剩余柔度模态与附着模态在模态综合法中的等价性

在早期的模态综合法中,引起计算误差的主要原因是由于截去了高阶模态。文献1～4]从不同角度揭示,剩余柔度模态和附着模态可以有效地补偿这种截断误差。在此基础上,已派生出两类新的自由界面模态综合法。第一类方法的特点是将子结构位移用自由界面模态与剩余柔度模态来表示,第二类方法的特点是用自由界面模态与附着模态来表示子结构位移。本文将指出,这两类方法是等价的。其等价性表现在剩余柔度模态与附着模态可以相互替换而不影响模态综合的最终结果。本文将以文献4]提出的方法为例来证明该等价性,并在文末给出一个数值算例。

THE EQUIVALENCE BETWEEN THE RESIDUAL FLEXIBILITY MODE AND THE ATTACHMENT MODE IN MODAL SYNTHESIS TECHNIQUES

In the early modal synthesis techniques, the main cause of computation error comes from the truncation of higher order natural vibration modes. In reference1]~4]it is revealed from various respects that the residual flexibility mode or attachment mode could be used to compensate the above mentioned truncation error. Based on the conclusions of 1]- 4], two kinds of new free boundary synthesis techniques have been developed. The first kind is presented in 3] and 4],in which the displacements of substructures are represented by linear combination of the free boundary modes and the residual flexibility modes. The second kind is presented in2],in which the free boundary modes and the attachment modes are used together to represent the displacements of substructures. In this papet it is pointed out that the two kinds of techniques are equivalent to each other. The equivalence lies in the fact that the residual flexibility modes and the attachment modes could be replaced by each other. The theoretical proof is given to show that this replacement has no effect upon the final synthesis results. Besides, a more general conclusion is drawn. At the end of the paper, a numerical example is given.