This paper presents a simplified structural model for continuous variable cross-section single-pile foundations of offshore wind turbines， considering the water-pile-soil interaction， using the Euler-Bernoulli beam theory. The simplified model is solved using the differential transform method to obtain the transverse vibration control equation. The investigation focuses on the impact of tower diameter， transition section height， water-added mass， impeller-nacelle assembly mass， and the stiffness of three springs on the transverse natural frequency. The results show that the influence of the bottom diameter of the variable cross-section tower on the natural frequency is greater than that of the top diameter. In offshore wind turbine installations with greater water depths， the effect of water-added mass on the structural natural frequency cannot be overlooked. The transverse natural frequency of the wind turbine decreases as the impeller-nacelle assembly mass increases. The sensitivity of the soil modulus to the spring stiffness is ranked as follows： horizontal spring > coupling spring > rotational spring. Similarly， the sensitivity of the natural frequency to the spring stiffness is ranked as： coupling spring > horizontal spring > rotational spring. When variations occur in the soil modulus， the primary influence on the natural frequency is predominantly exerted by the horizontal spring and the coupling spring.