Resumen
Generally, the high-fidelity finite element models of aero-engines comprise millions of degrees of freedom (DOFs). Although they can provide precise predictions of structural dynamics, the computational cost will be often unaffordable if appropriate dimension reduction techniques are not adopted. The homogenization of the substructure, also termed as the physical replacement, reduces the model scale by simplifying the unnecessary details of the substructure, thus speeding up the dynamic analysis of the whole engine. In this study, we design the physical replacements for the stators of an aero-engine based on the long-wave assumption. These replacements have the same wave features as the stators in long-wave cases while possessing fewer DOFs. The core steps include the analytical description of the stators and the corresponding physical replacement design through two homogenizations. Specifically, we first investigate the wave characteristics of the stators using the wave finite element method and find two dominant waves: flexural and flexural?torsional coupled waves. The first homogenization introduces two analytical Timoshenko beams to describe the two wave motions of the stators. These two analytical beams are subsequently solidified into physical replacements with I, box, and open cross-sections in the second homogenization. The mechanical and geometric parameters are identified through a combination of the static analysis and the genetic algorithm (GA). The search processes are of great efficiency, because all the descriptions are analytical. Results show that the relative errors of the natural frequencies between the pristine stators and the physical replacements associated with the nodal diameters 6?15 are less than 5%.