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Exact estimation of vibration fundamental period of structures plays a vital role in their designing procedure. The proposition of a relatively exact expression which considers the effects of a pile group on the fundamental period of the structures was of less interest to previous researchers. This study aims to propose an analytical model and expression so as to estimate the free vibration period of the structures located on a pile group. To reach the objectives of this study, several numerical analyses has been carried out using the method of equivalent spring which takes into account the effects of soil-pile-structure interaction on the fundamental period of the structures. In the next step of the study the effects of a pile group on the fundamental period of the structures have been analyzed analytically. In this analytical study two cases have been considered for the piles which are end-bearing and floating piles. In the case of floating piles a five degrees-of-freedom analytical model and its corresponding expression have been proposed considering the soil-pile-structure system. The numerical modelling has been performed using the direct method due to the neglect of the soil in analytical expression and the results have been compared with those of the proposed analytical expression. The soil mass participation coefficient (λ) has been obtained using the discrepancy between the results of the two different methods to modify the analytical expression. In the case of end-bearing piles an analytical model with three degrees-of-freedom and its corresponding expressions has been proposed. Then the soil has been neglected and a new analytical expression has been proposed using the mass participation coefficients adopted from other researches to calculate the fundamental period of the structures. The comparison between the results of the proposed expression and those of case and numerical studies confirms that the proposed expressions benefit from a relative accuracy and can be used as an initial criterion in designing procedure.

An Analytical Model for Estimating the Vibration Frequency of Structures Located on the Pile Group in the Case of Floating Piles and End-bearing Pile