The vibration characteristics of gas insulated switch (GIS) busbars have garnered attention from researchers, and the establishment of similitude models for experimental validation has become a practical engineering requirement. There is an urgent need for the development of distorted similitude models that retain the original wall thickness, particularly for busbars with excessively thin walls. The scaling laws of variable exponent of busbars with respect to length, radius, and wall thickness are first established in this study. Subsequently, based on the scaling laws, models with three fold distorted reduction are used to predict the first three bending natural frequencies of the prototype busbar. The prediction errors of the distorted similitude models for length and radius with respect to the prototype natural frequencies are both less than 8.2%, while for wall thickness, the prediction error is at the thousandth level. The monotonic impact of distorted factors on natural frequencies is the reason why the established scaling laws have predictive ability. This research holds significant importance for the study of dynamic characteristics in electrical equipment.