Application of three-degree-of-freedom modal equation in seismic analysis of storey isolated structure

According to the actual seismic response characteristics of storey isolated structures, the two degree-of-freedom modal equation proposed by previous scholars is studied and improved to put forward three degree-of-freedom modal equation in this paper by dividing the undamped modal shape and normal coordinate into three parts, which can explain the inconsistent structural vibration caused by non-proportional damping inherent in the storey isolated structures. Compared with the forced decoupling method, the new method can improve the accuracy of the analytical results without obviously increasing computational efforts, and is more efficient than direct integration method, so in fact it´s a trade-off strategy of computation efficiency and precision. This paper firstly derivates the theory formulations of three degree-of-freedom modal equation, and then numerical study is performed to verify the new method´s advantages by comparing with the results obtained by the forced decoupling method and direct integration method, by the study it can be obviously seen that the new method is effective and efficient in the seismic analysis of storey isolated structures.