累积矩删去法分析过滤白噪声地震输入的随机响应
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摘要
分析了地基土－非线性结构相互作用体系在过滤白噪声地震输入下的随机响应．在控制运动方程中增加一个过滤方程，再把它们转化成伊藤方程，并应用伊藤微分规则即可建立矩方程．采用累积矩删去法可使原来的无穷系列矩方程组成为闭合方程组，从而求出各阶统计矩．数例表明，用本方法所算得的均方根响应与用Ｗｉｅｎｅｒ－Ｈｅｒｍｉｔｅ展开式方法所算得的结果非常接近，这说明本方法可应用于求解工程实际问题并具有足够的精度．
In this paper the random responses of a soil-nonlinear structure interaction system subjected tO filtered white-noise earthquake excitation are analysed. By adding a filtering equation to the governing motion equations and converting them into Ito equations, the moment equations can be established by using Ito's differential rule. The infinite hierarchy of the moment equations is closed by means of the Cumulant-Neglect Closure Techniques, so that the statistical moments can then be calculated. The numerical example shows that the standard deviations of the responses computed by the proposed method are very close to those obtained by Wiener-Hermite Expansion Method. This illustrates that the present method can be applied to solve practical engineering problems with sufficient accuracy.
In this paper the random responses of a soil-nonlinear structure interaction system subjected tO filtered white-noise earthquake excitation are analysed. By adding a filtering equation to the governing motion equations and converting them into Ito equations, the moment equations can be established by using Ito's differential rule. The infinite hierarchy of the moment equations is closed by means of the Cumulant-Neglect Closure Techniques, so that the statistical moments can then be calculated. The numerical example shows that the standard deviations of the responses computed by the proposed method are very close to those obtained by Wiener-Hermite Expansion Method. This illustrates that the present method can be applied to solve practical engineering problems with sufficient accuracy.
引文
1俞载道，宋雷，曹国敖．累积矩删去法分析地基土与滞变结构相互作用体系的随机地震反应．同济大学学报，1992，20（4）：371－3782陈晓东，俞载道．地基土－非线性单自由度结构相互作用体系的随机地震反应分析．同济大学学报，1987，15（1）：13—243VeletsosAS．Vibrationofviscoelasticfoundations．EESD，1973，2（2）：87－1024张炳根，赵玉芝．科学和工程中的随机微分方程．北京：海洋出版社，19805IbrahimRA，SoundararajanA，HeoH．Stochasticresponseofnonlineardynamicsystemsbasedonanon－Gaussianclosure，JournalofAppliedMechanics，1985，52（12）：965－9706俞载道，曹国敖．随机振动理论及其应用．上海：同济大学出版社，1988
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