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针对传统模态综合法中由于高阶截断模态带来的计算误差问题,提出了一种改进的固定界面模态综合法。该方法将传统方法中截断舍弃掉的高阶模态部分展开成级数的形式,并保留级数的前r项参与计算,然后将子结构界面协调条件推广至高阶,剔除了这些级数保留项之间可能出现的线性相关问题,并将保留的前r项级数改写为广义坐标的形式,作为传统模态综合法中约束模态和低阶模态的修正项以提高计算精度。与其它改进方法相比,该方法既保留了高阶截断模态的影响,又不会出现非线性特征值迭代求解问题或Ritz基线性相关的问题。数值算例的结果表明本文提出的方法可以在参与综合的模态阶次不变的前提下,有效地提高计算精度,也说明了本文方法的有效性。
Aiming at the calculation error caused by high-order truncated modal in the traditional modal synthesis method, an improved fixed modal synthesis method is proposed. In this method, the truncated and discarded high-order modal part of the traditional method is expanded into the form of series, and the first r items of the series are involved in the calculation. Then, the coordination of the substructures interface is extended to higher order, excluding these series The linear correlation problems that may appear between the two equations are rewritten in the form of generalized coordinates in the form of generalized coordinates, which are used as the corrections of the constraint mode and the low-order modal in the traditional modal synthesis method to improve the calculation accuracy. Compared with other improved methods, this method not only retains the effect of high-order truncated modes, but also does not have the problem of iteratively solving nonlinear eigenvalues or the linear correlation of Ritz bases. The numerical results show that the proposed method can effectively improve the accuracy of the proposed method while keeping the modal order intact, and also shows the effectiveness of the proposed method.