Application of the finite-element method to the vibration of a rectangular plate with elastic support at the boundary

Mathematical and Computer Modelling

Volumn 38, Issue 3-4, 2003, Pages 309-322

  Zietsman, L ^a   Van Der Merwe, A J ^b   Geldenhuys, J J ^b   Van Rensburg, N F J ^b  

^a UNIVERSITY OF SOUTH AFRICA   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Finite element method; Natural frequencies; Plate beam system; Vibration

Indexed keywords

EID: 0141615714     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(03)90089-6     Document Type: Article

References (16)

1. H.T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems, Control-Theory and Advanced Technology 4 (1), 73-90, (1988).
2. G. Chen, M.C. Delfour, A.M. Krall and G. Payre, Modeling, stabilization and control of serially connected beams, J. Control and Optimization 25 (3), 526-546, (May 1987).
3. J.E. Lagnese, Modelling and controllability of plate-beam systems, In Lecture Notes in Control and Inform. Sci., Volume 185, pp. 423-435, Springer, Berlin, (1993).
4. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, Kokakusha, (1959).
5. M. Grobbelaar-van Dalsen and A. van der Merwe, Boundary stabilization for the extensible beam with attached load, Mathematical Models and Methods in Applied Sciences 9 (3), 379-394, (1999).
6. L. Zietsman, N.F.J. van Rensburg and A.J. van der Merwe, A numerical study of the vibrations of a damaged beam, Mathl. Comput. Modelling 31 (6/7), 51-60, (2000).
7. J.N. Reddy, An Introduction to the Finite Element Method, Second Edition, McGraw-Hill, New York, (1993).
8. O.C. Zienkiewicz, The Finite Element Method, Third Edition McGraw-Hill, London, (1977).
9. G.R. Cowper, E. Kosko, G.M. Lindberg and M.D. Olson, Formulation of a new triangular plate bending element, Canadian Aeronautics and Space Institute, Trans. 1, 86-90, (1968).
10. G.R. Cowper, E. Kosko, G.M. Lindberg and M.D. Olson, Static and dynamic applications of a high-precision triangular plate bending element, AIAA J. 7, 1957-1965, (1969).
11. G.R. Cowper, E. Kosko, G.M. Lindberg and M.D. Olson, A high-precision triangular plate bending element, Aeronautical Dept. LR-514, National Research Council of Canada, (December 1968).
12. N.F.J. van Rensburg, A mathematical model for transverse vibration of a plate with elastic support at the boundary, Technical Report, UPWT 2000/02, University of Pretoria, Pretoria, (2000).
13. Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, (1965).
14. H. Reismann, Elastic Plates: Theory and Application, John Wiley & Sons, New York, (1988).
15. D.J. Inman, Engineering Vibration, Prentice-Hall, Englewood Cliffs, NJ, (1994).
16. G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, (1972).