This thesis is on the improved mode superposition methods for non-classically damped systems by considering the truncated high modes. Generally, the mode superposition methods use a relatively small subset of the modes of the structures. The mode acceleration and the modal truncation augmentation methods improve the results of the mode superposition method by considering effect of the truncated high modes. For using these methods to non-classically damped systems, the non-classically damped systems are approximated to the classically damped systems. The errors are induced by these approximations.
In this paper, therefore, the mode acceleration and the modal truncation augmentation methods are expanded to analyze the non-classically damped systems. The applicability of expansion is verified by closed form solutions and numerical examples. Two numerical examples are carried out. In the first example, the responses of cantilever beam due to the earthquake loading and the step loading are evaluated respectively and the results of each method are compared. In the second example, to show the characteristics of the expanded modal truncation augmentation method, the responses of ten-story building by each method are compared. The expanded methods are found to be superior to the simple mode displacement methods.
The expanded modal truncation augmentation method is conditionally stable in the non-classically damped systems, depending on the pattern of the external loading whereas the expanded mode acceleration method is stable for the all cases of loading in the non-classically damped systems. When the expanded modal augmentation method is used to non-classically damped systems, the results are the same with that of the expanded mode acceleration method. To stably analyze the non-classically damped systems, it is better to use the expanded modal truncation augmentation method for classically damped systems.
