Energy Similitude Correction Method for Free Vibration of Cylinders

Similitude theory has been applied to design scale models in many fields of engineering. As for free vibration of cylinders, the wall thickness is too thin to manufacture scale model, which leads to similitude distortion. The aim of this study is to correct the similitude distortion and establish the distorted similitude relationship for free vibration of cylinders. First, the complete and partial similitude relationships are deduced while the similitude distortion of wall thickness is discussed. Then, with analysis of similitude for energy, an equation with prediction of modal frequencies for prototype is established and the energy similitude correction method is proposed. Finally, through numerical examples, this method is verified and the influence of wall thickness variation on the accuracy of the proposed method is analyzed.