Similitude analysis of free vibration of functionally graded material cylinders under thermal environment

• The similitude of free vibration of functionally graded material cylinders under thermal environment is studied for the first time. • A novel similitude method named energy similitude correction method is proposed. • The similitude distortion problem caused by FGM and thermal environment is solved. • The distorted similitude relationship of FGM cylinders under thermal environment is established. • Through numerical verification, the method proposed reaches high accuracy. In order to obtain the thermal modal characteristics of FGM (Functionally graded material) cylinders, scaled model test is an efficient experimental approach, and its theoretical core is to establish the similitude relationship. However, under the influence of non-scalability of FGM and thermal environment, the traditional similitude method will lead to serious dynamic distortion. In this article, the similitude of free vibration of FGM cylinders under thermal environment is studied for the first time, and a novel similitude method is proposed to solve the complex similitude distortion problem. Firstly, the similitude distortion problem caused by FGM and thermal environment is analyzed in details. Secondly, the mechanical analyses of FGM cylinders are carried out. Then, a novel similitude method named energy similitude correction method is proposed, and the distorted similitude relationship of FGM cylinders under thermal environment is derived. Finally, this method is verified through various numerical examples. The results show that, for FGM cylinders under thermal environment, the proposed method can solve the similitude distortion and establish the distorted similitude relationship with high accuracy. Moreover, the method can be applied to various FGM cylinders with different thicknesses, gradient coefficients and temperature conditions.