Enhanced Modeling of the Rocking and Overturning of Objects on a Moving Base

由于基础运动（如地震激励）造成的物体摇摆和倾覆占损失的很大一部分，在许多情况下，设施的功能中断。虽然自20世纪60年代以来，已有几位研究人员研究了摇摆动力学，但令人惊讶的是，我们在充分模拟与该问题相关的复杂动力学响应的能力方面存在很大的差距。在这种情况下，相对简单的机械原理的组合导致高度复杂的非线性现象，这些现象对问题中的参数变化很敏感。该项目将考虑基础变形和阻尼特性，基础摩擦相互作用，隆起（当身体在摇摆过程中反弹时），三维分析（包括三轴基础运动）与物体的质量偏心率，非矩形基础形状等。该项目计划的重点是开发先进的计算模拟工具，以模拟摇摆物体的复杂非线性动力学。此外，一个增强的模型将提供各种物体的风险分析，包括从变压器到砖石文物的一切。有了这样一个模型，将大大提高从古代“不稳定的岩石”和结构的非倾覆或在某些情况下的倾覆中推断历史地震记录的能力。这种更好的理解有可能更好地了解地震的历史事件。此外，将在底座处添加类似推车的轮子（以模拟医院医疗设备推车）等特征作为额外的自由度，并在摇摆响应开始时添加底座限制器（可能会失效）。为了进行逆向分析，将开发一种概率方法来确定在一个仍然存在的古代物体的历史上可能发生了什么地震（或地震序列）。该研究计划包括一个实验计划，将在PI的中型振动台设施进行。

The rocking of objects and their overturning due to base motions such as earthquake excitations accounts for a substantial fraction of losses and in many cases functional disruption of facilities. While the rocking dynamics have been studied by several researchers since the 1960's surprisingly there are very large gaps in our ability to adequately simulate the response of the complex dynamics associated with the problem. This is a case where the combination of comparatively simple mechanical principles leads to highly complex nonlinear phenomena which are sensitive to parameter variations within the problem. The project will consider base deformability and damping properties, friction interactions at the base, uplift (when the body bounces during rocking), 3-dimensional analysis (which includes tri-axial base motion) with mass eccentricities of the object, non-rectangular base shapes, and more. The project plan focuses on the development of advanced computational simulations tools to model the complex nonlinear dynamics of rocking objects.In addition, an enhanced model would provide risk analysis of a wide variety of objects including everything from electrical transformers to masonry antiquities. Having such a model would greatly improve the ability to infer the historic earthquake record from the non-overturning or in some cases the overturning of ancient "precarious rocks" and structures. This improved understanding has the potential to better understand the historical events of earthquakes. In addition, features such as cart-like wheels (to simulate hospital medical equipment carts) will be added as extra degrees of freedom at the base, and also base restrainers (which may fail) at the beginning of the rocking response. In order to perform the inverse analysis, a probabilistic approach will be developed to determine what earthquakes (or sequence of earthquake) might have occurred over the history of a still standing ancient object. The research plan includes an experimental plan to be carried out on the PI's medium-scale shake table facility.