Engineering Transactions, 56, 3, pp. 187–200, 2008
10.24423/ENGTRANS.195.2008

Vibrations of Timoshenko beams on two-parameter elastic soil

N. M. AUCIELLO
Department of Structural Engineering, University of Basilicata, Potenza
Italy

In this paper the influence of the two-parameter elastic soil on the dynamic behaviour of a beam with variable cross-section is examined, in the presence of conservative axial loads. The beams are assumed to follow the well-known Timoshenko hypotheses, in order to take into account both the rotary inertia and shear deformation effect. The Rayleigh–Ritz approach is used and Boundary Characteristic Orthogonal Polynomials are chosen as trial functions; (BCOPs method [2]). The theory is concisely presented in a matrix form, so that the contribution of the rotary inertia and of the soil can be easily recognized. Various examples and comparisons are illustrated, in order to emphasize the influence of the soil properties and of the beam taper ratio. Finally, the results are also compared with the results given by other authors, using exact and approximate approaches.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

M. Hetenyi, Beams on elastic foundation, Ann. Arbor, University of Michigan Press, 1961.

S. Chakraverty, R. B. Bhat, I. Stiharu, Recent reserch on vibration of structures using Boundary Characteristic Orthogonal Polynomials in the Rayleigh-Ritz method, The Shock and Vibration Digest, 31, 3, 187–194, 1999.

F. Y. Chen, C. P. Pantelides, Dynamic Timoshenko beam-columns on elastic media, ASCE J. Struct. Engng., 114, 1524–1550, 1988.

M. C. Bruno, V. Di Capua and C. Franciosi, New interpolation functions in eigenfrequency analysis of Timoshenko beams on two-parameter elastic soil, Engng. Trans., 44, 2, 283–294,1996.

M. A. De Rosa, Free vibration of Timoshenko beams on two-parameter elastic foundation, Comput. & Struct., 57, 151–156, 1995.

C. Franciosi, A. Masi, Free vibration of foundation beams on two-parameter elastic soil, Comput. & Struct., 47, 419–426, 1993.

C. P. Filipich, M. B. Rosales, A variant of Rayleigh’s method applied to Timoshenko beams embedded in a Winkler-Pasternak medium, J. Sound and Vibr., 124, 443–451, 1988.

V. Z. Vlasov, U. N. Leontiev, Beams, plates and shells on elastic foundation. Jerusalem, Israel Program for Scientific Translations.

G. V. C. Vallabhan, K. R. Das, A refined model for beams on elastic foundation, Int. J. Solid Structures, 27, 629–637, 1991.

T. Yokoyama, Vibration and transiet response of Timoshenko beams resting on elastic foundations, Ingenieur Archiv, 57, 81–90, 1987.

T. Yokoyama, Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations, Comput. & Struct., 61, 995–1007, 1996.

K. Rektorys, Variational methods in mathematics, science and engineering, D. Reidel Publishing Comp., Boston 1977.




DOI: 10.24423/ENGTRANS.195.2008