A Timoshenko beam with tip body and boundary damping

Wave Motion

Volumn 39, Issue 3, 2004, Pages 199-211

  Zietsman, L ^a   van Rensburg, N F J ^b   van der Merwe, A J ^c  

^a UNIVERSITY OF SOUTH AFRICA   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c CAPE PENINSULA UNIVERSITY OF TECHNOLOGY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; SPECTRUM ANALYSIS; VIBRATIONS (MECHANICAL);

BOUNDARY DAMPING; TIMOSHENKO BEAMS;

CANTILEVER BEAMS;

DAMPING;

EID: 1042278532     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2003.08.003     Document Type: Article

References (20)

1. G. Chen, J. Zhou, Vibration and Damping in Distributed Systems I, CRC Press, Tokyo, 1993.
2. Chen G.Delfour M.C.Krall A.M.Payre G.Modeling, stabilization and control of serially connected beams J. Control Opt. 253 1987 526-546
3. Grobbelaar-van Dalsen M.van der Merwe A.Boundary stabilization for the extensible beam with attached load Math. Models Meth. Appl. Sci. 93 1999 379-394
4. M. Grobbelaar-van Dalsen, A. van der Merwe, Boundary stabilization of a dynamically coupled vibrating system, in: Proceedings of the Second South African Conference on Applied Mechanics, 1998, pp. 423-443.
5. Littman W.Marcus L.Stabilization of a hybrid system of elasticity by feedback boundary damping Ann. Mat. Pura Appl. 152 1988 281-330
6. Littman W.Marcus L.Exact boundary controllability of a hybrid system of elasticity Arch. Rational Mech. Anal. 103 1988 193-236
7. Rao B.Stabilisation uniforme d'un systèmehybride en élasticité, Série I CR Acad. Sci. Paris t.316 1993 261-266
8. Rao B.Stabilisation du modele SCOLE par un contrôle a priori borné, Série I CR Acad. Sci. Paris t.316 1993 1061-1066
9. Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1965.
10. D.J. Inman, Engineering Vibration, Prentice-Hall, Englewood Cliffs, NJ, 1994.
11. Kim J.U.Renardy Y.Boundary control of the Timoshenko beam Siam J. Contr. Opt. 256 1987 1417-1429
12. Coleman M.P.Wang H.Analysis of vibration spectrum of a Timoshenko beam with boundary damping by the wave method Wave Motion 17 1993 223-239
13. Shubov M.A.Asymptotic and spectral analysis of the spatially nonhomogeneous Timoshenko beam model Math. Nachr. 241 2002 125-162
14. S. Timoshenko, Vibration Problems in Engineering, 2nd ed., Van Nostrand, New York, 1937.
15. G. Strang, G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1972.
16. J.N. Reddy, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, New York, 1993.
17. D. Braess, Finite Elements, 2nd ed., Cambridge University Press, Cambridge, 2001.
18. Huang T.C.The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions J. Appl. Mech. 28 1961 579-584
19. N.F.J. van Rensburg, Natural frequencies and modes of a Timoshenko beam, Technical Report UPWT 2001/04, Department of Mathematics and Applied Mathematics, University of Pretoria, 2001.
20. D.E. Newland, Mechanical Vibration Analysis and Computation, Longman, Essex, 1989.