New Interpolation Functions in Eigen-Frequency Analysis of Timoshenko Beams on Two-Parameter Elastic Soil
The aim of the paper is to study the dynamic behaviour, limited to the eigen-value problem, of Timoshenko beams on variable two-parameter elastic soil. The analysis is performed by means of two different finite elements, with cubic and quintic interpolation laws, the mass and stiffness matrices are analytically calculated, and their performances are briefly discussed. Some numerical examples end the paper, in which the good convergence rate of the elements is shown, and a comparison is made with a powerful Rayleigh-Ritz approximation.
References
M. HETENYI, Beams on elastic foundation, University of Michigan Press, Ann Arbor 1961.
J.M. DAVIES, An exact finite element for beam on elastic foundation problems, J. Struct. Mech., 14, 4, 489-499, 1986.
S.N. SIROSH, A. GHALI and A.G. RAZAQPUR, A general finite element for beams or beams-columns with or without elastic foundation, Int. J. Num. Meth. Engng., 28, 1061-1076, 1989.
M. EISENBERGER and J. CLASTORNIK, Vibrations and buckling of a beam on variable Winkler elastic foundation, J. Sound Vibr., 115, 233-241, 1987.
C.V.G. VALLABHAN and Y.C. DAS, A refined model for beams on elastic foundations, Int. J. Solids Struct., 27, 629-637, 1991.
G. PRATHAP and G.R. BHASHYAM, Reduced integration and the shear-flexible element, Int. J. Num. Engng., 18, 195-210, 1982.
D.L. THOMAS, J .M. WILSON and R.R. WILSON, Timoshenko beam finite elements, J. Sound Vibr., 31, 3, 315-330, 1973.
T. YOKOYAMA, Parametric instability of Timoshenko beams resting on an elastic foundation, Comp. Struct., 28, 2, 207-216, 1988.
B.A.H. ABBAS and J. THOMAS, Dynamic stability of Timoshenko beams resting on an elastic foundation problems, J. Sound Vibr., 60, 33-44, 1978.
C. FRANCIOSI, Finite elements and structures [in Italian], Liguori Editore, Naples, ltaly 1995.