Forced nonlinear oscillations of a semi-infinite beam resting on a unilateral elastic soil: Analytical and numerical solutions

Journal of Computational and Nonlinear Dynamics

Volumn 2, Issue 2, 2007, Pages 155-166

  Lancioni, Giovanni ^a   Lenci, Stefano ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

Asymptotic developments; Beams on tensionless foundations; Cutoff frequencies; Finite elements in an infinite domain

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MECHANICAL PROPERTIES; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES; SPRINGS (COMPONENTS);

ASYMPTOTIC DEVELOPMENTS; CUTOFF FREQUENCIES; INFINITE DOMAIN; TENSIONLESS FOUNDATIONS;

BEAMS AND GIRDERS;

EID: 34248402883     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2447406     Document Type: Article

References (26)

1. Tsai, N. C., and Westmann, R. E., 1967, "Beams of Tensionless Foundation," J. Engrg. Mech. Div., 93, pp. 1-12.
2. Ascione, L., and Grimaldi, A., 1984, "Unilateral Contact Between a Plate and an Elastic Foundation," Meccanica, 19, pp. 223-233.
3. Zhang, Y., and Murphy, K. D., 2004, "Response of a Finite Beam in Contact with a Tensionless Foundation under Symmetric and Asymmetric Loading," Int. J. Solids Struct., 41(24-25), pp. 6745-6758.
4. de Holanda, A. S., and Gonçalves, P. B., 2003, "Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation," J. Eng. Mech., 129(4), pp. 438-448.
5. Lin, L., and Adams, G. G., 1987, "Beam on Tensionless Elastic Foundation," J. Eng. Mech., 113, pp. 542-553.
6. Güler, K., 2004, "Circular Elastic Plate Resting on Tensionless Pasternak Foundation," J. Eng. Mech., 130(10), pp. 1251-1254.
7. Khathlanl, A. A., 1994, "Large-Deformation Analysis of Plates on Unilateral Elastic Foundation," J. Eng. Mech., 120(8), pp. 1820-1827.
8. Ioakimidis, N. I., 1988, "Beams on Tensionless Elastic Foundation: Approximate Quantifier Elimination with Chebyshev Series," Int. J. Numer. Methods Eng., 39(4), pp. 663-686.
9. Silva, A. R. D., Silveira, R. A. M., and Gonçalves, P. B., 2001, "Numerical Methods for Analysis of Plates on Tensionless Elastic Foundations," Int. J. Solids Struct., 38, pp. 2083-2100.
10. Weitsman, Y., 1970, "On Foundation that Reacts in Compression Only," ASME J. Appl. Mech., 37(4), pp. 1019-1030.
11. Celep, Z., Malaika, A., and Abu-Hussein, M., 1989, "Forced Vibrations of a Beam on a Tensionless Foundation," J. Sound Vib., 128(2), pp. 235-246.
12. Choros, J., and Adams, G. G., 1979, "A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation," ASME J. Appl. Mech., 46(1), pp. 175-180.
13. Cokşun, I., 2003, "The Response of a Finite Beam on a Tensionless Pasternak Foundation Subjected to a Harmonic Load," Eur. J. Mech. A/Solids, 22(1), pp. 151-161.
14. Cokşun, I., 2000, "Non-Linear Vibrations of a Beam Resting of a Tensionless Winkler Foundation," J. Sound Vib., 236(3), pp. 401-411.
15. Celep, Z., 1990, "In-Plane Vibrations of Circular Rings on a Tensionless Foundation," J. Sound Vib., 143(3), pp. 461-471.
16. Nayfeh, A. H., 1981, Introduction to Perturbation Methods, Wiley, New York.
17. Kevorkian, J., and Cole, J. D., 1981, Perturbation Methods in Applied Mathematics, Springer, Berlin.
18. Callegari, M., Lancioni, G., and Lenci, S., 2005, "A Numerical Model for the Nonlinear Dynamics of a Semi-infinite Beam on Unilateral Winkler Soil," Proceedings AIMETA05, Firenze, September 11-15 (CD-ROM).
19. Andersen, L., Nielsen, S. R. K., and Kirkegaard, P. H., 2001, "Finite Element Modelling of Infinite Euler Beams on Kelvin Foundation Exposed to Moving Loads in Convected Coordinates," J. Sound Vib., 241(4), pp. 587-604.
20. Liu, T., and Li, Q., 2003, "Transient Elastic Wave Propagation in an Infinite Timoshenko Beam on Viscoelastic Foundation," Int. J. Solids Struct., 40(2), pp. 3211-3228.
21. Graff, K. F., 1975, Wave Motion in Elastic Solids, Oxford University Press, London, UK.
22. Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, North-Holland, Amsterdam, The Netherlands.
23. McGhie, R. D., 1990, "Flexural Wave Motion in Infinite Beam," J. Eng. Mech., 116(3), pp. 531-548.
24. Hughes, T. J. R., 1987, The Finite Element Method; Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, N.J.
25. Callegari, M., Carini, C. B., Lenci, S., Torselletti, E., and Vitali, L., 2003, "Dynamic Models of Marine Pipelines for Installation in Deep and Ultra-deep Waters: Analytical and Numerical Approaches," Proceedings AIMETA03, Ferrara, Italy, September 9-12 (CD-ROM).
26. Lenci, S., and Callegari, M., 2005, "Simple Analytical Models for the J-lay Problem," Acta Mech., 178(1-2), pp. 23-39.