Free vibration of semi-rigid connected and partially embedded piles the effects of the bending moment, axial and shear force

摘要

The author thanks the discussers for their comments. But their comments are not acceptable for the reasons that are presented below: The shear force that remains normal to the initial pile axis or the deflect pile axis may be used to formulate the free vibration equations of the pile. The directions of the shear force and axial force which were used to formulate the equations in the paper remain normal and parallel to the initial pile axis, respectively. The directions of these forces at the first and the second regions are presented in Fig. 1(a) and (b). As in the literature, the deformed shapes of the pile which were assumed in the paper are presented in Fig. 1(a) and (b) by using a dashed line.