Piles with non-circular cross-sections are characterized by their non-circular shapes. Due to their complex boundary conditions

their mechanical behavior differs from that of circular piles. Currently

there is a lack of theoretical analysis methods for the lateral dynamic response of such piles. In order to investigate the lateral dynamic response of these piles in homogeneous viscoelastic soil

the soil is approximated as a continuous medium

and the governing equations of the pile-soil system in Cartesian coordinates are derived based on the variational principle and Hamilton’s principle. The displacement function of the soil

considering complex boundary conditions

is solved using the partial differential equation (PDE) interface in COMSOL Multiphysics

while the displacement function of the pile is solved using the BVP4c function in Matlab. An iterative procedure is implemented in Matlab to obtain semi-analytical solutions for both the pile and soil displacement functions. The obtained results are compared with existing theoretical solutions for circular piles

showing good agreement. Analysis of the irregular-shaped piles reveals that

when the cross-sectional area is constant

the shape significantly affects the dynamic response at the pile head

with H-shaped piles exhibiting the highest impedance. When the cross-sectional moment of inertia is constant

X-shaped piles show the highest impedance. Taking X-shaped piles as an example

the impedance at the pile head increases with the pile-soil modulus ratio. As the length-to-diameter ratio increases

the resonance frequency and damping at the pile head decrease

while the stiffness at the pile head increases.