周期对称性在失谐叶盘瞬态响应求解中的应用

Application of cyclic symmetry property in transient response solution of mistuned bladed disks

提出了利用周期对称性仅使用一个扇区进行失谐叶盘瞬态响应分析的方法,给出了其理论和算法实现过程。该算法的核心思想是将失谐部分移至运动方程的右端作为非线性激励,将失谐问题转化为谐调非线性问题,并采用迭代法或预测位形法进行非线性响应的求解,以单自由度（DOF）系统验证时域推进方法的有效性。最后使用简化失谐叶盘的有限元模型验证了该方法的有效性。结果表明：采用扇区模型可将自由度数从3 888减少至324,而每一时间步仅需2-3次迭代即可收敛,扇区模型与整体模型计算结果吻合良好,最大幅值误差为0.14%，

Theory and algorithm for using cyclic symmetry property ent response of mistuned bladed disk was presented. The mistuning parts to calculate transiwere moved to the right-hand side of the equations of motion, and were treated as the nonlinear excitation force of the corresponding tuned bladed disk. Therefore, the mistuned problem was transformed to a nonlinear tuned one, and could be solved using only one sector of the bladed disk. The iterative and prediction-correction time-marching schemes were proposed to handle the non- linear mistuning force, and were validated using a single degree of freedom （DOF） model. A simplified mistuned bladed disk finite element model was used as the numerical example to validate the effectiveness of the proposed method. Result shows that, the number of DOF is reduced from 3 888 to 324 by using the cyclic model, and it only takes 2--3 iterations to obtain the converged solution for each time step. The response results obtained using full model and cyclic model agree very well with the maximum amplitude error of 0.14%.