Finite element modelling of the coupled bending and torsional free vibration of uniform beams with an arbitrary cross-section

Applied Mathematical Modelling

Volumn 21, Issue 6, 1997, Pages 339-344

  Tanaka, M ^a   Bercin, A N ^a  

^a SHINSHU UNIVERSITY   (Japan)

Author keywords

Arbitrary cross section beams; Coupled bending and torsion; Finite element method; Free vibration

Indexed keywords

BEAMS AND GIRDERS; BENDING (DEFORMATION); BOUNDARY CONDITIONS; NATURAL FREQUENCIES; STIFFNESS MATRIX; VIBRATIONS (MECHANICAL);

ARBITRARY CROSS-SECTION BEAMS; TORSIONAL FREE VIBRATIONS;

FINITE ELEMENT METHOD;

EID: 0031164438     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(97)00030-9     Document Type: Article

References (15)

1. Bishop, R. E. D. and Johnson, D. C. The Mechanics of Vibration, Cambridge University Press, Cambridge, UK, 1979
2. Mei, C. Coupled vibrations of thin walled beams of open section using the finite element method. Int. J. Mech. Sci. 1970, 12, 883-891
3. Hallauer, W. L., Jr. and Liu, R. Y. L. Beam bending-torsion dynamic stiffness method for calculation of exact vibration modes. J. Sound Vibr. 1982, 85, 105-113
4. Dokumaci, E. An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry. J. Sound Vibr. 1987, 119, 443-449
5. Banerjee, J. R. Guo, S., and Howson, W. P. Exact dynamic stiffness matrix of a bending torsion coupled beam including warping. Comput. Struct. 1996, 59, 613-621
6. Bishop, R. E. D., Cannon, S. M., and Miao, S. On coupled bending and torsional vibration of uniform beams. J. Sound Vibr. 1989, 131, 457-464
7. Klausbruckner, M. J. and Pryputniewicz, R. J. Theoretical and experimental study of coupled vibrations of channel beams. J. Sound Vibr. 1995, 183, 239-252
8. Gere, J. M. and Lin, Y. K. Coupled vibration of thin walled beams of open cross section. J. Appl. Mech. 1958, 25, 373-378
9. Rao, J. S. and Carnegie, W. Solution of the equations of motion of coupled bending-bending-torsion vibrations of turbine blades by the method of Ritz-Galerkin. Int. J. Mech. Sci. 1970, 12, 875-882
10. Friberg, P. O. Coupled vibrations of beams - an exact dynamic element stiffness matrix. Int. J. Num. Methods Eng. 1983, 19, 479-493
11. Tanaka, M. and Bercin, A. N. Free vibration solution for uniform beams of nonsymmetrical cross section using mathematica. Comput. Struct., in press
12. Williams, F. W. and Wittrick, W. H. An automatic computational procedure for calculating natural frequencies of skeletal structures. Int. J. Mech. Sci. 1970, 12, 871-891
13. Richards, T. H. and Leung, Y. T. An accurate method in structural vibration analysis. J. Sound Vibr. 1977, 55, 363-376
14. Vlasov, V. Z. Thin Walled Elastic Beams, 2nd edition, National Science Foundation, Washington, DC, 1961
15. Zienkiewicz, O. C. The Finite Element Method, 3rd edition, McGraw-Hill, New York, 1977