Modeling the Planar Rocking of a Rigid Body with Irregular Geometry
Publication: Journal of Engineering Mechanics
Volume 149, Issue 9
Abstract
The nonlinear dynamics of rocking rigid bodies with simple geometries, such as rectangular blocks and cylinders, have been the focus of the rocking community over the last six decades. However, many objects that are prone to rocking or overturning do not conform to such geometries. These objects include museum artifacts and precariously balanced rocks in the natural world. Even in cases where the response of the rocking body is planar, the geometry of the body is much more complicated than the commonly studied geometry of a rocking block or a body with only two rocking corners. This paper introduces a complete model that can examine the planar motion of a body with an irregular in-plane polygonal geometry when subjected to a vibrational excitation, utilizing the geometry of the body as an input—for example, in the form of a stereolithography (STL) file. The model is used for studying the rocking response of an object while taking into account sliding and free flight. The problem is formulated and solved using Newtonian equations of motion, and impacts are treated as hard. A robust framework for integrating the occurring discontinuous equations of motion and for detecting transitions between patterns of motion and impacts, using MATLAB, is presented. Suitably chosen examples demonstrate the importance of accounting for the actual geometry of the studied rocking body, whose dynamic response is substantially richer than an object with simplified geometry.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. All input data to the models have been made available to the user. The output data have been presented in figures in the paper but can be made available upon reasonable request. All models used for the studies have been fully described in the paper.
Acknowledgments
The authors thank the Clarendon Fund for providing funding to the first author for this research.
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 9 • September 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Sep 5, 2022
Accepted: Dec 21, 2022
Published online: Jun 17, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 17, 2023
ASCE Technical Topics:
- Buildings
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- Design (by type)
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- Engineering fundamentals
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- Structural engineering
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