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.%An improved fixed-interface modal synthesis method is proposed in this paper for reducing the error in calculating eigenproperties of a structural system caused by the higher order modal truncations. In the proposed method, the truncated part is expanded into Taylor Series, and the first r terms of which are retained in the computation for keeping the influence of truncated higher order modes. And then by extending the substructure interface compatibility conditions to higher order, not only the potential linear dependence of the retained Taylor Series terms can be eliminated, but also the retained Taylor Series terms can be rewritten into a generalized coordinate form to correct the constrained modal vector and the lower modal vector. Compared with some other improved methods, the proposed method is free of nonlinear eigen-problem or potential linear dependence problem. The result of a numerical example has shown that with the same number of retained modes, the accuracy of the calculation can be improved significantly, and effectiveness of the proposed method is verified.
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