Based on the dynamic theory of elastic media

the horizontal vibration of end-bearing piles embedded in a transversely isotropic soil is studied via an analytical scheme. By introducing displacement potential functions

the governing equations of the soil are decoupled

and the general solutions for the displacement and stress fields around the pile are derived using the method of separation of variables. Applying the continuity conditions at the pile–soil interface

the horizontal complex impedance of the surrounding soil is incorporated into the motion equation of the pile

leading to analytical solutions for the displacement

rotation angle

bending moment

and shear force of the pile. In addition

explicit expressions for the horizontal

rocking

and coupled horizontal–rocking dynamic impedances at the pile head are derived. Comparison with existing theoretical solutions confirms the accuracy and reliability of the proposed method. Furthermore

the influence of soil anisotropy parameters on the horizontal vibration characteristics of the pile is systematically analyzed. The results indicate that the anisotropic modulus ratio has a significant impact on the dynamic impedance at the pile head

as well as on the distribution of horizontal displacement

rotation angle

bending moment

and shear force along the pile depth.