Automated Truncation of Ritz Vector Basis in Modal Transformation

Abstract

The number of load‐dependent Ritz vectors required for an accurate dynamic analysis, using the mode superposition method, depends on both the spatial distribution and the spectral (frequency) content of the loading. In this paper we demonstrate that, by monitoring two modal truncation criteria for spectral content and spatial representation of the loading, in the progress of algorithm we can predetermine the accuracy of subsequent dynamic analysis. In the case of earthquake excitation, the loading spatial representation truncation criterion is a participating mass. The spectral content truncation criterion exploits the analogy to the static correction method and unique properties of the load‐dependent vector algorithm. The numerical effort required for the calculation of modal truncation criteria is slight compared to the numerical effort of generating the Ritz vectors. Therefore, monitoring truncation criteria should become a standard step in the load‐dependent vector algorithm. In addition, it provides a possibility for automated truncation of Ritz vector basis in the modal dynamic analysis of complex structures.