结构在水平与竖向地震同时作用的非平稳响应

NON-STATIONARY RANDOM RESPONSE OF STRUCTURES TO HORIZONTAL-VERTICAL EARTHQUAKE EXCITATIONS

本文对单自由度结构在水平与竖向地震同时作用下的随机地震响应问题进行了系统研究。首先用简明的推导方法,建立了结构参激随机振动方程;其次利用Stratonovich随机微分方程、It随机微分方程、FokkerPlanck方程和矩微分方程的相互转换关系,用统一的公式法,建立了结构响应矩方程;然后根据Hurwitz随机稳定准则,获得了结构一阶和二阶响应矩渐近稳定条件的解析判断式;最后针对非平稳水平地震激励的最典型四种强度包络函数,综合应用复模态法,获得了结构非平稳响应二阶矩的解析解,给出了算例,并综合分析了各种参数对结构响应和稳定性的影响。

In this paper,the random earthquake response of structures with single degree of freedom subjected to horizontal-vertical random earthquake excitations is studied systematically.The stochastic differential equation for structures with parametric and external excitations is established by using a concise derivation methods.According to the mutual relationships between Stratonovich stochastic differential equation, It stochastic differential equation, Fokker-Planck equation and moment differential equation,the moment differential equations of structural response are established by using the unitary formula method,then using the Hurwitz[BF]'[BFQ]s random stability criterion,the exact formula of stability for the first and second-order moments of structural response are obtained.For the most typical four deterministic envelope functions of the non-stationary horizontal random earthquake excitations,the exact solutions of the second-order moments of structural response are obtained by using the complex mode theory.An example is given to synithetically analyze the influence of various parameters on structural response.