Solutions for the natural response of partially supported piles assuming soil to be a Winkler model are presented for the two cases when both ends are either simply supported or free. The effect of axial load is considered in the analysis and numerical results are presented for a range of parameters applicable to marine and harbor structures. It was found that if the magnitude of the axial force is less than the Euler buckling load, the effect on the natural response is not appreciable.
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Valsangkar et al. (1987) studied this question.
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