Efficient Mode Superposition Method for Non-Classically Damped Systems

비비례 감쇠시스템의 해석을 위한 효율적인 모드 중첩법

The improved mode superposition methods for non-classically damped systems are presented in this paper. Generally, the mode superposition method uses a relatively small subset of the normal modes of structures. The mode acceleration method and the modal truncation augmentation method improve the results of the mode superposition method by considering effects of truncated high modes. For using these methods to analyze non-classically damped systems, the systems are approximated to the classically damped systems and thereby the errors are induced. In this paper, the mode acceleration method and the modal truncation augmentation method are expanded to analyze the non-classically damped systems. The applicability of the expanded methods is verified by closed form solutions and numerical examples. The expanded modal truncation augmentation method is conditionally stable depending on the pattern of the external loading in the non-classically damped systems whereas the expanded mode acceleration method is stable for the all cases of loading. In the stable case, the results are the same with those of the expanded mode acceleration method.