Abstract In this paper the rocking response of a rigid block randomly excited at its foundation is examined. A nonlinear flexible foundation model is considered accounting for the possibility of uplifting in the case of strong excitation. Specifically, based on an appropriate nonlinear impact force model, the foundation is treated as a bed of continuously distributed springs in parallel with nonlinear dampers. The statistics of the rocking response is examined by an analytical procedure which involves a combination of static condensation and stochastic linearization methods. In this manner, repeated numerical integration of the highly nonlinear differential equations of motion is circumvented, and a computationally efficient semi-analytical solution is obtained. Comparisons with pertinent Monte Carlo simulations demonstrate the efficiency and reliability of the proposed approach. Finally, the survival probability related to toppling of the blocks subject to filtered white noise excitation is investigated, for different kinds of block geometries, foundation materials, and filter parameters.

中文翻译：

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非线性柔性地基块体随机摇摆分析

摘要 本文研究了在其基础上随机激发的刚性块的摇摆响应。非线性柔性地基模型被认为是考虑到在强激励情况下抬升的可能性。具体而言，基于适当的非线性冲击力模型，将基础视为与非线性阻尼器平行的连续分布弹簧床。摇摆响应的统计通过涉及静态冷凝和随机线性化方法的组合的分析程序来检查。以这种方式，避免了高度非线性运动微分方程的重复数值积分，并且获得了计算效率高的半解析解。与相关蒙特卡罗模拟的比较证明了所提出方法的效率和可靠性。最后，针对不同类型的块几何形状、基础材料和过滤器参数，研究了与受过滤白噪声激励的块倾倒相关的生存概率。