平稳地震动过程的随机函数-谱表示模拟  

Simulation of stationary ground motion with random functions and spectral representation

作　　者：刘章军[1] 方兴[1] 

机构地区：[1]三峡大学水利与环境学院,宜昌443002

出　　处：《振动与冲击》2013年第24期6-10,37,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51278282;50808113);三峡地区地质灾害与生态环境湖北省协同创新中心;湖北省教育厅自然科学研究重点项目(D20111206)

摘　　要：在平稳随机过程的谱表示基础上，采用随机函数的思想，将谱表达式中的标准正交随机变量表示为基本随机变量的正交函数形式。通过两组随机正交三角函数的构造，实现了非高斯正交随机变量和高斯独立随机变量的随机函数表达。与经典的谱表示方法相比，采用随机函数表达，仅需1～2个基本随机变量即可描述原随机过程的概率特性，而且可以直接由功率谱密度函数生成具有给定概率的非高斯平稳过程和高斯平稳过程的样本函数。最后，结合平稳地震动加速度过程的功率谱密度函数，验证了随机函数一谱表示方法的有效性。Using an idea of random functions, standard orthogonal random variables in a spectral representation were expressed as an orthogonal function form of basic random variables. Through constructing two different forms of stochastic orthogonal trigonometric functions, non-Gaussian orthogonal random variables and Gaussian independent random variables were represented with the stochastic orthogonal trigonometric functions of basic random variables. Compared with existing spectral representations of stochastic processes, one or two basic random variables were needed to describe the probabilistic features of an original stochastic process with representation of random functiones, and the sample functions with the assigned probabilities of a non-Gaussian stationary process or a Gaussian stationary process could be directly generated with power spectral density functions. Finally, combining the power spectral density function of a stationary ground motion acceleration process, a numerical example was given to illustrate the effectiveness of the proposed hybrid random functions and spectral representation approach.

关 键 词：模拟 平稳地震动 谱表示 随机函数 功率谱密度函数 

分 类 号：O324[理学—一般力学与力学基础] P315.9[理学—力学]