行波效应下结构非平稳随机地震峰值响应分析

Peak-value Responses of Structures Subjected Non-stationary Differential Random Ground Excitations

地震运动在本质上是非平稳随机过程。对于一个典型的地震记录,如果地震平稳段持续时间较短,采用非平稳随机过程描述其地震动特性较为合理。目前被最广泛接受的地震非平稳随机振动模型是演变随机激励模型。本文将虚拟激励法和精细积分法相结合,高精度计算了结构在这种随机地震激励下的时变均方根响应,并等效转化为相应的平稳随机过程后进行结构峰值响应计算。不仅考虑了激励的非平稳性,同时高效精确地考虑了结构的动力特性和地震行波效应。能够方便地应用于大型复杂结构,特别是为大跨度桥梁抗震分析提供了高效的计算手段。实际结构算例表明平稳假设会得到偏于保守的结果。当阻尼比较小时,这种差别会更明显。采用非平稳激励模型,显然更为合理;采用本文提出的方法可以很方便地处理这类问题。

Earthquakes are non-stationary random processes in nature. For a typical earthquake record, if the duration of its stationary portion is rather short, such a record should be described in terms of a non-stationary random process. The most widely accepted for this purpose is the evolutionary random excitation model. The pseudo excitation method (PEM) combined with the precise integration method (PIM) was used to compute the time-dependant standard deviations of interested structural responses, which are then transformed into equivalent stationary random responses so as to evaluate the corresponding peak-value responses. By doing so, not only the non-stationarity of the excitations, but also the dynamic characters of the structure and the wave passage effect of the differential ground motion were taken into account quite accurately. Such a combined method can deal with large-scale complex structures efficiently. Therefort it provides a powerful means for the' seismic analysis of long-span bridges. The numerical computations for practical structures show that the stationary assumption will usually lead to conservative results, in particular for lightly damped structures. Instead the non-stationary assumption is more reasonable, and the proposed method can deal with such problems quite conveniently.