Considerable amount of time and computing resources will be saved when the cyclic symmetric features are considered in the solution of eigenvalue problems if the components still have cyclic symmetric features after they were coupled. In this study

tangential and normal contact stiffness was solved by combining the Weierstrass-Mandelbrot(W-M)fractal geometry model and Herz contact theory. Then

the stiffness and mass matrices of each component were obtained by commercial finite element software

the total stiffness and mass matrices of the coupled structure were assembled by enlarging the obtained matrices

and the spring elements were used to simulate the contact stiffness of the coupled structure. The complex constraint condition was applied to the coupled structure

and the program for solving the eigenvalue problems by using only one sector model was developed with the software MATLAB. The program was used to analyze the eigenvector problem of a coupled aircraft spiral bevel gear-damper bowl structure

and the results were verified by the overall finite element model of the coupled structure. It is shown that the developed program could deal with the eigenvector problems with high efficiency and enough accuracy. The relative error was less than 1%

and 67% of computation time was saved

meanwhile

the memory resource was also saved. In addition

it is shown that the eigenvalues were obtained

accompanied with the eigenvectors revealing the vibration of the damper bowl. So sufficient attention should be paid in the following calculation including frequency response or vibration alleviation.