连拱坝交叉模态综合法的完备性

Completeness of cross modal synthesis method for multiarch dams

对笔者提出的连拱坝动力特性计算的子结构交叉综合法的正确性进行了证明.利用证明子结构子模态向量组成的线性空间是完备的基础上,说明当交叉子结构中所取的截尾模态趋向于完备时,其结果等同于整体计算,并表明近似计算将收敛于正确的结果.

In this paper the validity of the cross modal synthesis model for modal analysis of multi-arch dams proposed by the author is demonstrated. It is demonstrated firstly that the linear space consisting of the submodal vectors of the substructures is complete. As the number of truncated submodal vectors of the substructures is increased to the full number, the calculation result will be equal to that of the global calculation. So it is also demonstrated that the approximation calculation will approach to the valid result .