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Revisiting the rocking block: closed-form solutions and similarity laws

Dimitrakopoulos, Elias G. ; DeJong, Matthew J.

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2012-08, Vol.468 (2144), p.2294-2318 [Periódico revisado por pares]

The Royal Society Publishing

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  • Título:
    Revisiting the rocking block: closed-form solutions and similarity laws
  • Autor: Dimitrakopoulos, Elias G. ; DeJong, Matthew J.
  • Assuntos: Angular velocity ; Approximation ; Blocking ; Closed-Form Solutions ; Coefficient of restitution ; Contrapuntal motion ; Dimensional analysis ; Dynamic response ; Earthquake Engineering ; Earthquakes ; Exact solutions ; Excitation ; Geometry ; Ground motion ; Mathematical analysis ; Mathematical expressions ; Orientational Analysis ; Rocking ; Self-Similarity ; Similarity ; Sine function ; Transcendentals
  • É parte de: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2012-08, Vol.468 (2144), p.2294-2318
  • Notas: href:rspa20120026.pdf
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  • Descrição: 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.
  • Editor: The Royal Society Publishing
  • Idioma: Inglês
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