二维相关地震动作用下结构的随机反应

Random Response Analysis of Structures Due to Two Dimensional Coherence Earthquake Ground Motions

假定两水平方向的地震动为平稳随机过程,基于地震动主轴模型的假设,讨论了二维地震动分量的空间相关性,在单分量平稳模型的基础上给出了二维水平地震动随机模型的相关函数矩阵。该相关函数模型可以为二维地震下结构随机反应分析提供地震动输入。利用状态空间方法和随机振动理论建立了线性多自由度体系在二维地震激励下的随机反应分析方法,导出了结构的位移反应相关函数和速度反应相关函数,可在时域内直接计算结构的二维随机地震反应的统计特征。最后,通过一个二层框架结构计算实例,说明了这种方法的运用,讨论了地震动强度以及地震动主轴方位角对结构反应的影响。该方法可以为结构抗震可靠性评估提供基础。

In this paper,two horizontal components of earthquake-induced ground motions are considered to be stationary random processes.On the basis of the single-dimensional random model,the spatial correlation of ground motions in two horizontal directions is analyzed in time domain and the correlation function matrix of two-dimensional horizontal random earthquake ground motion model is established according to the concept of principal axes of motions.Considering the spatial correlation of earthquake ground motions,the correlation function matrix is not only related to the intensity ratio of ground motions in two horizontal directions but also related to the angle of position between structural axes and principal axes of ground motions.The correlation function matrix can be used as the inputs of ground motions of random response analysis for structures due to two-dimensional earthquake motions.The equation of motion of the structures subjected to two-dimensional horizontal seismic excitations is represented by the state equations in state space,and the complex vibration characteristics and responses are analyzed.The method of a complex mode superposition is used to deduce the covariance response matrix of linear time-invariant structures under excitation of two-dimensional random model.The statistic characteristics of the responses may be obtained directly from the correlation function response matrix in time domain.Finally,a two-story single-span frame structure is given for numerical illustration of this method and the effects of intensity ratio of two components inputs and position angle on structural responses are discussed.This method can be developed to analyze the stationary responses of the structures subjected to multi-dimensional inputs in practice and the results can provide a basis for reliability assessment of the seismic structures.