随机输入条件下的楼层反应谱分析

采用随机振动理论及叠加原理推导出概率反应的楼层反应谱，避免了时程分析与解大型特征值问题。由随机地面反应谱作为输入条件直接求解楼层反应谱，并考虑主次结构系统间的调谐、干扰及模态间的相互影响，使反应谱的精度得到改善。

A Better Analysis of Floor Response Spectrum under Random Input for Seismic Design

Existing analyses of floor response spectrum under random input are, in our opinion, not satisfactory as discussed in some detail at the beginning of this paper. We venture to propose a better analysis method, by using the random ground response spectrum, to calculate directly the floor response spectrum, successfully avoiding the time processing analysis and the large eigenvalue problems. This development is based on the random vibration theory and the superposition principle. Firstly, the dynamic properties of a complex system, including a secondary structure in interaction with a main structure, can still be deduced in terms of the dynamic properties of the main structure alone and of the secondary structure alone. In deducing the dynamic properties of the complex system the tuning, the disturbance and the influence of them are taken into consideration to improve the response precision. Secondly, we assume the seismic input is a stationary random process and the mass of the secondary structure is extremely small compared with that of the main structure. The power spectrum density function and the response spectrum moment of the complex system are used to establish the relations between the input response spectrum and the probability response parameters, i.e., the floor response spectrum can be directly formed from the ground response spectrum. A numerical example shows different results corresponding to different ground inputs. Even when the natural frequency of the secondary structure coincides with one of the natural frequencies of the main structure, the numerical example shows that our analysis still gives highly accurate results.