<p>The dynamic stability and durability of quasicrystal materials (QCMs) hinge on their corresponding contact vibration analysis. This study examines the axisymmetric vibrational characteristics induced by a one-dimensional hexagonal quasicrystal semi-infinite medium subjected to a rigid spherical indenter. By employing perturbation techniques combined with the Hankel transforms, this study determines the pressure distribution and displacement field during dynamic contact and establishes the dynamic contact stiffness (DCS) formulation under two different displacement boundary conditions. The numerical section presents the effects of various factors, including vibration frequency, displacement constraints, internal friction coefficient, phason field, and material elastic properties on the DCS behavior. The findings demonstrate that the phason field significantly decreases the stiffness characteristics of the one-dimensional hexagonal quasicrystal material and accelerates energy dissipation. The phonon field's elastic properties exert a greater influence on dynamic contact behavior compared to those associated with the phason field. The results obtained from this investigation make contributions towards unveiling the mechanisms of vibration transmission and energy dissipation at the contact interface of quasicrystal structures.</p>