a UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Boundary control; Dynamic; Hybrid structure; Reissner Mindlin plate; Stabilization; Strong stability; Timoshenko beam

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FEEDBACK CONTROL; FUNCTIONS; MATHEMATICAL MODELS;

BOUNDARY CONTROL; HYBRID STRUCTURES; REISSNER-MINDLIN PLATE; STRONG STABILITY; TIMOSHENKO BEAM;

PLATES (STRUCTURAL COMPONENTS);

EID: 3142720390     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.506     Document Type: Article

References (31)

1. Budak M, Samarskii AA, Tikhonov AN. A Collection of Problems in Mathematical Physics. Pergamon Press: Oxford, 1964.
2. Littman W, L. Markus WJ. Stabilization of a Hybrid System of Elasticity of Feedback Boundary Damping. Annali di Matematica Pura ed Applicata 1988; 152:281-330.
3. Ahmed NU, Skowronski JM. Stability and control of non-linear flexible systems. Dynamic Systems and Applications 1993; 2:149-162.
4. Rao B. Stabilisation du modèle SCOLE par un Contrôle a priori bornè. Comptes Rendus des Séances de l'Academie des Sciences 1993; 316:1061-1066.
5. Mifdal A. Stabilisation uniforme d'un Système Hybride. Comptes Rendus des Séances de l'Academic des Sciences 1987; 324:37-42.
6. Grobbelaar-Van Dalsen M. On the solvability of the boundary-value problem for the elastic beam with attached load. Mathematical Models & Methods in Applied Sciences 1994; 4:89-105.
7. Grobbelaar-Van Dalsen M. On the initial-boundary-value problem for an extensible beam with attached load. Mathematical Methods in the Applied Sciences 1996; 19:943-957.
8. Grobbelaar-Van Dalsen M. Boundary stabilization for the extensible beam with attached load. Mathematical Models & Methods in Applied Sciences 1999;9(3):379-394.
9. Timoshenko S. Théorie des Vibrations. Beranger: Paris, 1947.
10. Deng Y. Exponential uniform stabilization of cantilevered timoshenko beam with a tip body via boundary feedback control. Proceedings of the 5th Symposium on Control of Distributed Parameter Systems. Perpignan, France, 1989.
11. Morgul O. Boundary control of a Timoshenko beam attached to a rigid body: planar motion. International Journal of Control 1991; 54:763-791.
12. Lagnese JE, Leugering G, Schmidt EJPG. Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures. Birkhauser: Boston, 1994.
13. Arosio A. Inhomogeneous Timoshenko beam equations. Mathematical Methods in the Applied Sciences 1992; 15:621-630.
14. Grobbelaar-Van Dalsen M. Uniform stabilization of a one-dimensional hybrid thermo-elastic structure. Mathematical Methods in the Applied Sciences 2003; 26(14):1223-1240.
15. You Y. Boundary stabilization of two-dimensional Petrovsky equation: vibrating plate. Differential and Integral Equations 1991; 4:617-638.
16. You Y. Pointwise boundary stabilizability of hyperbolic evolution equations: two-dimensional hybrid elastic structures. Journal of Mathematical Analysis and Applications 1992; 165:239-265.
17. Reissner E. On the theory of bending of elastic plates. Journal of Mathematics and Physics 1944; 23:184-191.
18. Grobbelaar-Van Dalsen M. Thermal effects in a two-dimensional hybrid elastic structure. Journal of Mathematical Analysis and Applications 2002; 265(1):49-75.
19. Grobbelaar-Van Dalsen M. On fractional powers of a pair of matrices and a plate-beam problem. Applicable Analysis 1999; 72:369-390.
20. Grobbelaar-Van Dalsen M. Interlude of operator pairs and a Von Kármán plate-beam problem with rotational inertia. Applicable Analysis 2000; 75:349-369.
21. Lasiecka I. Boundary stabilization of a 3-dimensional structural acoustic model. Journal de Mathématiques Pures et Appliquées 1999; 78:203-232.
22. Lasiecka I, Lebiedzik C. Asymptotic Behaviour of nonlinear structural acoustic interactions with thermal effects on the interface. Nonlinear Analysis 2002; 49:703-735.
23. Lagnese JE. Boundary Stabilization of Thin Plates. SIAM: Philadelphia, 1989.
24. Ebenfeld S. A comparison of the plate theories in the sense of Kirchoff-Love and Reissner-Mindlin. Mathematical Methods in the Applied Sciences 1999; 22:1505-1534.
25. Sauer N. Empathy theory and the Laplace transform. Linear Operators Banach Center Publications 1997; 38: 325-338.
26. Zietsman L, Van der Merwe AJ, Van Rensburg NFJ. A numerical study of the stabilization of a Timoshenko beam by boundary control. Technical Report UPWT 2001; 10:1-24.
27. Kim JU, Renardy Y. Boundary control of the Timoshenko beam. SIAM Journal on Control and Optimization 1987;25:1417-1429.
28. Dautray R, Lions J-L. Mathematical Analysis and Numerical Methods for Science and Technology, vol. 2. Springer: Berlin, 1988.
29. Benchimol CD. A note on weak stabilization of contraction semi-groups. SIAM Journal on Control and Optimization 1978; 16:373-379.
30. Dautray R, Lions J-L. Mathematical Analysis and Numerical Methods for Science and Technology, vol. 3. Springer: Berlin, 1990.
31. Sauer N. Eigenvalue problems with the spectral parameter also in the boundary condition. Quaestiones Mathematicae 1982; 5:1-27.