部分モード法による建築構造物の固有値解析に関する研究 : 各層を部分構造とした取り扱いと層モードの連成効果について

Abstract

In this paper, the eigenvalue problem of multi-story structures is considered by means of the Component Mode Method. In the method, a multi-story structre is divided at each story into single-story substructures. The resuing component mode is the mode shape of each story (story mode). From the consideration in terms of the story mode, the following results are obtained. (1) Saving of Computation Time This method needs a certain time in the process of dividing a structure into substructures, but the total computation time including eigenvalue analyses is much shorter, as the size of the eigenvalue analyses is sufficiently small in comparison with that of the orignal eigenvalue problem. Since, in the eigenvalue analysis of each story, basic modes such as translational and torsional ones are easily obtained in a few lowest modes, and since the modes of the whole structure can be constructed by the combination of such basic modes, the computation time will be sufficiently saved. (2) Extration of Necessary Modes The mode shapes of a structure depend on its story modes. It means that the mode shapes of the whole strure can be changed by selecting its story modes. For example, if only a translational mode is adopted at each story, only translational modes appear in the synthesized modes. Thus, the necessary modes which are important for the evaluation of structural responses can easily be exracted by the appropriate selection of story modes. Accordingly, for this Component Mode Method, one can expect a kind of filtering effects in order to extract the necessary modes. (3) Evaluation of Inter-story Relations in terms of Story Modes In the process of the Component Mode Method, inter-story relations are stored only in a matrix M, which shows the mutual orthogonality of story modes. Therefore, the coupling relations among stories are grasped as the coupling relations among story modes. The evaluation of such coupling effects is possible if and only if the Component Mode Method with substructures of each story is introduced