This research introduces an equivalent circuit model and a computational method to address complex mechanical motion issues through electromechanical analogies. The study initially refines core vibration characteristics using single- and multi-degree-of-freedom models

subsequently establishing equivalent circuit models for these various degrees of freedom. However

employing high degree-of-freedom models for detailed modelling of the core proves overly cumbersome. The research advocates for a distributed equivalent circuit model to more accurately represent the core's layered structure

thus facilitating enhanced core modelling. Moreover

the study formulates a mechanical wave transmission equation pertinent to the vibration of the iron core

which constitutes the foundation of the distributed mechanical vibration model. This model comprehensively assesses the impact of three critical factors on core vibration: the non-linearity of winding resistance

the electromechanical coupling coefficient

and the dynamic stiffness of the core. A case study elucidates the distinct influences of each factor on vibration characteristics. Furthermore

this study derives vibration calculations from a 60-day overload ageing test conducted on a 10 kV transformer under 135°C overload conditions. The methodology involves integrating measured compression force values and the calculated dynamic stiffness of the core into an equivalent circuit model. Subsequent analysis compares the results from the equivalent circuit model with experimental measurements. These comparisons indicate an agreement between the calculated and measured values in the time–frequency domain

thereby confirming the accuracy of the equivalent circuit model calculations.