| Issue |
MATEC Web Conf.
Volume 211, 2018
The 14th International Conference on Vibration Engineering and Technology of Machinery (VETOMAC XIV)
|
|
|---|---|---|
| Article Number | 04001 | |
| Number of page(s) | 7 | |
| Section | DS: Dynamic Stability, Deterministic, Chaotic and Random Post-Critical States; TP10: Vibration and waves; TP13: Wave propagation | |
| DOI | https://doi.org/10.1051/matecconf/201821104001 | |
| Published online | 10 October 2018 | |
Singular solutions of a non-holonomic system as limits separating solution groups of particular type
Inst. of Theoretical and Applied Mechanics, CAS,
Prosecká 76,
CZ-190 00
Prague,
Czech Republic
* e-mail: naprstek@itam.cas.cz
** e-mail: fischerc@itam.cas.cz
The non-holonomic system represents a model of the ball tuned mass damper (TMD), as used to absorb vibration of selected engineering structures, where conventional absorber types are inapplicable. The device consists of a ball moving within a spherical cavity fixed with the structure. To deduce a governing differential system the Appel-Gibbs formulation has been employed. The non-linear mathematical model includes six degrees of freedom and three non-holonomic constraints. The system has an auto-parametric character. The homogeneous differential system in the normal form is formulated. Its general properties are investigated for various settings of non-homogeneous initial conditions. Several singular solutions are extracted and physically interpreted. In principal, they represent limits separating solution groups of a certain character. The shape and general character of regular solutions within individual domains staked out by these limits are analyzed in order to facilitate a practical application of this theoretical background.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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