Quantitative Evaluation of Seismic Performance for Truss Structures Based on the Condition Number of Dynamic Matrix

The quantitative analysis of seismic performance under small and moderate earthquakes is of great significance. However, only using the stiffness distribution index is no longer applicable to seismic performance evaluation, and the influence of mass distribution must be introduced. In this study, under the action of small and medium earthquakes, the equation of motion can be simplified into the equilibrium equation of the dynamic matrix by the quasi-static method. Furthermore, a condition number index of dynamic matrix is proposed to evaluate the seismic performance of truss structures, which can consider both stiffness distribution and mass distribution. Then, the correctness of the proposed index is verified by comparing with the displacement and strain indexes. In addition, the performance of truss structure is studied by the condition number of stiffness matrix, mass matrix and dynamic matrix. It is found that since the condition number of stiffness matrix and the condition number of mass matrix cannot consider both stiffness and mass, it is not comprehensive to use these two indexes to evaluate the seismic performance of truss structures. The evaluation result based on the condition number of dynamic matrix is more reasonable under small and medium earthquakes.

Automated summary

The quantitative analysis of seismic performance under small and moderate earthquakes is important. Using only the stiffness distribution index is no longer applicable, and the influence of mass distribution must be considered. In this study, the equation of motion is simplified into the equilibrium equation of the dynamic matrix by the quasi-static method. A condition number index of dynamic matrix is proposed to evaluate the seismic performance of truss structures, considering both stiffness and mass distribution. The correctness of the proposed index is verified and it is found that it provides a more reasonable evaluation result compared to other indexes.