Study of the vibration mechanisms of transformer windings may lead to useful applications of vibration techniques to transformer online diagnosis. In a power transformer, the clamping force provides a boundary mechanical constraint to ensure the integrity of the winding. Thus, the looseness of the clamping force is an important health indicator for a transformer. Although the effect of clamping force on a winding's stiffness and natural frequencies is known, the effect of time-varying load current on these natural frequencies remains unsolved. In this paper, this effect is investigated by studying the mechanical frequency response function of an on-load single-phase winding under different clamping forces and variation of the harmonic amplitude of in-service transformers with load current. Then, a gated recurrent unit (GRU) neural network is used to explore the relationship between current sequence and vibration sequence for operating transformers. This study shows that the electromagnetic force induced by the load current affects the vibration response of the winding structure, especially when the looseness of the clamping force is significant. A potential application of the observed phenomenon for online detection of winding conditions is also illustrated.