中文摘要：

利用一些循环对称结构件经耦合后仍呈现循环对称的特点进行耦合结构的振动特性分析,以节约计算时间和计算资源。应用Weierstrass-Mandelbrot分型模型结合赫兹接触理论求解了耦合结构接触面的切、法向刚度,再用商业有限元软件导出了各结构件的刚度及质量矩阵,并通过扩维来组装耦合扇区的刚度矩阵;应用弹簧元模拟了接触面的切、法向刚度;对耦合结构施加复约束条件,用MATLAB开发出利用结构单扇区求解耦合结构振动特性的计算流程。将该流程应用于航空弧齿锥齿轮-阻尼碗耦合结构振动特性的求解,并与耦合结构的整体有限元模型计算结果进行了对比,结果表明：开发的计算流程在保证准确性的前提下,可以高效率地完成结构振动特性分析,计算误差控制在1%之内,运算时间节省了67%以上,同时可以有效节约存储资源。另外,通过对航空锥齿轮-附加阻尼碗的振动特性分析得知,该耦合结构增加了以阻尼碗振动为主振型的特征频率,在后续的结构减振或频响计算时应引起足够重视。

英文摘要：

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 geardamper 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%,and67% 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.