TY - JOUR
T1 - Motion complexity in a non-classically damped system with closely spaced modes
T2 - From standing to traveling waves
AU - Krack, Malte
AU - Bergman, Lawrence A.
AU - Vakakis, Alexander F.
N1 - The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work leading to this publication was supported by the German Academic Exchange Service (DAAD) with funds from the German Federal Ministry of Education and Research (BMBF) and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 605728 (P.R.I.M.E. Postdoctoral Researchers International Mobility Experience).
PY - 2016
Y1 - 2016
N2 - This article addresses the phenomenon of motion complexity in a periodically oscillating system, i.e. the occurrence of non-trivial phase lags among the system’s coordinates. Specifically, the steady-state forced response of a linear, weakly damped, self-adjoint system is studied, for which the extent of motion complexity is typically expected to be small. Yet, it is shown that under the condition of closely spaced modes, weak non-classical damping may lead to a transition from standing waves to traveling waves. A system of two oscillators weakly coupled via a linear spring-damper element is considered. The emergence of these motions is related to the distribution of the applied forces and the effect of adding nonlinearity in the form of a cubic spring to the system is investigated. Moreover, it is demonstrated that under certain conditions, the traveling wave response is critical, i.e. it is associated with a resonance or anti-resonance.
AB - This article addresses the phenomenon of motion complexity in a periodically oscillating system, i.e. the occurrence of non-trivial phase lags among the system’s coordinates. Specifically, the steady-state forced response of a linear, weakly damped, self-adjoint system is studied, for which the extent of motion complexity is typically expected to be small. Yet, it is shown that under the condition of closely spaced modes, weak non-classical damping may lead to a transition from standing waves to traveling waves. A system of two oscillators weakly coupled via a linear spring-damper element is considered. The emergence of these motions is related to the distribution of the applied forces and the effect of adding nonlinearity in the form of a cubic spring to the system is investigated. Moreover, it is demonstrated that under certain conditions, the traveling wave response is critical, i.e. it is associated with a resonance or anti-resonance.
KW - Mode complexity
KW - damping
KW - internal resonance
KW - modal interactions
KW - traveling waves
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U2 - 10.1177/1464419315593431
DO - 10.1177/1464419315593431
M3 - Article
AN - SCOPUS:84959462295
SN - 1464-4193
VL - 230
SP - 178
EP - 190
JO - Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
JF - Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
IS - 2
ER -