The rocking motion of a solid block on a moving deformable base is a dynamic problem, that despite its apparent simplicity, involves a number of complex dynamic phenomena such as impacts, sliding, geometric and material nonlinearities and, under some circumstances, chaotic behavior. For that reason, since the first model proposed by G. W. Housner in 1963, a number of alternative models have been proposed for its mathematical simulation. Although, with very few exceptions, the previous models in the literature make the simplified assumption that this motion is planar, this is usually not true since a body will probably not be aligned with the direction of the ground motion. Thus, even in the case where the body is fully symmetric, the rocking motion involves three dimensional rotations and displacements. Moreover, for reasons more related to functionality than safety, it is not uncommon for heavy mechanical and electrical equipment to be placed on wheels. Examples of such devices are medical carts, mechanical equipment in hospitals, electrical transformers and recently even supercomputers. Although wheels facilitate the operation of these devices, they also affect the response of these objects during earthquakes; not necessarily in a beneficial way. This dissertation develops suitable models for simulating the previous dynamic problems. The equations of motion and suitable contact models are developed for each case. The importance of phenomena often neglected in the literature is stressed. Suitable examples illustrate the complex dynamic character of the problems examined. Finally, a static contact problem is examined. A model is developed for systems of multiple jointed elastic beams, using exact shape functions. A special application of the method for the definition of pressure loads in the wires of the main cable of a suspension bridge is presented. Examples illustrate the robustness of the method and the special properties associated with pressure loads.
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机译：固体块在可移动的可变形基座上的摇摆运动是一个动力学问题，尽管它看起来很简单，但仍涉及许多复杂的动力学现象，例如冲击，滑动，几何和材料非线性以及在某些情况下的混沌行为。因此，自从G. W. Housner在1963年提出第一个模型以来，已经提出了许多可供选择的模型进行数学模拟。尽管除了极少数例外，文献中的先前模型都简单地假设此运动是平面运动，但这通常是不正确的，因为物体很可能不会与地面运动的方向对齐。因此，即使在身体完全对称的情况下，摇摆运动也涉及三维旋转和位移。此外，出于功能而非安全性的原因，将重型机械和电气设备放置在车轮上并不少见。这样的设备的例子是医疗车，医院的机械设备，变压器以及最近的超级计算机。尽管轮子有助于这些设备的操作，但它们也会影响地震过程中这些物体的响应。不一定是有益的方式。本文为模拟先前的动力学问题建立了合适的模型。针对每种情况开发了运动方程式和合适的接触模型。强调了文献中经常忽略的现象的重要性。适当的例子说明了所研究问题的复杂动态特性。最后，检查静态接触问题。使用精确的形状函数为多个节理弹性梁的系统开发了一个模型。提出了一种方法的特殊应用，用于定义吊桥主缆线中的压力载荷。实例说明了该方法的鲁棒性以及与压力载荷相关的特殊性能。
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