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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary
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The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary

机译：弹性三维半空间对边界上随机相关位移扰动的响应

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摘要

The response of an elastic half-space to random excitations of displacements on the boundary under the condition of no shearing forces is studied. We analyze the white noise excitations and general random fluctuations of displacements prescribed on the boundary. We consider the case of partially ordered defects on the boundary whose positions are governed by an exponentialcosine-type correlation function. The analysis is based on a Poisson-type integral formula which we derive here for the case of zero shearing forces on the boundary. We obtain exact representations for the displacement correlation tensor and the KarhunenLove expansion for the solution of the Lam equation itself, and analyze some features of the correlation structure of the displacements. The Monte Carlo technique developed can be applied to a wide class of differential equations with random boundary conditions.
机译：研究了无剪切力条件下弹性半空间对边界位移随机激励的响应。我们分析了边界上规定的白噪声激励和位移的一般随机波动。我们考虑边界上部分有序缺陷的情况，其位置由指数余弦型相关函数控制。该分析基于泊松型积分公式，对于边界上的剪切力为零的情况，我们在此推导。对于Lam方程本身的解，我们获得了位移相关张量和KarhunenLove展开的精确表示，并分析了位移相关结构的一些特征。所开发的蒙特卡洛技术可以应用于具有随机边界条件的各种微分方程。

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