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The effects of soil-structure-interaction on the modal characteristics of a cantilever beam of increasing mechanical complexity are investigated. Concentrated mass characteristics are provided at the free end of the continuous beam, while translational and rotational springs are provided at the elastic support. The governing equations of the cantilever beam are presented for a hierarchy of three beam theories: Euler-Bernoulli; Rayleigh; Timoshenko-Ehrenfest. The eigenfrequencies and the eigenfunctions are established for two boundary conditions: fixed based; elastic support. Three cases are analyzed according to the cut-off frequency of Timoshenko-Ehrenfest beam theory. Two validation examples are conducted to compare the results of the proposed equations with analytical and experimental results from the literature. Numerical results are produced concerning the effect of soil-structure interaction in terms of: frequency spectrum; dispersion curve; eigenfrequencies; and eigenfunctions. The effects are studied under various assumptions regarding the soil configuration, the constant and the frequency-dependent values of the impedance functions, the foundation inertia and the three beam theories. |
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