In this paper, the transient vibration responses of power transformer windings subjected to the mechanical and electrical impacts are studied with the aim of detecting the structural degradation of windings. The axial vibration mechanism of windings is described as a multi-degrees-of-freedom model with the Rayleigh damping formulation. Then, the nonlinear damping curves are extracted from the original vibrations by using Morlet wavelet transform. During the laboratory experiment, the model was validated on a full-size winding model, and the free vibrations from different coils were acquired when the mechanical impact was applied. Furthermore, the clamping force adjustment experiment was performed to simulate the structural degradation of windings, and the nonlinear relationship between the clamping force and the damping coefficients was investigated. Finally, the proposed method is applied to the tank vibrations collected during the de-energizing process for in-service transformers, and the results of the normal and the anomalous transformers are compared. It is concluded that the proposed method not only reveals the relationship between the transient vibration and the winding structure but also can effectively identify the winding condition.