Revisiting the rocking block: closed-form solutions and similarity laws
Revisiting the rocking block: closed-form solutions and similarity laws
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DOI：
10.1098/rspa.2012.0026
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
E. Dimitrakopoulos;M. DeJong
中科院分区：
文献类型：
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作者：
E. Dimitrakopoulos;M. DeJong
本文重新研究了摇块在基底激励下的动力响应问题。我们的目标是提供新的封闭形式的解决方案和原来的相似性法律，阐明的基本方面的摇摆块。重点是在有限持续时间的激励下的摆动块的瞬态动力学。另一种方法来描述响应的摇摆块，信息的行为摇摆结构下的不同强度的激励，提供。在这个过程中，标准量纲分析的局限性，涉及的物理量的方向，被揭示。建议的无量纲和无方向的群体凝聚的响应，并提供了一个清晰的描述摇摆现象。当表示在适当的无量纲-无取向组中时，对于细长块体（在小旋转范围内），摇摆响应变得完全自相似，而对于非细长块体（较大旋转），摇摆响应变得几乎自相似。利用这一公式，非线性和非光滑的摇摆响应脉冲型地面运动可以直接确定，只需要按比例的强度和频率的激励。
In this paper, the dynamic response of the rocking block subjected to base excitation is revisited. The goal is to offer new closed-form solutions and original similarity laws that shed light on the fundamental aspects of the rocking block. The focus is on the transient dynamics of the rocking block under finite-duration excitations. An alternative way to describe the response of the rocking block, informative of the behaviour of rocking structures under excitations of different intensity, is offered. In the process, limitations of standard dimensional analysis, related to the orientations of the involved physical quantities, are revealed. The proposed dimensionless and orientationless groups condense the response and offer a lucid depiction of the rocking phenomenon. When expressed in the appropriate dimensionless–orientationless groups, the rocking response becomes perfectly self-similar for slender blocks (within the small rotations range) and practically self-similar for non-slender blocks (larger rotations). Using this formulation, the nonlinear and non-smooth rocking response to pulse-type ground motion can be directly determined, and need only be scaled by the intensity and frequency of the excitation.