Free vibration of semi-rigidly connected piles embedded in soils with different subgrades

This paper is concerned with the free vibration analysis of Timoshenko piles partially embedded in elastic soil, semi- rigidly connected at the upper end, and subjected to an axial force. The pile is divided into three regions: the pile portion above the soil constitutes the first region, while the second and third regions are the pile portion that is embedded in two different layers of the soil type. The pile material is assumed to be linearly elastic and the axial force is constant along the pile length. The soil is idealized by the Winkler model and the semi- rigid connection of the pile is modeled by a rotational spring. The natural frequencies of the piles are calculated from the transfer matrix for different axial forces, rotational spring constants, subgrade reaction moduli and embedded lengths of the pile. The results indicate that the natural frequency of the pile decreases as the axial force increases. Further, the increase in the stiffness of the rotational spring at the upper end of the pile causes only a small increase in the natural frequency. Finally, both the pile length and the subgrade reaction of the soil influence significantly the natural frequency of the pile.