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基于固定界面模态综合的Craig-Bampton方法,提出了模态综合的直接变换方法,该法在形式上更简洁,适用于大规模动力学系统的模态分析和动力学模型减缩。对采用直接变换法模态综合过程的计算误差做了分析,给出了计算误差界,阐明了模态综合后总体结构的固有频率与子结构保留主模态个数之间的关系。针对子结构界面自由度太大的情况,提出了直接变换法的分部算法,不需组集系统总刚度、总质量矩阵,仅在子结构的基础上完成系统的减缩。计算实例表明该算法的有效性及计算的稳定性。
Based on the Craig-Bampton method of fixed interface modal synthesis, a method of direct transformation of modal synthesis is proposed. This method is more concise in form and suitable for modal analysis and dynamic model reduction of large-scale dynamic systems. The calculation error of modal synthesis using direct transformation method is analyzed. The calculation error bound is given, and the relationship between the natural frequency of the overall structure and the number of main modal of substructure retained after modal synthesis is clarified. Aiming at the problem that the degree of freedom of the sub-structure interface is too large, the algorithm of the direct transformation method is proposed. It does not need to set the total stiffness of the system and the total mass matrix, and only reduces the system based on the substructure. The calculation example shows the effectiveness of the algorithm and the stability of the calculation.