非Gauss分布随机波浪力对海洋平台的非线性作用  

Nonlinear Action of Non Gaussian Random Wave Loads upon Ocean Platforms

作　　者：祁德庆[1] 王天竹[1] 乐嘉春[2] 

机构地区：[1]同济大学土木学院建筑工程系 [2]上海市应用数学和力学研究所,上海大学

出　　处：《力学季刊》2005年第2期276-279,共4页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10372056)

摘　　要：为避免求解决定Markov过程转移概率密度的Fokker-Planck方程,基于尺度分离的假设导出了一组描述非线性海洋平台受非Gauss分布随机波浪载荷作用所产生响应的矩量的常微分方程组。矩量方程清楚地反映出分别对应随机载荷和结构响应的两种不同统计特性的相互关系。由于矩量方程不依赖载荷的概率分布的具体细节,以它来模拟随机激励作用下的非线性系统将免于MonteCarlo方法所面临的正确模拟载荷概率分布的困难任务。将摄动法用于矩量方程可使线性化不再需要,这样就不会因为线性化而产生不可预料的误差。In order to avoid solving the Fokker-Planck equation determaining the transition probability density function of Markov process, a system of ordinary differential equations governing the moments of the response of nonlinear ocean platform driven by non Gaussian random wave loads was derived based on the assumption of scale separation. The moment equations clearly reflect the relation between two different kinds of statistical properties of the random loading and structure response respectively. As the moment equations do not depend upon the details of probability distribution of the loads, numerical simulation of nonlinear systems under stachastic excitation using moment equations will be exampted from the difficult task demanding Monte Carlo method to properly simulate the probability distribution of the loads. The application of perturbation to moment equations also make linearization unnecessary, therefore not to suffer from unpredictable errors caused by linearization.

关 键 词：非Gauss分布白噪声 随机微分方程 非线性系统 矩量方程 

分 类 号：O324[理学—一般力学与力学基础] TB126[理学—力学]