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A vibration isolation structure is composed of a superstructure and a vibration isolation layer including vibration isolation bearings and dampers with different damping features from those of superstructure, which possess typically non-proportional damping features. So, the damping matrix of this system can't be decomposed via the system's undamped modal shapes and the traditional modal shapes superposition response spectrum method is not applicable to this system. Here, based on the random vibration theory and considering features of vibration isolation structures, a multi-dimensional earthquake complex modal shapes superposition response spectrum method was proposed, it could consider non-proportional damping features. The error of the forced decoupling method, an approximate approach commonly used, was studied. It was found that the energy transfer between the superstructure and the vibration isolation layer is prevented with this method to cause smaller seismic responses of the superstructure. The vibration isolation benchmark model was taken as an example to implement the time-history method, the forced decoupling method and the proposed complex modal shapes superposition response spectrum method, respectively. Three results were compared, it was shown that the proposed method has a better accuracy and can fully reflect the non-proportional damping characteristics in vibration isolation systems; when the damping of the vibration isolation layer is larger, the forced decoupling approach has a worse accuracy, it can't reflect the amplification effects of the superstructure seismic responses due to damping of the vibration isolation layer. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.
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