Engineering Transactions, 56, 3, pp. 187–200, 2008

Vibrations of Timoshenko beams on two-parameter elas- tic soil

Department of Structural Engineering University of Basilicata

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 ac-
count 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.
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