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Dynamic motion of a conical frustum over a rough horizontal plane

Authors
Journal
International Journal of Non-Linear Mechanics
0020-7462
Publisher
Elsevier
Volume
46
Issue
1
Identifiers
DOI: 10.1016/j.ijnonlinmec.2010.07.008
Keywords
  • Conical Frustum
  • Dynamic Motion
  • Wobbling
  • Rocking
  • Ancient Classical Columns
Disciplines
  • Mathematics

Abstract

Abstract An analytical and numerical study of the dynamic motion of a conical frustum over a planar surface is presented resulting to a non-linear system of ordinary differential equations. Wobbling and rocking components of motion are discussed in detail concluding that, in general, the former component dominates the latter. For small inclination angles an asymptotic approximation of the angular velocities is possible, revealing the main characteristics of wobbling motion and its differences from rocking. Connection is made of the analysis with the behavior of the ancient classical columns, whose three dimensional dynamic response challenges the accuracy of the two dimensional models, usually applied in practice. The consideration of such discrete-blocky systems can benefit from the present study, through qualitative results and benchmarks for more complicated numerical methods, like the Distinct Element Method.

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